Lorentz Invariance of Entanglement

2002 ◽  
Vol 2 (6) ◽  
pp. 487-512
Author(s):  
P.M. Alsing ◽  
G. Milburn
Keyword(s):  
Lorentz Invariance ◽  
Bell States ◽  
Explicit Calculation ◽  
Particle State ◽  
Lorentz Transformations ◽  
Wigner Rotation ◽  
Bipartite State ◽  
Relativistic Analog ◽  
Massive Spin ◽  
Inertial Frames

We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipartite state. The details of how these unitary transformations are manifested are explicitly worked out for the Bell states comprised of massive spin $1/2$ particles and massless photon polarizations. The relevance of this work to non-inertial frames is briefly discussed.

scholarly journals WIGNER ROTATIONS, BELL STATES, AND LORENTZ INVARIANCE OF ENTANGLEMENT AND VON NEUMANN ENTROPY

2004 ◽  
Vol 02 (02) ◽  
pp. 183-200 ◽  
Author(s):  
CHOPIN SOO ◽  
CYRUS C. Y. LIN
Keyword(s):  
Lorentz Invariance ◽  
Zeta Functions ◽  
Bell States ◽  
Von Neumann Entropy ◽  
Lorentz Transformations ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Einstein Podolsky Rosen ◽  
Definition Of ◽  
Reduced Density

We compute, for massive particles, the explicit Wigner rotations of one-particle states for arbitrary Lorentz transformations; and the explicit Hermitian generators of the infinite-dimensional unitary representation. For a pair of spin 1/2 particles, Einstein–Podolsky–Rosen–ell entangled states and their behaviour under the Lorentz group are analyzed in the context of quantum field theory. Group theoretical considerations suggest a convenient definition of the Bell states which is slightly different from the conventional assignment. The behaviour of Bell states under arbitrary Lorentz transformations can then be described succinctly. Reduced density matrices applicable to systems of identical particles are defined through Yang's prescription. The von Neumann entropy of each of the reduced density matrix is Lorentz invariant; and its relevance as a measure of entanglement is discussed, and illustrated with an explicit example. A regularization of the entropy in terms of generalized zeta functions is also suggested.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

scholarly journals SPIN–MOMENTUM CORRELATION IN RELATIVISTIC SINGLE-PARTICLE QUANTUM STATES

2010 ◽  
Vol 08 (03) ◽  
pp. 517-528 ◽  
Author(s):  
M. A. JAFARIZADEH ◽  
M. MAHDIAN
Keyword(s):  
Single Particle ◽  
Inertial Frame ◽  
Quantum States ◽  
Moving Frame ◽  
Lorentz Transformations ◽  
Mixed States ◽  
Wigner Rotation ◽  
Lorentz Boost ◽  
Momentum Correlation ◽  
Spin Momentum

This paper is concerned with the spin–momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin and momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not an observer-dependent quantity in the inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and have shown that entanglement decreases with respect to the increase in observer velocity. Finally, we argue that Wigner rotation is induced by Lorentz transformations and can be realized as a controlling operator.

Teleportation of an unknown bipartite state via non-maximally entangled two-particle state

2006 ◽  
Vol 15 (5) ◽  
pp. 915-918 ◽  
Author(s):  
Cao Hai-Jing ◽  
Guo Yan-Qing ◽  
Song He-Shan
Keyword(s):  
Particle State ◽  
Bipartite State

Lorentz Transformation as a Galilei Transformation with Physical Length and Time Contractions

1988 ◽  
Vol 43 (10) ◽  
pp. 859-864
Author(s):  
H. E. Wilhelm
Keyword(s):  
Rest Frame ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Analogous Structure ◽  
Galilean Relativity ◽  
Symmetry Properties ◽  
Inertial Frames ◽  
Ether Frame ◽  
Light Signals ◽  
Time Variables

Abstract The Lorentz transformations between the space-time coordinates of a point in two inertial frames with arbitrary relative velocity, are reformulated as Galilei transformations with length and time contractions, by introducing the ether rest frame (in which light signals propagate isotropically with the vacuum speed of light). The generalized Galilei transformations for the (longitudinal) space coordinates (x1,2) and the time variables (t1,2) of a point in two inertial frames ∑1,2 are not only of analogous structure, but have remarkable symmetry properties, too. The appearing length and time contractions are absolute effects in the sense of Lorentz-Fitzgerald, i.e., a rod has its largest length and a clock its fastest rate when at rest in the ether frame ∑0. Thus, an analytical reformulation and a physical interpretation of the Lorentz transformations within Galilean relativity physics is achieved.

Entanglement of Semi-Bell States in Non-Inertial Frames

2019 ◽  
Vol 58 (12) ◽  
pp. 4152-4169
Author(s):  
Leili Esmaeilifar ◽  
Zeynab Harsij ◽  
Behrouz Mirza
Keyword(s):  
Bell States ◽  
Inertial Frames

Thomas–Wigner rotation and Thomas precession in covariant ether theories: novel approach to experimental verification of special relativity

2015 ◽  
Vol 93 (5) ◽  
pp. 503-518 ◽  
Author(s):  
Alexander L. Kholmetskii ◽  
Tolga Yarman
Keyword(s):  
Inertial Frame ◽  
Empty Space ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Thomas Precession ◽  
Wigner Rotation ◽  
Novel Approach ◽  
Inertial Frames ◽  
Crucial Test ◽  
Ether Theories

We continue the analysis of Thomas–Wigner rotation (TWR) and Thomas precession (TP) initiated in (Kholmetskii and Yarman. Can. J. Phys. 92, 1232 (2014). doi:10.1139/cjp-2014-0015 ; Kholmetskii et al. Can. J. Phys. 92, 1380 (2014). doi:10.1139/cjp-2014-0140 ), where a number of points of serious inconsistency have been found in the relativistic explanation of these effects. These findings motivated us to address covariant ether theories (CET), as suggested by the first author (Kholmetskii. Phys. Scr. 67, 381 (2003)) and to show that both TWR and TP find a perfect explanation in CET. We briefly reproduce the main points of CET, which are constructed on the basis of general symmetries of empty space–time, general relativity principles, and classical causality, instead of Einstein’s postulates of the special theory of relativity (STR). We demonstrate that with respect to all known relativistic experiments performed to date in all areas of physics, both theories, STR and CET, yield identical results. We further show that the only effect that differentiates STR and CET is the measurement of time-dependent TWR of two inertial frames, K1 and K2, related by the rotation-free Lorentz transformation with a third inertial frame, K0, in the situation, where the relative velocity between K1 and K2 remains fixed. We discuss the results obtained and suggest a novel experiment, which can be classified as a new crucial test of STR.

scholarly journals ENTANGLEMENT ENTROPY: HELICITY VERSUS SPIN

2008 ◽  
Vol 06 (01) ◽  
pp. 181-186 ◽  
Author(s):  
SONG HE ◽  
SHUXIN SHAO ◽  
HONGBAO ZHANG
Keyword(s):  
Density Matrix ◽  
Entanglement Entropy ◽  
Specific Form ◽  
Von Neumann Entropy ◽  
Particle State ◽  
Inertial Reference Frame ◽  
Helicity State ◽  
Von Neumann ◽  
Left Handed ◽  
Massive Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish, and their Von Neumann entropy has no dependence on the specific form of momentum distribution, as long as it is isotropic.

scholarly journals Homogeneously Modified Special relativity (HMSR)

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Marco Danilo Claudio Torri ◽  
Vito Antonelli ◽  
Lino Miramonti
Keyword(s):  
Lorentz Invariance ◽  
Space Time ◽  
Lorentz Transformations ◽  
Interacting Particles ◽  
Standard Model Extension ◽  
Invariance Violation ◽  
Space Time Structure ◽  
Model Extension ◽  
Physical Effects ◽  
Invariance Preserving

Abstract This work explores a Standard Model extension possibility, that violates Lorentz invariance, preserving the space-time isotropy and homogeneity. In this sense HMSR represents an attempt to introduce an isotropic Lorentz Invariance Violation in the elementary particle SM. The theory is constructed starting from a modified kinematics, that takes into account supposed quantum effects due to interaction with the space-time background. The space-time structure itself is modified, resulting in a pseudo-Finsler manifold. The SM extension here provided is inspired by the effective fields theories, but it preserves covariance, with respect to newly introduced modified Lorentz transformations. Geometry perturbations are not considered as universal, but particle species dependent. Non universal character of the amended Lorentz transformations allows to obtain visible physical effects, detectable in experiments by comparing different perturbations related to different interacting particles species.

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