Complete complementarity relations and its Lorentz invariance

Marcos Basso, Jonas Maziero

Published 2020-07-28Version 1

It is well known that entanglement under Lorentz boosts is highly dependent on the boost scenario in question. For single particle states, a spin-momentum product state can be transformed into an entangled state. However, entanglement is just one of the aspects that completely characterizes a quantum system. The other two are known as the wave-particle duality. Although the entanglement entropy does not remain invariant under Lorentz boosts, and neither do the measures of predictability and coherence, we show here that these three measures taken together, in a complete complementarity relation (CCR), are Lorentz invariant. In addition, we explore relativist scenarios for single and two particle states, which helps understand the exchange of these different aspects of a quantum system under Lorentz boosts. For instance, by using discrete momentum states, we discuss the fact that for a spin-momentum product state to be transformed into an entangled state, it needs coherence between the momentum states. Otherwise, if the momentum state is completely predictable, the spin-momentum state remains separable, and the Lorentz boost will at most generate superposition between the spin states.