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International Journal of Quantum Information

Helicity rotation induced by Lorentz boosts

Massimo Blasone A, Victor A. S. V. Bittencourt, Alex E. Bernardini

Published Dec 1, 2019• 2 citations
Publisher

Abstract

In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.

DOI
10.1142/s0219749919410053

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In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.
The effects of Lorentz boosts on the quantum entanglement encoded by a pair of massive spin-12\frac{1}{2}21​ particles are described according to the Lorentz covariant structure described by Dirac bispinors. The quantum system considered incorporates four degrees of freedom: two of them related to the bispinor intrinsic parity and the other two related to the bispinor spin projection, i.e., the Dirac particle helicity. Because of the natural multipartite structure involved, the Meyer-Wallach global measure of entanglement is preliminarily used for computing global quantum correlations, while the entanglement separately encoded by spin degrees of freedom is measured through the negativity of the reduced two-particle spin-spin state. A general framework to compute the changes on quantum entanglement induced by a boost is developed and then specialized to describe three particular antisymmetric two-particle states. According to the results obtained, two-particle spin-spin entanglement cannot be created by the action of a Lorentz boost in a spin-spin separable antisymmetric state. On the other hand, the maximal spin-spin entanglement encoded by antisymmetric superpositions is degraded by Lorentz boosts driven by high-speed frame transformations. Finally, the effects of boosts on chiral states are shown to exhibit interesting invariance properties, which can only be obtained through such a Lorentz covariant formulation of the problem.
In this work we analyse the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin- particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner rotation that correlates the spin and momentum degrees of freedom. We show that the natural basis to discuss the geometrical effects of the boost are the helicity eigenstates in the rest frame. In the mid-relativistic regime (where the Wigner rotation angle is limited by ) we prove for states with equal helicity that the entanglement with respect to the Wigner rotation angle is monotonically decreasing, however, in the ultra-relativistic regime ( ) the entanglement is increasing. If the states are prepared as a superposition of unequal helicity eigenstates, the monotonic behaviour is inverted. This implies that in the ultra-relativistic regime a geometrical setup can be found such that the amount of entanglement exhibits local maxima or minima. This shows a counter-intuitive behaviour of the relative amount of entanglement, an effect due to the internal and external geometrical configuration space, and points towards the difficulties in achieving a Lorentz invariant formulation of entanglement in general.
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.
In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity-spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking diffrences between the appropriate approach for this case and the one usually treated in the literature are discussed.
This paper was 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 eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial frame. Likewise, we have calculated the measure of entanglement (by using the concurrence) and has shown that entanglement decreases with respect to the increasing of observer velocity. Finally, we argue that, Wigner rotation is induced by Lorentz transformations can be realized as controlling operator.
In this paper we describe the transformation properties of quantum entanglement encoded in a pair of spin 1/2 particles described via Dirac bispinors. Due to the intrinsic parity- spin internal structure of the bispinors, the joint state is a four-qubit state exhibiting multipartite entanglement, and to compute global correlation properties we consider the averaged negativities over each possible bi-partition. We also consider specific bipartitions, such as the spin-spin and the particle-particle bipartitions. The particle-particle entanglement, between all degrees of freedom of one particle and all degrees of freedom of the other particle, is invariant under boosts if each particle has a definite momentum, although the spin-spin entanglement is degraded for high speed boosts. Correspondingly, the mean negativities are not invariant since the boost drives changes into correlations encoded in specific bipartitions. Finally, the results presented in the literature about spin-momentum entanglement are recovered by considering the projection of bispinorial states into positive intrinsic parity, and some striking differences between the appropriate approach for this case and the one usually treated in the literature are discussed.