Method and apparatus for determining quantum non-locality

Abstract

To provide a method for determining quantum non-locality.SOLUTION: A method of determining quantum non-locality performed by a computing system includes performing, by a first node, a first projection measurement corresponding to a predetermined first number, selecting, by the first node, a first input value based on the first projection measurement, obtaining, by the first node, a first output value when a second input value is selected by a second node, and calculating a probability distribution that the second output value is obtained by the second node, and determining, by the first node, that quantum non-locality exists when the calculated probability distribution exceeds a reference value.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present disclosure relates to methods for determining nonlocality associated with quantum mechanics, and more particularly to methods and apparatus for determining quantum nonlocality using Bell inequalities. [Background technology]

[0002] In quantum mechanics, quantum nonlocality can be determined by using Bell's inequality.

[0003] In 2009, the so-called Gisin elegant Bell inequality (EBI) was proposed as a Bell inequality. This Bell inequality has the property that it is maximally violated by measurements with high symmetry in the ground state and a two-body, two-dimensional maximally entangled state. Specifically, it is known that when the measurements of local system 1 (Alice) are defined in mutually unbiased bases (MUBs) and the measurements of local system 2 (Bob) are defined in symmetric informationally complete bases (SICs), these measurements give a maximal violation. This high symmetry is relevant to quantum cryptography, and a protocol has been proposed that utilizes quantum nonlocality discrimination based on this Bell inequality to verify the maximum amount of randomness per entanglement distribution in a device-independent (DI) manner.

[0004] However, there are no known results of generalizing this highly symmetric Bell inequality to higher-dimensional quantum systems, which are expected to have information-theoretic advantages. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Korean Patent Publication No. 10-2011-0062869 (June 10, 2011) Summary of the Invention

[0006] [Problem to be solved by the invention] A technical problem to be solved in some embodiments of the present disclosure is to provide a method and apparatus for determining quantum nonlocality using Bell inequality for which the maximum quantum violation is given by a mutually unbiased basis and a symmetric information complete basis.

[0007] Another technical problem that some embodiments of the present disclosure aim to solve is to provide a method and apparatus for determining quantum nonlocality for high-dimensional quantum systems using fewer computing resources than conventional methods.

[0008] The technical problems of the present disclosure are not limited to the technical problems described above, and other technical problems not mentioned will be clearly understood by a person of ordinary skill in the technical field of the present disclosure from the following description.

[0009] [Means for solving the problem] A method for determining quantum nonlocality performed by a computing system according to an embodiment of the present disclosure to solve the technical problem may include a step of a first node performing first projection measurements corresponding to a predetermined first number, a step of the first node calculating a probability distribution of a first output value obtained at the first node and a second output value obtained at the second node when a first input value is selected at the first node and a second input value is selected at a second node based on the first projection measurements, and a step of the first node determining that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

[0010] In addition, the reference value is

[0011]

number

[0012] It could be.

[0013] The step of calculating the probability distribution includes the step of the first node calculating the probability distribution using the following formula:

[0014]

number

[0015] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, and β is the second output value;

[0016]

number

[0017] may be a real number calculated based on the first input value, the second input value, the first output value, and the second output value.

[0018] The aforementioned

[0019]

number

[0020] is calculated using the following formula:

[0021]

number

[0022]

number

[0023] is a predefined value from

[0024]

number

[0025] Substituting the coefficients for the first input value x and the second input value y,

[0026]

number

[0027] can be calculated.

[0028] Further, the step of calculating the probability distribution includes the step of the first node calculating the probability distribution using the following formula:

[0029]

number

[0030] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, β is the second output value, and cc is the complex conjugate of the previous term;

[0031]

number

[0032] Furthermore, the method for determining quantum nonlocality may further include, before the step of performing the projection measurement, a step of sharing a quantum entangled state between the first node and the second node.

[0033] In addition, the quantum entangled state

[0034]

number

[0035] It could be.

[0036] The method for determining quantum nonlocality further includes calculating a maximum value associated with the quantum probability model using the following formula:

[0037]

number

[0038] where:

[0039]

number

[0040] is the Weyl-Heisenberg measurement, and in the definition of X,

[0041]

number

[0042] is used.

[0043] Also, the first input value

[0044]

number

[0045] and the second input value is

[0046]

number

[0047] and the first output value is

[0048]

number

[0049] and the second output value is

[0050]

number

[0051] is.

[0052] The first number may also be eight.

[0053] A method for determining quantum nonlocality performed by a computing system according to an embodiment of the present disclosure to solve the technical problem may include a step in which a second node performs second projection measurements corresponding to a predetermined second number; a step in which the second node calculates, based on the second projection measurements, a probability distribution in which a first output value is obtained at the first node and a second output value is obtained at the second node when a first input value is selected at the first node and a second input value is selected at the second node; and a step in which the second node determines that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

[0054] A computing system according to an embodiment of the present disclosure for solving the technical problem includes one or more processors and a memory that stores a computer program executed by the one or more processors, and the computer program may include instructions for the operations of performing a projective measurement, calculating a probability distribution that a first output value will be obtained at the first node and a second output value will be obtained at the second node when a first input value is selected at a first node and a second input value is selected at a second node based on the projective measurement, and determining that quantum nonlocality exists when the calculated probability distribution exceeds a reference value.

[0055] A computer program according to an embodiment of the present disclosure for solving the technical problem can be stored in a computer-readable recording medium, coupled to a computing device, to execute the steps of: performing a projection measurement; calculating a probability distribution of a first output value obtained at the first node and a second output value obtained at the second node when a first input value is selected at a first node and a second input value is selected at a second node based on the projection measurement; and determining that quantum nonlocality exists when the calculated probability distribution exceeds a reference value. [Brief explanation of the drawings]

[0056] [Figure 1] FIG. 1 illustrates a non-locality determination system according to an embodiment of the present disclosure. [Figure 2] 1 is a flowchart illustrating a method for determining non-locality in a computing system according to one embodiment of the present disclosure. [Figure 3] FIG. 2 illustrates a state in which a quantum entangled state is shared between a first node and a second node according to an embodiment of the present disclosure. [Figure 4] FIG. 1 is an exemplary hardware diagram in which a computing system may be implemented in accordance with various embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0057] Hereinafter, preferred embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. Advantages and features of the present disclosure, as well as methods for achieving them, will become clearer with reference to the following embodiments in detail with the accompanying drawings. However, the technical idea of ​​the present disclosure is not limited to the following embodiments and can be realized in various different forms. The following embodiments are provided merely to complete the technical idea of ​​the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art to which the present disclosure pertains, and the technical idea of ​​the present disclosure is defined only by the scope of the claims.

[0058] When assigning reference numerals to components shown in each drawing, it should be noted that the same components are assigned the same numerals whenever possible, even if they are shown in different drawings. Furthermore, in describing the present disclosure, if a specific description of related publicly known configurations or functions is deemed to obscure the gist of the present disclosure, such detailed description will be omitted.

[0059] Unless otherwise defined, all terms (including technical and scientific terms) used herein shall be used in the sense commonly understood by a person of ordinary skill in the art to which this disclosure belongs. Furthermore, terms defined in commonly used dictionaries should not be interpreted ideally or excessively unless specifically defined otherwise. The terms used herein are intended to describe the embodiments and are not intended to limit the present disclosure. In this specification, the singular form includes the plural form unless otherwise specified in the context.

[0060] Furthermore, when describing components of the present disclosure, terms such as first, second, A, B, (a), and (b) may be used. These terms are used to distinguish the component from other components, and do not limit the nature, order, or sequence of the components. When a component is described as being "coupled," "coupled," or "connected" to another component, it should be understood that this means that the component may be directly coupled or connected to the other component, and that other components may also be "coupled," "coupled," or "connected" between each component.

[0061] As used herein, the terms "comprises" and / or "comprising" are to be interpreted as meaning that a stated component, step, operation and / or element does not exclude the presence or addition of one or more other components, steps, operations and / or elements.

[0062] Hereinafter, several embodiments of the present disclosure will be described in detail with reference to the accompanying drawings.

[0063] FIG. 1 is a diagram illustrating a non-locality determination system according to one embodiment of the present disclosure.

[0064] 1, the nonlocality determination system may include a first node 10 and a second node 20. The first node 10 may be referred to as "Alice" for use as an example in explaining Bell's inequality, and the second node 20 may be referred to as "Bob" for use as an example in explaining Bell's inequality.

[0065] Each of the first node 10 and the second node 20 may be implemented as a computing device including one or more processors and memory. The first node 10 and the second node 20 may communicate with each other via a network, which may include a quantum channel, a mobile communication network, or a wired communication network.

[0066] The first node 10 and the second node 20 may share the entangled state over the network. According to some embodiments, each of the first node 10 and the second node 20 may share the entangled state by retrieving the entangled state from a respective storage device.

[0067] The first node 10 may perform a first projection measurement corresponding to a first number, and the second node 20 may perform a second projection measurement corresponding to a second number. According to an embodiment, each of the first node 10 and the second node 20 may calculate a probability distribution based on at least one of the first projection measurement and the second projection measurement, indicating that when a first input value is selected at the first node 10 and a second input value is selected at the second node 20, a first output value is obtained at the first node 10 and a second output value is obtained at the second node 20. Furthermore, each of the first node 10 and the second node 20 may compare the calculated probability distribution with a reference value to determine quantum nonlocality.

[0068] According to one embodiment, each of the first node 10 and the second node 20 may use Bell inequality to determine nonlocality. Each of the first node 10 and the second node 20 may determine that nonlocality exists if the calculated probability distribution violates Bell inequality.

[0069] Below, with reference to FIG. 2, a method for determining nonlocality and Bell's inequality used for determining nonlocality will be described.

[0070] FIG. 2 is a flowchart illustrating a method for determining non-locality in a computing system according to one embodiment of the present disclosure.

[0071] Referring to FIG. 2, a quantum entangled state is established between a first node 10 and a second node 20.

[0072]

number

[0073] may be shared (S110). For example, the first node 10 and the second node 20 may share the entangled state over the network. According to some embodiments, each of the first node 10 and the second node 20 may share the entangled state by retrieving the entangled state from a respective storage device. According to one embodiment, the entangled state shared between the first node 10 and the second node 20 is

[0074]

number

[0075] It could be.

[0076] The first node 10 may then perform a predetermined first number of projection-valued measures, and the second node 20 may perform a predetermined second number of projection-valued measures (S120). In one embodiment, the first number may be eight, and the second number may be eight. For example, a first input value "x" used in the projection measurements at the first node 10 may belong to a first set of {1, 2, ..., 8}, and a second input value "y" used in the projection measurements at the second node 20 may belong to a second set of {0, 1, 2, ..., 8}, which can be expressed as follows:

[0077]

number

[0078] The measurement at the first node 10 and the measurement at the second node 20 may each have one of three measurement values ​​(i.e., output values). That is, the first measurement value (output value) α output from the first node 10 may belong to {0, 1, 2}, and the second measurement value (output value) β output from the second node 20 may belong to {0, 1, 2}, which can be expressed as follows:

[0079]

number

[0080] where:

[0081]

number

[0082] It can be expressed as:

[0083] A Bell test can be performed under the above measurement conditions to calculate the probability distribution (P). That is, when a first input value (x) is selected at the first node 10 and a second input value (y) is selected at the second node 20, the probability distribution that a first output value (α) is obtained at the first node 10 and a second output value (β) is obtained at the second node 20 is calculated.

[0084]

number

[0085] The probability distribution may be calculated in each of the first node 10 and the second node 20 (S130).

[0086] Each of the first node 10 and the second node 20 may determine whether the calculated probability distribution exceeds a reference value (S140).

[0087]

number

[0088] It could be.

[0089] The first node 10 determines whether the calculated probability distribution is a reference value.

[0090]

number

[0091] Similarly, the second node 20 may determine that non-locality exists if the calculated probability distribution exceeds a reference value

[0092]

number

[0093] For example, if at least one of all values ​​associated with the calculated probability distribution exceeds a reference value, it may be determined that nonlocality exists (S150).

[0094] The first node 10 determines whether the calculated probability distribution is a reference value.

[0095]

number

[0096] Similarly, the second node 20 may determine that non-locality does not exist if the calculated probability distribution is equal to or less than the reference value (S160).

[0097]

number

[0098] If the value is less than or equal to a reference value, it may be determined that nonlocality does not exist (S160). For example, if all values ​​associated with the calculated probability distributions are less than or equal to a reference value, it may be determined that nonlocality does not exist.

[0099] In addition, the calculated probability distribution is

[0100]

number

[0101] If the value of the Bell inequality is greater than 0, it may be determined that the Bell inequality is violated.

[0102] The first Bell inequality used in the embodiments of the present disclosure is as follows:

[0103]

number

[0104] where P may be a probability distribution, x may be a first input value selected at the first node 10, y may be a second input value selected at the second node 20, α may be a first output value output at the first node, and β may be a second output value output at the second node.

[0105] The first Bell inequality associated with Equation 1 can be expressed as the second Bell inequality associated with Equation 2 below.

[0106]

number

[0107] Here, cc is the complex conjugate of the previous term. In Equation 1 and Equation 2, P represents a probability distribution, and S(P) can be a function for calculating P.

[0108] In addition, in Equation 2, E(x, y) is an expectation function, which can be expressed as Equation 3 below.

[0109]

number

[0110] where:

[0111]

number

[0112] It could be.

[0113] The probability can be obtained experimentally. According to one embodiment, the first node 10 may randomly select an input value from a first input list to perform a first projection measurement, and the second node 20 may randomly select an input value from a second input list to perform a second projection measurement. The output value output from each of the first node 10 and the second node 20 may be one of the output values ​​included in the output list.

[0114] where the first list may include integers from 1 to 8,

[0115]

number

[0116] and the second list may contain integers from 0 to 8,

[0117]

number

[0118] The output list can also contain integers between 0 and 2,

[0119]

number

[0120] It can be expressed as:

[0121] As described above, when repeated experiments are performed with the range of input values ​​of the first node 10, the range of output values ​​of the first node 10, the range of input values ​​of the second node 20, and the range of output values ​​of the second node 20 defined, a probability distribution (P) can be calculated for when the first node 10 selects a first input value (x) and the second node 20 selects a second input value (y), and the first node 10 outputs a first output value (α) and the second node 20 outputs a second output value (β). For example, through successive experiments, when “1” is selected at the first node 10 and “0” is selected at the second node 20, a first probability that “0” will be output at the first node 10 and “0” will be output at the second node 20 can be calculated, and a second probability that “0” will be output at the first node 10 and “0” will be output at the second node 20 can be calculated when “1” is selected at the first node 10 and “1” is selected at the second node 20. Furthermore, the probabilities for other situations are calculated by repeated experiments, and the probability distribution (P) can be calculated based on the calculated probabilities for each case.

[0122] According to one embodiment, the complex conjugate (cc) of the previous term can be introduced into Equation 2 to derive the probability distribution (P) as real valued.

[0123] The fact that Equation 1 and Equation 2 are equal to each other can be proven by Equation 4.

[0124]

number

[0125] In Equation 2 and Equation 4, f x,y denotes a coefficient and can be expressed as follows:

[0126]

number

[0127] where:

[0128]

number

[0129] are values ​​associated with measurements, each having three measurements,

[0130]

number

[0131] where,

[0132]

number

[0133] and

[0134]

number

[0135] where:

[0136]

number

[0137] It can be calculated based on the following.

[0138] Also,

[0139]

number

[0140] can be expressed as the following Equation 5.

[0141]

number

[0142] In formula 5, by substituting {0,1,...,2} for each of the side numbers r, s, p, and q, we can obtain the

[0143]

number

[0144] can be calculated, which can be expressed as Equation 6.

[0145]

number

[0146] On the right side of Equation 4

[0147]

number

[0148] can be derived from Equation 5.

[0149] In addition, in Equation 2, the expected value (E(x, y)) can be expressed as in Equation 7 below.

[0150]

number

[0151] where:

[0152]

number

[0153] is the xth measurement of the first node 10,

[0154]

number

[0155] denotes the y-th measurement of the second node 20.

[0156] Quantum expectation value (E(x,y))

[0157]

number

[0158] Substituting this into Equation 2, the theoretical upper limit of S is

[0159]

number

[0160] Furthermore, "S" can be calculated using the following Equation 8.

[0161]

number

[0162] However, the upper limit in Equation 8 is the reference value related to Equation 1 and Equation 2, which are related to Bell's inequality.

[0163]

number

[0164] Because it is larger, the Bell inequalities (Equations 1 and 2) can be violated using quantum mechanics.

[0165] Such a violation condition, i.e., the measurement and state to satisfy the inequality in Equation 8, may be as follows:

[0166]

number

[0167] where:

[0168]

number

[0169] is the Weyl-Heisenberg measurement, and in the definition of X,

[0170]

number

[0171] is used.

[0172] According to some embodiments, each of the first node 10 and the second node 20 may use Equation 9 to calculate a maximum value associated with the quantum probability model.

[0173] The measurement of the second node 20 is obtained from B0 as per Equation 9, and B0 can be expressed as Equation 10.

[0174]

number

[0175] Substituting the shared entangled state between the first node 10 and the second node 20 and the measurement associated with Equation 9 into Equation 8, we obtain the upper bound

[0176]

number

[0177] can be calculated.

[0178] Related to Equation 9

[0179]

number

[0180] from,

[0181]

number

[0182] These measurement bases can be a set of four mutually unbiased bases (MUBs).

[0183] Related to Equation 10

[0184]

number

[0185] Considering the measurement basis of the nine measurements in

[0186]

number

[0187] symmetric informationally complete bases (SICs) induced by

[0188]

number

[0189] It can be seen that defines nine measurement basis states. Therefore, it can be proved that the measurement basis of the first node 10 and the second node 20 are given by MUBS and SICs, respectively.

[0190] FIG. 3 illustrates a quantum entangled state between a first node 10 and a second node 20 according to one embodiment of the present disclosure.

[0191]

number

[0192] 10 is a diagram illustrating a state in which the information is shared.

[0193] As shown in Fig. 3, the quantum entangled state may be shared in advance. The first node 10 and the second node 20 may share the quantum entangled state with each other via a network in advance, or the quantum entangled state may be stored in each of the first node 10 and the second node 20 at the time of shipment, or the quantum entangled state may be registered in each of the first node 10 and the second node 20 via a storage means.

[0194] Based on quantum entanglement states, the maximum value associated with the quantum probability model

[0195]

number

[0196] can be calculated from each of the first node 10 and the second node 20.

[0197] As shown in Figure 3, the first node 10 may perform a first projection measurement corresponding to a first number, and the second node 20 may perform a second projection measurement corresponding to a second number. As shown in Figure 3, the first number may be eight, and the second number may be nine.

[0198] The first node 10 may perform a first projection measurement based on a value randomly obtained through a random seed, and similarly, the second node 20 may perform a second projection measurement based on a value randomly obtained through a random seed.

[0199] According to the embodiment of the present disclosure, the Bell inequality proposed by Formula 1 or Formula 2 can utilize a three-dimensional quantum system, which is higher in dimension than Gisin's elegant Bell inequality (EBI), which is based on a conventional two-dimensional quantum system. As a result, according to the present embodiment, it is possible to achieve an effect of newly deriving a three-dimensional Bell inequality, which is an important element technology of DI quantum cryptography protocols that ensure a high level of security, while maintaining the violation property with high symmetry as in the case of EBI.

[0200] Furthermore, according to this embodiment, the number of measurements to be performed to determine whether Bell inequality is violated is smaller than the Bell inequality that shows the largest violation by conventional SICs [Sci. Adv. 2021; 7: eabc3847]. Therefore, the method according to this embodiment can determine nonlocality for multidimensional systems more quickly using fewer computing resources.

[0201] The hardware configuration of an exemplary computing system according to some embodiments will now be described with reference to FIG.

[0202] 4 is a diagram showing an exemplary hardware configuration in which a computing system according to various embodiments can be implemented. A computing system 1000 according to this embodiment can include one or more processors 1100, a system bus 1600, a communication interface 1200, a memory 1400 into which a computer program 1500 executed by the processor 1100 is loaded, and a storage 1300 into which the computer program 1500 is stored.

[0203] The computing system 1000 shown in Fig. 4 may include at least one of the first node 10 and the second node 20 shown in Fig. 1 and Fig. 3. Only components related to the embodiment are shown in Fig. 4. Therefore, a person skilled in the art to which the embodiment of the present specification pertains will understand that other general-purpose components may be further included in addition to the components shown in Fig. 4.

[0204] The processor 1100 can control the overall operation of each component of the computing system 1000. The processor 1100 can be configured to include at least one of a central processing unit (CPU), a microprocessor unit (MPU), a microcontroller unit (MCU), a graphic processing unit (GPU), or any other type of processor known in the art. The processor 1100 can also execute calculations for at least one application or program for performing methods / operations according to various embodiments. The computing system 1000 can include two or more processors.

[0205] The memory 1400 stores various data, instructions, and / or information. The memory 1400 can load one or more programs 1500 from the storage 1300 to perform the methods / operations according to various embodiments of the present disclosure. An example of the memory 1400 includes, but is not limited to, a RAM. The system bus 1600 provides communication between components of the computing system 1000.

[0206] The bus may be implemented as various types of buses, such as an address bus, a data bus, and a control bus. The communication interface 1200 may be connected to a communication network. The storage 1300 may non-temporarily store one or more computer programs 1500. The storage 1300 may include a non-volatile memory such as a flash memory, a hard disk, a removable disk, or any other type of computer-readable recording medium known in the art to which the embodiments of this specification pertain.

[0207] The computer program 1500 may include one or more instructions that implement the methods / operations according to various embodiments of the present disclosure. When the computer program 1500 is loaded into the memory 1400, the processor 1100 can execute the one or more instructions to perform the methods / operations according to various embodiments of the present disclosure. The computer program 1500 may include instructions for the methods described with reference to FIGS. 1 to 3.

[0208] The computer program 1500 may include instructions for performing a first projection measurement corresponding to a predetermined first number, calculating a probability distribution that a first output value will be obtained at the first node and a second output value will be obtained at the second node when a first input value is selected at the first node and a second input value is selected at the second node based on the first projection measurement, and determining that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

[0209] According to one embodiment, the computer program 1500 may be coupled to a computing device and stored on a computer-readable recording medium to cause the computer to perform the steps of: performing first projection measurements corresponding to a predetermined first number; calculating a probability distribution of a first output value at the first node and a second output value at the second node when a first input value is selected at the first node and a second input value is selected at the second node based on the first projection measurements; and determining that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

[0210] In some embodiments, the computing system 1000 described with reference to Figure 4 may be configured using one or more physical servers included in a server farm based on cloud technology such as virtual machines. In this case, at least some of the components shown in Figure 4, such as the processor 1100, the memory 1400, and the storage 1300, may be virtual hardware, and the communication interface 1200 may also be configured with a virtualized networking element such as a virtual switch.

[0211] Various embodiments of the present disclosure and the effects of those embodiments have been described above with reference to Figures 1 to 4. The effects based on the technical idea of ​​the present disclosure are not limited to the effects described above, and other effects not described will also be clearly understood by those skilled in the art from the following description.

[0212] The methods according to the embodiments of the present invention described above may be performed by executing a computer program embodied as computer-readable code. The computer program may be transmitted from a first computing device to a second computing device over a network, such as the Internet, and installed on the second computing device, thereby enabling it to be used on the second computing device. Also, although acts are shown in a particular order in the figures, the acts need not necessarily be performed in the particular order shown or in a sequential order, or should not be understood as requiring all shown acts to achieve desired results. In certain situations, multitasking and parallel processing may be advantageous.

[0213] Although the embodiments of the present disclosure have been described above with reference to the accompanying drawings, those skilled in the art will understand that the present disclosure can be embodied in other specific forms without changing the technical idea or essential features thereof. Therefore, it should be understood that the above embodiments are illustrative in all respects and are not limiting. The scope of protection of the present invention should be interpreted by the scope of the claims, and all technical ideas within the scope equivalent thereto should be interpreted as being included in the scope of rights of the technical ideas defined by the present disclosure.

Claims

1. 1. A method for determining quantum nonlocality performed by a computing system, comprising: a first node making first projection measurements corresponding to a predetermined first number; calculating, by the first node, a probability distribution of a first output value obtained at the first node and a second output value obtained at the second node when a first input value is selected at the first node and a second input value is selected at the second node based on the first projection measurement; 10. A method for determining quantum nonlocality, comprising: determining, by the first node, that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

2. The reference value is [Equation 1] The method for determining quantum nonlocality according to claim 1 ,

3. The step of calculating the probability distribution includes: The first node calculates the probability distribution using the following formula: [Equation 2] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, and β is the second output value; [Equation 3] The method for determining quantum nonlocality according to claim 1 , wherein is a real number calculated based on the first input value, the second input value, the first output value, and the second output value.

4. The aforementioned [Equation 4] is calculated using the following formula: [Equation 5] [Equation 6] is a predefined value, [Equation 7] and inputting the coefficients for the first input value x and the second input value y. [Equation 8] The method for determining quantum nonlocality according to claim 3 , wherein:

5. The step of calculating the probability distribution includes: The first node calculates the probability distribution using the following formula: [Equation 9] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, β is the second output value, and c.c. is the complex conjugate of the previous term, [Equation 10] The method for determining quantum nonlocality according to claim 1 ,

6. before the step of performing the projection measurement, The method of claim 1 , further comprising the step of sharing an entangled state between the first node and the second node.

7. The quantum entangled state is [0011] The method for determining quantum nonlocality according to claim 6, wherein

8. further comprising calculating a maximum value associated with the quantum probability model using the following formula: [0012] where: [0013] is the Weyl-Heisenberg measurement, and in the definition of X, [0014] The method for determining quantum nonlocality according to claim 7, wherein

9. The first input value is [Equation 15] and the second input value is [0016] and the first output value is [Equation 17] and the second output value is [Equation 18] The method for determining quantum nonlocality according to claim 1 ,

10. The method of claim 1 , wherein the first number is eight.

11. 1. A method for determining quantum nonlocality performed by a computing system, comprising: a second node making second projection measurements corresponding to a second predetermined number; the second node calculating, based on the second projection measurement, a probability distribution of a first output value being obtained at the first node and a second output value being obtained at the second node when a first input value is selected at the first node and a second input value is selected at the second node; The second node determines that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

12. The method of claim 11 , wherein the second number is nine.

13. The reference value is [Equation 19] The method for determining quantum nonlocality according to claim 11, wherein

14. The step of calculating the probability distribution includes: the second node calculating the probability distribution using the following formula: [Equation 20] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, and β is the second output value, [0000] The method for determining quantum nonlocality according to claim 11 , wherein is a real number calculated based on the first input value, the second input value, the first output value, and the second output value.

15. The aforementioned [Equation 22] is calculated using the following formula: [Equation 23] [0000] is a predefined value from [Equation 25] and inputting the coefficients for the first input value x and the second input value y. [Equation 26] The method for determining quantum nonlocality according to claim 14, wherein:

16. The step of calculating the probability distribution includes: the second node calculating the probability distribution using the following formula: [0000] P is the probability distribution, x is the first input value, y is the second input value, α is the first output value, β is the second output value, and c.c. is the complex conjugate of the previous term; [0000] The method for determining quantum nonlocality according to claim 11, wherein

17. The first input value is [0000] and the second input value is [Equation 30] and the first output value is [Equation 31] and the second output value is [Equation 32] The method for determining quantum nonlocality according to claim 11, wherein

18. one or more processors; a memory for storing a computer program to be executed by the one or more processors; The computer program comprises: an operation of performing a projective measurement; calculating a probability distribution of a first output value obtained at the first node and a second output value obtained at the second node when a first input value is selected at a first node and a second input value is selected at a second node based on the projection measurement; A computing system comprising instructions for determining that quantum nonlocality exists if the calculated probability distribution exceeds a reference value.

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