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arXiv:2307.08333

Coherence and incoherence in quadrature basis

Laura Ares, Alfredo Luis

Published Jul 17, 2023• 0 citations
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Abstract

How to manage coherence as a continuous variable quantum resource is still an open question. We face this situation from the very definition of incoherent states in quadrature basis. We apply several measures of coherence for some physical states of light relative to a quadrature basis. We examine the action on the coherence of several transformations such as beam splittings and squeezing.

DOI
10.48550/arxiv.2307.08333

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How to manage coherence as a continuous variable quantum resource is still an open question. We face this situation from the very definition of incoherent states in quadrature basis. We apply several measures of coherence for some physical states of light relative to a quadrature basis. We examine the action on the coherence of several transformations such as beam splittings and squeezing.
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Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate definition of incoherent operations induced via coherence measures and quantify dynamical coherence based on this definition. Finally, we apply our proposed definition to quantify POVM-based dynamical coherence.
We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (``position'' and ``momentum'') measurements. A contradiction is shown possible for two quantum states: a pair-coherent state, and a superpositions of two coherent states, where the superposition state has been squeezed by the action of a two-mode squeezing operator. In one case a contradiction is still possible for states of increasing photon number, though the effect becomes smaller and more difficult to observe. The high efficiency of the homodyne method of measurement of quadrature phase amplitudes may open a way for a loophole-free test of local hidden variable theories, and the effect of detection loss on the contradiction with local hidden variables is calculated.
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