Localized qubits in curved spacetimes

Details Localized qubits in curved spacetimes Localized qubits in curved spacetimes

2011-08-19

arxiv.org/abs/1108.3896v1

Annals of Physics 327 (2012) pp. 1078-1131

Physics

Quantum Physics

50 pages, 8 figures

Scientific paper

10.1016/j.aop.2011.10.009

We provide a systematic and self-contained exposition of the subject of localized qubits in curved spacetimes. This research was motivated by a simple experimental question: if we move a spatially localized qubit, initially in a state |\psi 1>, along some spacetime path \Gamma\ from a spacetime point x1 to another point x2, what will the final quantum state |\psi 2> be at point x2? This paper addresses this question for two physical realizations of the qubit: spin of a massive fermion and polarization of a photon. Our starting point is the Dirac and Maxwell equations that describe one-particle states of massive fermions and photons. In the WKB limit we show how one can isolate an two-dimensional quantum state which evolves unitary along \Gamma. The quantum states for these two realizations are represented by a left-handed two-spinor in the case of massive fermions and a four component complex polarization vector in the case of photons. In addition to this we show how to obtain from this WKB approach a fully general-relativistic description of gravitationally induced phases. Our formalism reproduces the gravitational phase shift observed in the COW experiment and reduces to the standard formula for the phase shift in the non-relativistic weak field limit. We provide a concrete physical model for a Stern-Gerlach measurement of spin and obtain a unique spin operator which can be determined given the orientation and velocity of the Stern-Gerlach device and velocity of the massive fermion. Finally, we consider multipartite states and generalize the formalism to incorporate basic elements from quantum information theory such as quantum entanglement, quantum teleportation, and identical particles. The resulting formalism provide a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.

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