An entanglement detection method based on positive transformation and entanglement witness

Abstract

Quantum entanglement is one of the key problems in quantum information theory. Judging whether a given state is entangled or not and precisely delimiting the boundary between entanglement and separation become the primary problems in quantum information science. The entanglement criterion of two-body problem has been studied sufficiently. At present, the entanglement problem of multi-body quantifier still needs to be studied. Aiming at the problem of complete separability of 'X' type three qubit states, the present invention provides an entanglement detection method based on a positive transformation and an entanglement witness. Unlike the previous direct calculation methods for the density matrix of quantum states, At first, that density matrix of the 'X' type three quantum bit state is carry out 11 positive transformation to reduce eight antiangular elements with imaginary part to two, and then the analytical results of the entanglement and separability problems when phi = pi are given by the entanglement witness, and how to find phi when phi < pi, so that the value of phi satisfies the separability criterion of the invention.

Description

technical field [0001] The present invention proposes an entanglement detection method based on unitary transformation and entanglement witness, which performs unitary transformation on the density matrix of the "X" type three-qubit state, and uses the method of entanglement witness to construct a suitable measurement operator, which is accurate The part of quantum state entanglement is detected, and finally the analytical results of entanglement and separability when φ=π are obtained, and how to find φ when φ<π, so that the value of φ satisfies the separability criterion of the present invention. Background technique [0002] As an important physical resource, quantum entanglement plays an extremely important role in the field of quantum information processing. In quantum communication, quantum computing, and quantum teleportation [1], quantum entanglement is the key factor. Therefore, for quantum entanglement The research on entanglement, especially the detection of ent...

AI Technical Summary

Problems solved by technology

At present, the problem of many-body quantum entanglement remains to be studied. For a given quantum state, it is still difficult to accurately distinguish its completely separable and entangled parts. For any "X" type three-qubit state , so far it is not possible to obtain its completely separable or entangled parts directly through the density matrix

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