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arXiv:quant-ph/0608061 · Physical Review A

Lorentz transformations that entangle spins and entangle momenta

Thomas F. Jordan, Anil Shaji, E. C. G. Sudarshan

Published Feb 7, 2007• 58 citations
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Abstract

Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin $1∕2$. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz transformations of states for finite momenta, and describe entanglement of spins produced together with entanglement of momenta. From the entanglements considered, no sum of entanglements is found to be unchanged.

DOI
10.1103/physreva.75.022101

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In this work we study the entanglement properties under a Lorentz boost of a pair of spin- 1 massive particles, with spin and momentum as the sole degrees of freedom of the system. Different cases for entanglement between spins and momenta are considered as initial states and it is shown that entanglement between the different degrees of freedom is, in general, not invariant. We analyze the entanglement change in terms of the Wigner rotation induced by the transformation and show that, for the case of spin-1 particles, the relative entanglement change between different states depends strongly on the boost velocity.