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arXiv:1409.1814 · Physical Review A

Contrast in multipath interference and quantum coherence

Kai von Prillwitz, Łukasz Rudnicki, Florian Mintert

Published Nov 19, 2015• 27 citations
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Abstract

We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of interference patterns, properly defined statistical moments permit a reliable characterization of quantum coherence in terms of the number of coherently superposed state vectors.

DOI
10.1103/physreva.92.052114

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We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of interference patterns, properly defined statistical moments permit a reliable characterization of quantum coherence in terms of the number of coherently superposed state vectors.
We analyze the notion of quantum coherence in an interference experiment. We let the phase shifts fluctuate according to a given statistical distribution and introduce a decoherence parameter, defined in terms of a generalized visibility of the interference pattern. One might naively expect that a particle ensemble suffers a greater loss of quantum coherence by interacting with an increasingly randomized distribution of shifts. As we shall see, this is not always true. Decoherence is an interesting phenomenon and a topic that attracts widespread attention [1]. However, it is not easy to give a quantitative definition of decoherence [2]. All attempts at defining it always depend on the experimental configuration and on the authors ’ taste. An interesting related quantity is the
Quantum coherence, present whenever a quantum system exists in a superposition of multiple classically distinct states, marks one of the fundamental departures from classical physics.Quantum coherence has recently been investigated rigorously within a resource-theoretic formalism.However, the finer-grained notion of multilevel coherence, which explicitly takes into account the number of superposed classical states, has remained relatively unexplored.A comprehensive analysis of multilevel coherence, which acts as the singleparty analogue to multipartite entanglement, is essential for understanding natural quantum processes as well as for gauging the performance of quantum technologies.Here, we develop the theoretical and experimental groundwork for characterizing and quantifying multilevel coherence.We prove that nontrivial levels of purity are required for multilevel coherence, as there is a ball of states around the maximally mixed state that do not exhibit multilevel coherence in any basis.We provide a simple, necessary, and sufficient analytical criterion to verify the presence of multilevel coherence, which leads to a complete classification of multilevel coherence for three-level systems.We present the robustness of multilevel coherence, a bona fide quantifier, which we show to be numerically computable via semidefinite programming and experimentally accessible via multilevel coherence witnesses, which we introduce and characterize.We further verify and lower bound the robustness of multilevel coherence by performing a semi-device-independent phase discrimination task, which is implemented experimentally with four-level quantum probes in a photonic setup.Our results contribute to understanding the operational relevance of genuine multilevel coherence, also by demonstrating the key role it plays in enhanced phase discrimination-a primitive for quantum communication and metrology-and suggest new ways to reliably and effectively test the quantum behavior of physical systems.
We calculate the radiative characteristics of emission from a system of entangled atoms which can have a relative distance larger than the emission wavelength. We develop a quantum multipath interference approach which explains both super- and subradiance though the entangled states have zero dipole moment. We derive a formula for the radiated intensity in terms of different interfering pathways. We further show how the interferences lead to directional emission from atoms prepared in symmetric WWW states. As a byproduct of our work we show how Dicke's classic result can be understood in terms of interfering pathways. In contrast to the previous works on ensembles of atoms, we focus on finite numbers of atoms prepared in well characterized states.
Accurate characterization and validation is essential for the performance and security of quantum communication systems. For example, in quantum random number generators (QRNGs) based on vacuum state measurements [1], [2], rigorous system characterization minimizes parameter uncertainties that could degrade output quality by causing deviations from the stochastic model underlying random number generation. Similarly, continuous-variable quantum key distribution (CV-QKD) systems, particularly those using Gaussian-modulated coherent states, rely on precise detection efficiency characterization to maintain security. Inaccurate loss assessment can introduce exploitable vulnerabilities, leaving these systems open to eavesdropping. Despite advancements in quantum technologies, a lack of metrologically sound, traceable standards for key system parameters limits their reliability and commercialization.