Single particle entanglement in the mid-and ultra-relativistic regime

Abstract

In this work we analyze the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin-$\frac{1}{2}$ 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 $\delta <\frac{\pi }{2}$) 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 ($\delta >\frac{\pi }{2}$) 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.

9 pages, 3 figures

References in corpus (9)

• Quantum Entanglement of Moving Bodies
• Relativistic-invariant quantum entanglement between the spins of moving bodies
• Helicity correlations of vector bosons
• Quantum Helicity Entropy of Moving Bodies
• Generation of maximally entangled states with sub-luminal Lorentz boost
• Entanglement properties of a two spin-one particle system under a Lorentz transformation
• Entanglement Entropy: Helicity versus Spin
• Heisenberg uncertainty relations for relativistic bosons
• Helicity Entanglement of Moving Bodies

Cited by in corpus (3)

• Bell-type inequalities for systems of relativistic vector bosons
• Is bound entanglement Lorentz invariant?
• Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory