Quantum entanglement under Lorentz boost

Abstract

In order to understand the characteristics of quantum entanglement of massive particles under Lorentz boost, we first introduce a relevant relativistic spin observable, and evaluate its expectation values for the Bell states under Lorentz boost. Then we show that maximal violation of the Bell's inequality can be achieved by properly adjusting the directions of the spin measurement even in a relativistically moving inertial frame. Based on this we infer that the entanglement information is preserved under Lorentz boost as a form of correlation information determined by the transformation characteristic of the Bell state in use.

Spin quantum correlations of relativistic particles

“…Recently questions regarding the behaviour of the entropy and entanglement of quantum systems in different reference frames gave rise to the field of relativistic quantum information [4][5][6]. Since then, many studies of relativistic effects on spin quantum correlations of massive particles have appeared in the literature [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20].In the seminal work of Peres, Scudo and Terno [5], they showed that the reduced density matrix for the spin of a relativistic particle, that should give "the statistical predictions for the results of measurements of spin components by an ideal apparatus which is not affected by the momentum of the particle" [5], is not covariant under Lorentz transformations. This occurs because under a Lorentz boost the particle spin undergoes a Wigner rotation [21,22], which correspond to a momentumdependent change of the particle spin state.…”

“…Recently questions regarding the behaviour of the entropy and entanglement of quantum systems in different reference frames gave rise to the field of relativistic quantum information [4][5][6]. Since then, many studies of relativistic effects on spin quantum correlations of massive particles have appeared in the literature [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Frame Independent Nonlocality for Three Qubit State

“…Their results strongly suggested that the entanglement is not preserved under the Lorentz boost. Lee et al [1] showed that maximal violation of the Bell's inequality can be achieved by properly adjusting the directions of the spin measurement even in a relativistically moving inertial frame. Kim et al [2] obtained an observer-independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.…”

Spin Fidelity for Three-Qubit Greenberger-Horne-Zeilinger and W States Under Lorentz Transformations

“…Fidelity for the spin part of a system of two spin- 1 2 particles described by a Gaussian momentum distributed wave packet is studied from the view point of moving observers and it is shown that the fidelity decreases by increasing the boost velocity [7]. Bell's inequality in moving frames has been considered in several papers [8][9][10][11][12][13]. The degree of violation of Bell's inequality will decrease with increasing the velocity of the observers if the directions of the measurements are fixed.…”