Relativistic quantum information and time machines

Abstract

Relativistic quantum information combines the informational approach to understanding and using quantum mechanical systems – quantum information – with the relativistic view of the Universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves – effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.

Keywords:

• quantum information
• relativity
• quantum communication
• space–time curvature
• closed timelike curves

Notes

1. Strictly, we must either give up locality or realism. By realism we mean the notion that particles have objective properties before measurement.

2. A bit-flip takes |0⟩→|1⟩ and |1⟩→|0⟩. A phase flip takes |0⟩→|0⟩ and |1⟩→ −|1⟩.

3. That is, propagating the state of Equation (14) forward in time by the interval t_p  − t_s gives us the state exp[i(t_s  − t_p )ω](μ|0⟩ + ν|1⟩) which is Alice's initial state. The (global) phase factor multiplying the entire state has no physical significance.

4. This choice is justified by considering the stability of the circuit to very small amounts of decoherence in the unitary U.