Direct Measurement of Open-Path Gravitational Phases by Single-Photon Quantum-State Tomography

m el-rakhawi

Operational Measurement of Open-Path Gravitational Phases via Local Homodyne Tomography in Large-Scale Fiber Interferometry

Kenneth C. Littrell, Brendan E. Allman, S. A. Werner

Shan Gao

The gravitational phase accumulated by a quantum particle along an open path depends directly on the gravitational potential---which in general relativity is represented by the metric field---rather than solely on spacetime curvature. Although such open-path phases are gauge dependent and therefore usually regarded as unobservable, we show that this conclusion is incorrect. First, we argue that existing quantum optical experiments based on local homodyne tomography already reconstruct the open-path relative phase of spatially separated single-photon modes. Since the two photon paths experience different gravitational potentials, these measurements already contain an unnoticed gravitational open-path contribution. Second, we propose a modification of the large-scale fiber interferometer of Hilweg et al. that directly isolates and reads out the gravitational open-path phase without recombining the optical paths. The predicted signal is of the same order as the gravitational phase considered by Hilweg et al. but is obtained through quantum-state tomography rather than closed-loop interference. These results establish a direct operational method for measuring the gravitational potential through open-path quantum phases, providing strong evidence that the gravitational potential is a directly measurable physical quantity.

Farid Ya Khalili

J. L. Montenegro Ferreira, Bertúlio de Lima Bernardo

Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.

Farit Ya. Khalili