Localized qubits in curved spacetimes

Abstract

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 x_1 to another point x_2, what will the final quantum state |\psi_2> be at point x_2? 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 respectively the one-particle states of localized massive fermions and photons. In the WKB limit we show how one can isolate a two-dimensional quantum state which evolves unitarily along \Gamma. The quantum states for these two realizations are represented by a left-handed 2-spinor in the case of massive fermions and a four-component complex polarization vector in the case of photons. In addition we show how to obtain from this WKB approach a fully general relativistic description of gravitationally induced phases. We use this formalism to describe the gravitational shift in the COW 1975 experiment. In the non-relativistic weak field limit our result reduces to the standard formula in the original paper. 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 provides a basis for exploring precision quantum measurements of the gravitational field using techniques from quantum information theory.Comment: 53 pages, 7 figures; v2: published version with further corrections. v3: some references and equation typesetting fixe

Entanglement, space-time and the Mayer-Vietoris theorem

“…It is well known that the applicability domain of the above mentioned constructions is limited by the quantum field theoretical structure of our underlying theory. This has already been noticed in [54]. Such a formalism implies the spatial localisation of qubits, a property that cannot be exactly defined in quantum field theory.…”

“…Similar methods have already been employed in [54] and [55] with the aim of generalising the discussions focused on quantum information theory to quantum field theory and high energy physics in curved spacetime. It is well known that the applicability domain of the above mentioned constructions is limited by the quantum field theoretical structure of our underlying theory.…”

Comment on “Relativistic effects on the spin entanglement of two massive Dirac particles”

“…Notice also that some recent papers present a different approach to the problem of a spin operator for a relativistic particle (Refs. [15][16][17]). …”

An Order-Theoretic Quantification of Contextuality

“…In the example given in Figure 1, the object is a localized qubit. However, as pointed out in [25,26], in a strict sense, the "location" of a qubit on a world line is fundamentally a part of its state, i.e., a localized qubit is really best understood as a sequence of quantum states associated with points on a world line. In other words, quantum states are constantly changing, since they are associated with objects that possess world lines.…”