Recent work has argued that the concepts of entanglement and nonlocality must
be taken seriously even in systems consisting of only a single particle. These
treatments, however, are nonrelativistic and, if single particle entanglement
is fundamental, it should also persist in a relativistic description. Here we
consider a spin-1/2 particle in a superposition of two different velocities as
viewed by an observer in a different relativistically-boosted inertial frame.
We show that the entanglement survives right up to the speed of light and that
the boosted observer would see single-particle violations of Bell's inequality.
We also discuss how quantum gates could be implemented in this way and the
possible implications for quantum information processing.Comment: 4 page
Recent work [1] has studied entanglement between the spin and momentum components of a single spin-1/2 particle and showed that maximal entanglement is obtained only when boosts approach the speed of light. Here we extend the boost scenario to general geometries and show that, intriguingly, maximal entanglement can be achieved with boosts less than the speed of light. Boosts approaching the speed of light may even decrease entanglement. We also provide a geometric explanation for this behavior.Introduction.-Quantum entanglement is widely held to be the crucial feature that discriminates between quantum and classical physics; it is also at the heart of quantum information theory. While most of the theory of entanglement is non-relativistic, a complete account of entanglement requires that we understand its behavior in the relativistic regime.Studies in relativistic quantum information have found that single and two particle entanglement becomes an observer dependent phenomenon when viewed from different Lorentz boosted frames [2-10]. Recent work [1] has also investigated entanglement between the spin and momentum components of a single particle and showed that it reaches a maximum value only when boosts approach the speed of light. In this paper, however, we demonstrate that maximal entanglement can be obtained for realistic quantum states with boosts less than the speed of light. We furthermore show that this behavior can be given a natural geometric explanation.Properties of Wigner rotation.-We start by reviewing some of the properties of Wigner rotation that are key to our analysis. Wigner rotation arises from the fact that the subset of Lorentz boosts does not form a subgroup of the Lorentz group. Consider three inertial observers O, O and O where O has velocity v 1 relative to O and O has v 2 relative to O . Then the combination of two canonical boosts Λ(v 1 ) and Λ(v 2 ) that relates O to O is in general a boost and a rotation,
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