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Probing quantum coherence at a distance

Sebastian Horvat, Philippe Allard Guérin, Luca Apadula, Flavio Del Santo

Published Apr 27, 2020• 0 citations
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Abstract

In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam-splitter. However, it has been recently recognized that the phase can also be estimated via local measurements, by using an ancillary particle in a known superposition state. In this work, we further analyse these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an abelian gauge field. In that case, we show that the measurable quantities are spacetime loop integrals of the 4-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyse a recent proposal by Marletto and Vedral (arXiv:1906.03440).

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In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam-splitter. However, it has been recently recognized that the phase can also be estimated via local measurements, by using an ancillary particle in a known superposition state. In this work, we further analyse these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an abelian gauge field. In that case, we show that the measurable quantities are spacetime loop integrals of the 4-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyse a recent proposal by Marletto and Vedral (arXiv:1906.03440).
In a standard interferometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam splitter. However, it has been recognized that the phase can also be estimated via local measurements by using an ancillary particle in a known superposition state. In this work, we review and further explicate these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an Abelian gauge field. In that case, we show that the measurable quantities are space-time loop integrals of the four-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyze a recent proposal involving the time-dependent Aharonov-Bohm effect [C. Marletto and V. Vedral, Phys. Rev. Lett. 125, 040401 (2020)].
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.
Beam splitters are optical elements widely used in modern technological applications to split the initial light beam into a required number of beams and they play a very promising role for generating entangled optical states. Here, a potential scheme is proposed to generate Bell coherent-states superpositions through the action of a beam splitter when a Glauber coherent state is injected on one input mode and vacuum state is incident on the other one. Different quantifiers are used to measure the quantumness in the output state such as concurrence entanglement, entropic quantum discord, quantum coherence, geometric measure of quantum discord, local quantum uncertainty (LQU) and local quantum Fisher information. Thereby, we derive their analytical formulas and focus more on the behavior and bounds of each measure. Besides, we have introduced the notion of "weak measurement-induced LQU" captured by weak measurements as the generalization of normal LQU defined for standard projective measurement, and we investigate the effect of the measurement strength on the estimated phase enhancement if the generated Bell cat states are the probe states in quantum metrology. Our results suggest that the sensitivity of the interferometric phase estimation depends on how strongly one perturbs the probe state and that a weak measurement does not necessarily capture more quantumness in composite system.
The symmetrization postulate in quantum mechanics is formally reflected in the appearance of an exchange phase governing the symmetry of identical-particle global states under particle swapping. Many indirect measurements of this fundamental phase have been reported thus far, but a direct observation has been achieved only recently for photons. Here, we propose a general scheme capable of directly measuring the exchange phase of any type of particle (bosons, fermions, or anyons), exploiting the operational framework of spatially localized operations and classical communication. We experimentally implement it on an all-optical platform, providing a proof of principle for different simulated exchange phases. As a by-product, we supply a direct measurement of the real bosonic exchange phase of photons. Additionally, we analyze the performance of the proposed scheme when mixtures of particles of different nature are injected. Our results confirm the symmetrization tenet and provide a tool to explore it in various scenarios. Finally, we show that the proposed setup is suited to generating indistinguishability-driven NOON\mathrm{NOON}NOON states useful for quantum-enhanced phase estimation.
Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. ( Phys. Rev. Lett. 113 , 140401. (doi:10.1103/PhysRevLett.113.140401)), following Åberg ( http://arxiv.org/abs/quant-ph/0612146 ), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.
The problem of identifying the dynamic variable representing the phase difference between quantized electromagnetic fields is approached via the measurement process. By comparison with classical optics, certain operators corresponding to the measured sine and cosine of the phase difference are identified, but different measurement schemes lead naturally to different operators. First and second moments of the sine and cosine operators are calculated for a two-mode field in a coherent state. The theory is then tested in a photon counting experiment, for mean detected photon numbers varying from 30 to 10-2 which extends the range of previous measurements 300- fold. Good agreement is found between theory and experiment.