Apparatus for recovering a clock timing of a transmitting device on the basis of transmitted quantum particles

Abstract

The invention relates to an apparatus (100) for recovering a clock timing (13) of a transmitting device (10) on the basis of transmitted quantum particles (21). For this purpose, the transmitting device (10) is designed to transmit the quantum particles (21) in a temporal sequence on the basis of the clock timing (13). Furthermore, a receiving device (30) is designed to receive the quantum particles (21) and to produce a time stamp (31) for each received quantum particle (21). The apparatus (100) comprises an interface (110) which is designed to receive the time stamps (31), and a recovery module (120) which is designed to determine, on the basis of the time stamps (31) and an approximation frequency, a phase space position (121) and to recover the clock timing (13) on the basis of a temporal drift of the phase space position (121).

Description

[0001] Device for recovering a clock of a transmitter device using transmitted quantum particles

[0002] The present invention relates to an apparatus for recovering a clock of a transmitter device from transmitted quantum particles, to a method for recovering a clock from transmitted quantum particles, and in particular to a method for clock recovery from detection times of individual photons.

[0003] BACKGROUND

[0004] In order to precisely synchronize technical systems that are spatially distant from each other (in the range of a few kilometers to thousands of kilometers) with an absolute time accuracy of nanoseconds, various technical solutions exist, such as the Global Positioning System (GPS).

[0005] In the field of optical telecommunications technology, higher accuracies of well below one nanosecond are necessary to correctly reconstruct the signals transmitted by a transmitter at the receiver. In particular, quantum optical communication protocols, such as quantum key distribution (QKD) using light pulses, require such highly precise synchronization of spatially distant transmitter and receiver devices.

[0006] The synchronization problem can be broken down into the problem of establishing a reference time (t=0) at the beginning of the measurement and the problem of clock synchronization, which ensures that the clocks of the transmitting and receiving stations run at the same speed during the transmission, or that the clock deviation is precisely known and can be compensated for mathematically. In optical telecommunications technology, for example, special bit sequences are transmitted to align the reference time, and clock synchronization is achieved by using techniques for clock recovery from the received signal at the receiving device.

[0007] In quantum communication, optical signals are sent in the form of pulses with an intensity level of a few photons per pulse. Due to losses during signal transmission and detection, no photons are detected at the receiver for the majority of the pulses. This means that clock recovery methods known from telecommunications technology cannot be directly applied, as they are designed to ensure that every symbol is received. Therefore, other synchronization methods are used in quantum communication technology.

[0008] One method here is to equip the transmitter and receiver each with a GPS receiver and a very stable clock, and to regularly synchronize the clock with the GPS signal. However, the need for a GPS clock and the dependence on the GPS signal have disadvantages.

[0009] Another method uses stronger signals for synchronization, which are exchanged between the transmitter and receiver of the quantum signals. These are multiplexed with the quantum signals, for example, but this requires additional technical effort and blocks part of the transmission capacity of the quantum channel.

[0010] Another possibility is synchronization via a separate channel. This method requires additional effort. For example, EP 3 018 840 Ai discloses using the classical communication channel required for quantum communication as a separate synchronization channel. This solution has the disadvantage that it can only be used if a dedicated separate channel for classical communication is available, whose clock or timing can be controlled. Implementing the classical communication signal via a regular internet connection is not sufficient for this purpose.

[0011] Another possibility for synchronization is the use of quantum signals.

[0012] In the prior art, it is known to determine the reference time in quantum communication systems based on quantum entanglement by evaluating the cross-correlation function of the photon detection times. In other quantum communication systems, the reference time is determined by sending a predefined bit sequence at the beginning of a transmission.

[0013] In both cases, cross-correlation can also be used to synchronize the clock during the transmission. However, the quantum bits used for this purpose become unusable for things like quantum key exchange.

[0014] Alternatively, the pulsed quantum signals can be analyzed to utilize their periodicity for clock recovery. These methods often directly use Fourier analysis for spectral analysis to detect frequency deviations. This makes the methods relatively computationally intensive, as it is necessary to insert zeros at the positions of undetected photons. Since high transmission losses result in the vast majority of photons being lost, this represents a significant overhead.

[0015] There is therefore a need for devices or methods that reduce the technical effort required to synchronize transmitter and receiver devices.

[0016] SUMMARY OF THE INVENTION This object is at least partially achieved by a device according to claim 1 and a method according to claim 7. The dependent claims relate to advantageous developments of the subject matters of the independent claims.

[0017] The present invention relates to a device for recovering a clock of a transmitter device based on transmitted quantum particles. The transmitter device is configured to transmit the quantum particles in a temporal sequence based on the clock. Furthermore, a receiver device is configured to receive the quantum particles and generate a timestamp for each received quantum particle. The device comprises an interface configured to receive the timestamps and a recovery module configured to determine a phase-space position based on the timestamps and an approximate frequency, and to recover the clock based on a temporal drift of the phase-space position.

[0018] The quantum particles can be elementary particles such as electrons or, in particular, photons. More generally, quantum particles are physical systems whose behavior is described by quantum theory. In some embodiments, the quantum particles can be provided for transmitting a quantum signal for the purpose of quantum communication. However, this is not necessary; in other embodiments, the quantum particles may not be provided for any other communication besides synchronization.

[0019] The transmitter device can be designed to emit the quantum particles in pulses with a few quantum particles per pulse.

[0020] The clock of the transmitter device is a physical time measure that measures a time course in the transmitter device. For this purpose, the transmitter device can comprise a clock or a reference unit that determines the clock. In exemplary embodiments, the transmitter device can be configured to emit the quantum particles in pulses based on the clock and, in doing so, to modulate a number of quantum particles per pulse, a physical property of the quantum particles (such as a frequency), or an entanglement of quantum particles in order to generate and transmit a quantum signal using the quantum particles. The clock can, in particular, be a time period with which the transmitter device emits pulses of quantum particles (pulse cycle). The clock is then the inverse of the pulse frequency.

[0021] The clock pulse can deviate from a time measurement, particularly of the receiver device, for many reasons. In addition to external influences, the clock pulse can change over time due to technical conditions in the transmitter device, such as heat generation or temperature-related expansion or contraction. Compared to other systems, especially the receiver device, the clock pulse can also change over time due to a relative movement of the transmitter device, such as a resulting Doppler shift or relativistic time dilation or length contraction.

[0022] The receiving device can include its own clock or reference unit for determining a time unit. The receiving device will generally be configured to generate the time stamp based on its own clock or based on an external time reference. In exemplary embodiments, the only decisive factor is that the receiving device generally uses a different time unit than the transmitting device, and therefore synchronization is necessary. Whether an internal or another external time reference is used as the time unit of the receiving unit is then irrelevant.

[0023] The time stamps can be data sets that assign a characteristic time (or a characteristic point in time) to a received quantum particle according to the time reference of the receiving device. In exemplary embodiments, a time stamp can, in particular, be an arrival time or the time at which the receiving device registers the corresponding quantum particle. In exemplary embodiments, it can generally be assumed that not all emitted quantum particles are received by the receiving device.

[0024] The transmitter device and the receiver device can be provided together to implement a quantum optical communication protocol, in particular a quantum key distribution, by means of the quantum particles.

[0025] A cable or a substantially unrestricted transmission medium (wireless transmission) may be provided for transmitting the quantum particles from the transmitter device to the receiver device.

[0026] The device for recovering a clock of the transmitter device can be designed as a component of the receiver device or separately from it.

[0027] The device receives and processes the timestamps associated with the received quantum particles.

[0028] The proximity frequency can be transmitted to the device by the receiver device or by another system. The proximity frequency can also be stored in the device or calculated by the device from the quantum signal.

[0029] The recovery module can be designed to convert the time stamps into a dimensionless phase or a complex number of magnitude 1 using the approximate frequency. The complex plane or the unit circle in the complex plane can then serve as the phase space. The recovery module can be designed to determine a momentary accumulation point or mean value as the phase space position for the phases calculated in this way. The recovery module can be designed to track the momentary accumulation point over time and thus determine the drift of the phase space position. The drift is causally based on a deviation between the approximate frequency and frequencies in the spectrum of the clock of the emitted quantum particles, which in turn are determined by the clock of the transmitter device.Recovering the clock may refer to directly or indirectly determining the clock itself and / or temporal changes in the clock relative to the clock of the receiving device. Recovering the clock may also include compensating for a deviation in the further processing of the timestamps resulting from a determination of the clock or from a change in the clock.

[0030] A key aspect of the device is therefore that the clock is recovered from timestamps of individual quantum particles by determining a phase-space position or a frequency distribution, and from a drift of the phase-space position. Known methods for determining a phase-space position from a phase-space distribution and for determining a frequency difference between a frequency resulting from the phase-space position and an approximate frequency can also be used to recover the clock.

[0031] In embodiments, the recovery module can be configured to both determine the phase-space position based on the timestamps and to use the timestamps to obtain the temporal drift of the phase-space position (or the phase drift). In particular, the phase-space position and / or temporal drift can be based on differences in timestamps.

[0032] Optionally, the recovery module is configured to divide the timestamps of the received quantum particles into blocks, and it is optionally further configured to estimate the approximate frequency from timestamps of a block and / or to determine the phase-space position from timestamps of a block. In particular, the approximate frequency can be estimated from only a first block of received quantum particles. For this purpose, a Fourier transform can be performed to determine the spectrum of the clock of the timestamps.

[0033] The term "block" can mean a collection of consecutive timestamps. The length of a block can be determined by a fixed number of timestamps or by a fixed period of time. The lengths of the blocks can vary dynamically from block to block. In embodiments, a block length can be provided as a parameter that determines the accuracy and robustness of the clock recovery. It can be advantageous to design the block length adaptively and, for example, to adjust it dynamically if the strength of the temporal drift of the phase-space position or a rate of the received quantum particles changes during the course of a transmission. A block whose timestamps are used to estimate the approximate frequency can be defined differently than a block whose timestamps are used to determine the phase-space position.

[0034] The device can thus be configured to determine a relative change in the clock rate over time without any external input of the approximation frequency or storing a fixed approximation frequency in the device. In other words, the device can be configured to provide the approximation frequency based on the timestamps without any other external information.

[0035] Optionally, estimating the approximate frequency includes performing a spectral analysis. The spectral analysis may include a Fourier transform based on the timestamps of a corresponding block.

[0036] Optionally, the recovery module has a first filter for determining the phase-space position from timestamps based on the first filter. The first filter can be embodied as a digital or analog filter. In particular, the first filter can be a low-pass filter and / or form a running average based on the timestamps. The first filter can in particular be designed to determine the average directly from the phases assigned to the timestamps. Such a running average can then be used as the phase-space position. In exemplary embodiments, in addition to the phases calculated directly from the timestamps, the timestamp values ​​themselves or their differences can be incorporated into the determination of the phase-space position. In particular, the first filter can be embodied as a Kalman filter or a Bayesian filter.

[0037] Alternatively or additionally, the recovery module can have a second filter to smooth the drift of the phase-space position or phase drift values ​​determined from the phase-space position(s). The second filter can be configured as an analog or digital filter. In particular, the second filter can be a low-pass filter and / or form a running average. Smoothing can be performed, for example, by convolution with a Gaussian curve, rectangular function, or truncated sine function. Smoothing can be performed using spline interpolation or a Savitzky-Golay filter.

[0038] In exemplary embodiments, in addition to the phase values ​​and / or phase drift values ​​calculated directly from the timestamps, the timestamp values ​​themselves or their differences can be incorporated into the smoothing. In particular, the second filter can be implemented as a Kalman filter or a Bayesian filter.

[0039] Optionally, the recovery module is designed to calculate a correction for the phase space position and / or for the time stamps based on the temporal drift of the phase space position and / or the phase drift values.

[0040] Alternatively or additionally, the recovery module can also be configured to update the approximation frequency. The approximation frequency is advantageously close to a multiple of the pulse repetition frequency. Then, the drift of the phase-space position can be relatively small and therefore easier to determine. The recovery module can, for example, be configured to re-estimate or adjust the approximation frequency at specific time intervals or after a specific number of quantum particles have been received during the transmission. The approximation frequency can also be updated from one block to the next.

[0041] Optionally, the recovery module comprises a plurality of filters for determining a plurality of phase-space positions (121) based on these filters. In this way, additional sets of phase-space positions for the same time stamps can be generated in parallel using one or more additional approximation frequencies, and / or additional sets of phase-space positions can be generated in parallel by applying different filters for the same time stamps.

[0042] In advantageous embodiments, the recovery module is designed to convert the phase space position, which is determined by phase unwrapping from a value range that is periodically limited to values ​​between 0 and 2n, into a phase estimate, wherein the phase estimate can assume values ​​in a non-periodic range of more than 2n. The phase unwrapping allows the complete rotations by 2n in the phase space to be counted. As a result, the temporal drift of the phase position can have values ​​that can lie in a value range that encompasses significantly more than 2n. It can also be advantageous to define the phase space position taking into account a periodicity of 2n and the drift of the phase space position without such consideration.

[0043] Advantageously, especially when performing a phase wrap, multiple sets of phase-space positions generated by the parallel application of multiple filters and / or approximate frequencies can be used to determine the temporal drift. In particular, the use of multiple sets of phase-space positions can be used to improve the stability of the phase estimation and prevent the formation of artifacts (fake wraps). Multiple temporal drifts can also be determined, for example, to subsequently determine the most accurate temporal drift possible.

[0044] Embodiments also relate to a method for recovering a clock using transmitted quantum particles. The method comprises transmitting the quantum particles in a temporal sequence based on the clock; further, generating a timestamp for each received quantum particle, providing an approximate frequency as an approximation for the clock, determining a phase-space position based on the timestamps and the approximate frequency, and recovering the clock based on a temporal drift or change in the phase-space position, or on determining a phase drift.

[0045] Optionally, the method includes correcting the timestamps for further processing based on the recovered clock and / or the temporal drift of the phase-space position. In particular, a correction of the timestamps can be provided based on the recovered clock or the temporal drift within or for data processing in further modules.

[0046] Important aspects of the procedure can be described as follows.

[0047] The method is used to recover the clock frequency from pulsed quantum signals, in which no quantum particles (in particular, these can be photons) are detected in most of the clock pulses. Compared to typical problems in digital signal processing, in which signals are periodically sampled at a fixed rate, the arrival times of the quantum particles are sparse and statistically distributed. Therefore, the time stamps (characteristic times of reception) of the received or registered quantum particles are converted into phase-space coordinates. For this purpose, the time stamps are each multiplied by an approximate frequency, which is preferably close to a multiple of a pulse repetition frequency, and mapped onto the unit circle of complex numbers (phase space). The pulse repetition frequency is determined by the clock pulse and can exactly correspond to the inverse value of the clock pulse.

[0048] If the proximity frequency coincides with a multiple of the pulse repetition frequency, this leads to a static distribution of points in phase space, the shape of which is determined by the shape of the quantum particle pulses. The position of the distribution in phase space is determined by the phase difference between the receiver's clock and the transmitter's clock.

[0049] If the approximation frequency deviates from a constant multiple of the pulse repetition frequency, the distribution rotates in phase space. The speed of the rotation is determined by the difference between frequency and clock rate.

[0050] By tracking the position of the distribution in phase space over time, the total phase drift cp(t) accumulated between the clock of the transmitter and the receiver can be determined, from which the time deviation of the receiver time from the transmitter time is calculated. This time deviation can then be used to calculate a correction for the timestamps or detection times, for example, to obtain timestamps that the receiver would have measured if its clock had been running synchronously with the transmitter.

[0051] Digital filters can be used in particular to estimate the phase drift cp(t) from the phase space distribution.

[0052] Embodiments of the present invention provide the following advantages.

[0053] The device and the method achieve synchronization between the transmitter device and the receiver device with sub-nanosecond accuracy, which is required for a variety of quantum transmission protocols.

[0054] With the presented device and method, pulsed quantum signals transmitted by a transmitter device can be used for quantum communication as well as for clock recovery and thus for synchronization with a receiver device. This eliminates the need and technical effort for other measures for synchronizing such quantum communication systems. The device and method can also be used to synchronize other systems where only high-precision synchronization is relevant and where the quantum signals are not also used for quantum communication.

[0055] An important aspect of the method is to create a situation that resembles the initial situation of carrier recovery by transforming the statistically distributed time stamps or quantum particle arrival times into the phase space, so that the clock recovery is similar to the determination of carrier phase offset and carrier frequency offset, as used, for example, in optical transmission technology with classical light pulses.

[0056] This allows the application of established techniques in this field, as well as related techniques from signal processing, such as digital filters. The method thus makes carrier recovery methods from optical communications applicable to the problem of clock recovery from single photons in quantum key distribution.

[0057] Previously known methods for clock recovery rely on direct Fourier analysis of the photon timestamps. In the proposed method, a Fourier analysis can be used at the beginning of the transmission for a short period of time to initially determine the approximate frequency. If an estimate for the approximate frequency has been determined elsewhere, this can be omitted. No Fourier analysis is required for the remainder of the transmission time, which is why the computational effort is significantly lower than with other methods proposed in the literature.

[0058] Conventional solutions use stable clocks in the transmitter and receiver and synchronize them with an external time signal, e.g., via GPS. The clock recovery from the photon detection times presented here can be implemented purely in software, thus eliminating the need for stable clocks and GPS hardware.

[0059] Another advantage is the independence from an external time reference, as this is often not easily accessible and of high quality in buildings, for example, and thus incurs costs for installing an external GPS roof antenna, for example. Furthermore, especially relevant for applications such as quantum key distribution is that this is a high-security technology, and denial-of-service attacks can be carried out by disrupting the reference time signal, which must be avoided.

[0060] Compared to conventional methods, the presented device and the presented method for clock recovery from the timestamps of the quantum particles have the advantage that no additional resources such as a dedicated classical communication channel and additional hardware for synchronization at the transmitter and receiver are required.

[0061] The method proposed here for clock recovery from the arrival times of individual photons is simple to implement and computationally efficient compared to conventional methods. Compared to conventional clock recovery methods, which directly perform spectral analysis using the photon arrival times, the proposed method is less computationally intensive. This is particularly important because the transmission rates of quantum key systems continue to increase with technological advancements, and costs can be saved by using fewer, more powerful computers. Since quantum particles are only registered in a few pulse cycles, direct spectral analysis, e.g., using fast Fourier transformation, requires the insertion of many empty positions (zeros) where no quantum particles were registered.This is necessary because the fast Fourier transform can only be applied directly to regularly sampled data. In the method presented here, only the arrival times of the detected quantum particles are processed and no additional zero entries are added. The efficiency advantage thus increases with the loss of quantum particles. In particular, the losses can increase with the distance between the transmitter and receiver devices, so the method enables the efficient synchronization of quantum key exchange devices over longer distances.

[0062] By converting to phase space, established signal processing techniques such as digital filters can be applied to the problem of clock recovery, opening up numerous opportunities for optimization and allowing flexible adaptation of the device or method to the requirements of the specific application. This facilitates clock recovery from the arrival times of individual quantum particles, for example, for applications in quantum communication, because the computational effort is reduced and flexibility is increased.

[0063] BRIEF DESCRIPTION OF THE CHARACTERS

[0064] The embodiments of the present invention will be better understood from the following detailed description and the accompanying drawings of the various embodiments, which, however, should not be construed as limiting the disclosure to the specific embodiments, but are for explanation and understanding only.

[0065] Fig. 1 illustrates an embodiment of the presented device.

[0066] Fig. 2 shows steps of an embodiment of the presented method.

[0067] Fig. 3 illustrates an embodiment for providing an approximation frequency.

[0068] Fig. 4 illustrates an embodiment for determining the phase space position and a temporal drift.

[0069] Fig. 5 illustrates an estimation of the drift of the phase space position in one embodiment.

[0070] Fig. 6 shows an embodiment of the presented method with block-wise processing of the timestamps.

[0071] DETAILED DESCRIPTION

[0072] Fig. 1 illustrates an embodiment of the apparatus 100 for recovering a clock 13 of a transmitter device 10 based on transmitted quantum particles 21. The transmitter device 10 is designed to transmit the quantum particles 21 in a temporal sequence based on the clock 13. A receiver device 30 is designed to receive the quantum particles 21 and to generate a timestamp 31 for each received quantum particle 21. The apparatus 100 comprises an interface 110 designed to receive the timestamps 31. The apparatus 100 further comprises a recovery module 120 designed to determine a phase-space position 121 based on the timestamps 31 and an approximate frequency, and to recover the clock 13 based on a temporal drift of the phase-space position 121.In the present embodiment, the receiver device is designed to forward the time stamps to further modules 50 for data processing, which then, for example, carry out the evaluation of the quantum key transmission.

[0073] The transmitter device io can, for example, comprise a photon source and send a periodic pulsed signal with a few photons 21 per pulse to the receiver device 30. This situation arises, for example, in a pulsed system for quantum key distribution. The clock can be the temporal period of the pulse repetition. In most pulse cycles, no photon 21 arrives at the receiver device 30; occasionally, a single photon 21 arrives, and very rarely, two or more photons 21 arrive in the same pulse cycle. The pulse cycles are therefore sparsely populated. If one starts the clock once and records the arrival times of the photons 21 over a long period of time, one can record a histogram of the arrival time of the photons 21 if the arrival time is considered modulo the clock time.

[0074] The device 100 is thus configured to determine the drift of the clock of the receiver device relative to the clock 13 of the transmitter device 10 from the arrival times of the photons 21 and to calculate from this the arrival times 31 of the photons 21 that the receiver 30 would have measured if its clock had run at exactly the same speed as the clock 13 of the transmitter 10. Using the reconstructed clock, the arrival times of the photons can be corrected for further processing.

[0075] Fig. 2 shows steps of an embodiment of the presented method for recovering a clock 13 using transmitted quantum particles 21. The device 100 in Fig. 1 can be designed to carry out this embodiment of the method.

[0076] In this embodiment, the method comprises transmitting S110 the quantum particles, based on the clock 13, in a time sequence, generating S120 a time stamp 31 for each received quantum particle 21, dividing S130 the time stamps 31 of the registered quantum particles 21 into blocks, providing S140 an approximate frequency by estimating an approximate frequency which is a multiple of a pulse repetition frequency from the time stamps 31 in a first block, determining S150 a phase space position 121 based on the time stamps 31 and the approximate frequency, wherein determining S150 comprises converting the time stamps 31 of a block into phase space coordinates, estimating a drift of the phase position 121 due to a deviation of a receiver clock relative to the clock 13 orto a transmitter clock as a function of time, recovering S170 the clock 13 based on the temporal drift of the phase space position 121 as well as correcting S170 the measured time stamps 31 based on the drift of the phase position 121 and updating S190 the approximate frequency.

[0077] The steps mentioned can be repeated in whole or in part and carried out in a different order.

[0078] Fig. 3 illustrates an embodiment for providing S140 the proximity frequency. The figure shows a histogram modulo the clock time (9.1 ns) on the left and a spectrum on the right, each based on the timestamps 31 of received quantum particles 21.

[0079] The histogram shows a (smoothed) number of received quantum particles 21 (in units of 1000) over time in nanoseconds. In this example, the signal generated by the quantum particles 21 repeats periodically after 9.1 nanoseconds (signal repetition time) (not shown).

[0080] The spectrum results from a decomposition of the histogram into its spectral components; it shows the square of the spectral amplitude in arbitrary units over multiples of the inverse signal repetition time (one unit on the abscissa of the spectrum corresponds to 1 / 9.1 ns 1). In the spectrum, a maximum amplitude 141 of the spectrum can be seen at a six-fold inverse repetition time. The device 100 can be configured to select the approximate frequency corresponding to the maximum amplitude 141 in the spectrum, in this case six times the inverse repetition time. Fig. 4 illustrates an embodiment for determining S150 the phase-space position 121 based on the time stamps 31 and the approximate frequency, as well as a derivation of the temporal drift of the phase-space position 121.

[0081] The figure shows in an upper part two further histograms for the example shown in Fig. 3, as well as in a lower part two representations derived from them for the phase position 121 in the phase space (here the unit circle in the complex plane).

[0082] The histogram in the upper left corner of the figure is formed from the timestamps 31 according to the histogram in Fig. 3 modulo the inverse approximation frequency (9.1 / 6 ns). As with the histogram in Fig. 3, this histogram shows the number of received quantum particles 21 in arbitrary units over time in nanoseconds. For the present example, only one distinct maximum of 151 results.

[0083] The histogram in the upper right corner of the figure is a polar diagram representation of the histogram in the upper left corner. The angular coordinate corresponds to a phase relative to a clock cycle of 9.1 / 6 ns. The number of received quantum particles, 21, corresponding to the respective angle is plotted radially. This histogram shows a lobe 152, the outermost point of which corresponds to the maximum 151 in the histogram in the upper left corner of the figure.

[0084] In the bottom right of the figure, a phase space position 121 is illustrated. The time stamps 31, tj, of the quantum particles 21 can be determined using the approximate frequency / according to

[0085] Cj = exp(2 ri / b), qj = Re(c,), , = Im(c,) are converted into phase-space coordinates. The corresponding points lie on the unit circle, and each point corresponds to a detected quantum particle. The detection of individual quantum particles corresponds to drawing from the distribution in the histogram in the upper right of the figure, so that the points cluster in a certain region of the phase space.

[0086] However, since the probability according to the histogram in the upper right of the figure is not zero even for angles that deviate significantly from the maximum, it is advantageous not to determine the phase position 121 solely from a single isolated timestamp 31. Rather, a plurality of timestamps 31 or phase space points can be accumulated (for example, a predetermined number, or over a predetermined period of time). The phase position 121 can then be estimated from the plurality of phase space points 31. This can be done, in particular, by averaging.

[0087] If the approximation frequency does not exactly match a multiple of the clock 13 or the pulse repetition frequency, the distribution of points 31 in phase space 121 begins to rotate depending on the difference between the clock 13 and the approximation frequency. This is illustrated in the bottom right of the figure. Therefore, the position of the distribution in phase space is different at different times. By tracking the phase space position 121, it can be determined whether and to what extent the clock of the receiver device 30 is running slower or faster than the clock 13 of the transmitter device 10.

[0088] In particular, the number of complete orbits can be counted (phase unwrapping). The thus accumulated, time-dependent phase drift cp(t) can then be converted into a time difference T(t) = (p(t) / (271 / )) between the clocks of the transmitter device 10 and the receiver device 30. Using this time difference, the measured arrival times 31 of the quantum particles 21 can be corrected to t'j = tj + Δt(tj). The function Δt(t) indicates the time deviation between the clocks of the transmitter 10 and the receiver 30 since the beginning of the transmission.

[0089] Fig. 5 illustrates steps of an embodiment for estimating S160 the drift of the phase-space position 121. This embodiment uses two digital low-pass filters (complex-valued moving average 163 and Savitzky-Golay filter 167), with a phase unwrapping S165 between them. Those skilled in the art will recognize that a variety of other methods or other filters can also be used for estimating S160 the drift of the phase-space position 121 and / or smoothing the phase drift values.

[0090] In the histograms in the upper part of Fig. 4, which are again used as an example, only a single prominent maximum 151 is present. For this, the phase position 121 can be determined as an average angle of the distribution from the moving average of the phase-space coordinates q. In this way, values ​​{cj} and {qj} and {p} for the phase-space position 121 "at time tj" can be obtained. From these values, a phase value between -n and n can be calculated for each quantum particle 21, which can be converted into a phase drift cp'(t) running over time t using phase unwrapping S165. These values ​​can in turn be smoothed using a Savitzky-Golay filter to reduce the noise and obtain the phase drift cp(t).

[0091] A filter 163 used to determine the mean value, as well as the Savitsky-Golay filter 167 used as an example, are characterized by their window widths. The Savitsky-Golay filter 167 is also characterized by the filter order. The parameters of the filters 163, 167 can be optimized depending on the clock stability of the transmitter device 10 and the receiver device 30, the rate of the received quantum particles 21, and the histogram distribution.

[0092] In particular, the moving average of the phase-space coordinates q presented here by implementing a digital low-pass filter 163 is only one possible implementation. The Savitzky-Golay filter 167 used for smoothing can also be replaced by another filter.

[0093] In particular, the type of filtering presented here ignores information that can be used in further embodiments to make a reconstruction of the phases more stable and accurate. Thus, in addition to the values ​​qj and pj, the time stamps tj of the quantum particles 21 or their differences can also be processed. Since the time intervals between received quantum particles 21 are statistically distributed and thus not equidistant, additional information can be obtained therefrom for determining S150 the phase space position 121. For example, the histogram distribution or the distribution of the frequency fluctuations of the clocks of the transmitter device 10 and the receiver device 30 can also be used, and statistically optimized filters such as Kalman filters and Bayes filters can be employed.

[0094] The method described here has proven advantageous when the distribution of quantum particles 21 in phase space is suitable for determining a unique phase-space position 121. In the example presented above, a distribution with a single, distinct maximum 151 (within 2 ) is assumed. However, the method is also possible with distributions with multiple maxima, such as would arise, for example, if the approximation frequency were chosen not as six times, but as any integer multiple of the clock or repetition frequency of the quantum particle source.

[0095] The construction of a phase-space position from distributions with multiple regions in a phase space in which the measured events occur frequently is also known in the state of the art from carrier recovery methods in optical telecommunications. Some of the techniques developed for carrier recovery can thus also be used in the presented method.

[0096] A further condition under which the exemplary embodiments illustrated in the preceding figures prove advantageous is that the orbital speed of the phase-space position 121 or the distribution in phase space is relatively small and the rate of the measured quantum particles 21 is relatively large. This ensures that a distribution can be accumulated from the individual measurement events 31 of the received quantum particles 21, the position of which in phase space can be reliably estimated before this distribution has already rotated too far. If the orbital speed of the distribution is too large in relation to the rate at which quantum particles 21 are received, the phase-space position 121 or its drift can no longer be reliably estimated. The approximation frequency should therefore advantageously correspond as precisely as possible to a multiple of the clock 13 or the pulse repetition frequency of the quantum particle source 10.

[0097] It is therefore advantageous to continually adjust the approximation frequency during a transmission to achieve the best possible match. The timestamps 31 or arrival times of the quantum particles 21 can be divided into blocks, each of which is processed with an updated or adjusted approximation frequency.

[0098] The drift of the phase space position 121 resulting from a block, as well as the approximation frequency used in that block, can then be used to update the approximation frequency for the next block.

[0099] Fig. 6 shows an embodiment of the presented method with block-wise processing of the time stamps 31.

[0100] The approximate frequency is estimated S140 based on the first block (block A) and updated from block to block. To obtain an initial estimate of the approximate frequency, in this exemplary embodiment, a spectral analysis is performed in the first block using a portion of the time stamps 31, from which an initial estimate of the approximate frequency can be determined. The approximate frequency is updated S190 from one block A, B, C to the next.

[0101] For each block, the time stamps 31, tj, are converted into phase-space coordinates q, thus determining the phase-space position S150. Based on the phase-space coordinates q or the phase-space position 121, the drift cp(t) of the phase-space position 121 is estimated S160, and from this, the clock pulse is recovered S170, or the time stamps 31 are corrected S180 to values ​​t.

[0102] In the exemplary embodiment shown here, the determination S150 of the phase-space position 121 also includes time stamps 31 from overlap areas AB, BC, each of which encompasses a boundary between consecutive blocks. This procedure has proven advantageous when the filters 163, 167 used lead to edge effects at the beginning and end of each block. To avoid these edge effects, the overlap areas AB, BC of blocks A, B, and C are also included in the calculation. This is indicated by the dashed arrows 175.

[0103] LIST OF REFERENCE SYMBOLS

[0104] IO transmitter setup

[0105] 13 bars

[0106] 21 quantum particles

[0107] 30 Recipient facility

[0108] 31 timestamps

[0109] 50 additional modules

[0110] 100 device

[0111] 110 Interface for receiving timestamps

[0112] 120 recovery module

[0113] 121 Phase space position

[0114] 141 maximum amplitude (spectrum)

[0115] 151 Maximum (histogram)

[0116] 152 lobe (histogram)

[0117] 163 digital filter for determining an average value

[0118] 167 Savitzky-Golay filter for smoothing the drift of the phase space position

[0119] 175 Effect of overlap areas

[0120] A, B, C blocks

[0121] AB, BC overlap areas

[0122] S110, S120, ... steps of a procedure

Claims

CLAIMS 1. Apparatus (100) for recovering a clock (13) of a transmitter device (10) based on transmitted quantum particles (21), wherein the transmitter device (10) is designed to transmit the quantum particles (21) in a time sequence based on the clock (13), and wherein a receiver device (30) is designed to receive the quantum particles (21) and to generate a time stamp (31) for each received quantum particle (21), the apparatus (100) comprises: an interface (110) designed to receive the time stamps (31); and a recovery module (120) designed to - to determine a phase space position (121) based on the time stamps (31) and on an approximate frequency, and - to recover the clock (13) based on a temporal drift of the phase space position (121).

2. The device (100) according to claim 1, wherein the recovery module (120) is configured to be at least one of the following: - dividing the time stamps (31) of the received quantum particles (21) into blocks, - estimating (S140) the approximation frequency from timestamps (31) of a block, - Determining the phase space position (121) from time stamps (31) of a block.

3. The apparatus (100) of claim 2, wherein estimating the approximate frequency comprises performing a spectral analysis.

4. The device (100) according to any one of the preceding claims, wherein the recovery module (120) comprises at least one of the following: - a first filter (163) for determining a running average based on time stamps (31), - a second filter (167) to smooth the temporal drift based thereon.

5. The apparatus (100) of claim 4, wherein the first filter (163) is a low-pass filter, and wherein the second filter (167) is a low-pass filter, a Savitzky-Golay filter, a Kalman filter, or a Bayesian filter.

6. The device (100) according to any one of the preceding claims, wherein the recovery module (120) is configured to be at least one of the following: - calculating, based on the temporal drift of the phase space position (121), a correction for the phase space position (121) and / or for the time stamps (31), - Update (S190) the proximity frequency.

7. The device (100) according to any one of the preceding claims, wherein the recovery module (120) comprises a plurality of filters to determine a plurality of phase space positions (121) based on these filters.

8. Method for recovering a clock (31) using transmitted quantum particles (21), comprising: Sending (S110) the quantum particles (21) based on the clock (31) in a time sequence; Generating (S120) a timestamp (31) for each received quantum particle (21); Providing (S140) an approximation frequency; Determining (S150) a phase space position (121) based on the time stamps (31) and the proximity frequency; and Recovering (S170) the clock (13) based on a temporal drift of the phase-space position (121).

9. The method according to claim 8, wherein the determined temporal drift of the phase-space position (121) is used to correct (S180) the time stamps for data processing in further modules (50).

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