Quantifying the phase of quantum states

Sheng-Chuan Tang, Francesco Albarelli, Yue Zhang +2 more

Abstract The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we introduce a quantifier of complexity of continuous-variable states, e.g. quantum optical states, based on the Husimi quasiprobability distribution. This quantity is built upon two functions of the state: the Wehrl entropy, capturing the spread of the distribution, and the Fisher information with respect to location parameters, which captures the opposite behavior, i.e. localization in phase space. We analyze the basic properties of the quantifier and illustrate its features by evaluating complexity of Gaussian states and some relevant non-Gaussian states. We further generalize the quantifier in terms of s -ordered phase-space distributions and illustrate its implications.

L. Mandeļ

Petr Zapletal, Radim Filip

Single-photon states are basic resources for hybrid quantum technology with non-Gaussian states of light. Accelerating quantum technology is already able to produce high-quality single-photon states. These states can be used for hybrid quantum information processing, based on a nonclassical phase-space interference represented by negativity of a Wigner function. Therefore, new quantifiers, capable of evaluating such high-quality single-photon states, are required. We propose and analyze quantifiers which process multiple estimates of single-photon state's statistics. The quantifiers simulate basic capability of single photons to conditionally bunch into a single mode and form a Fock state. This state exhibits complex nonclassical phase-space interference effects making its Wigner function negative in multiple areas. The quantifiers directly evaluate a presence of the multiple negativities corresponding to the Fock state. We verify applicability of the quantifiers by using them to single-photon states from recent experiments. The quantifiers can be further extended to also test indistinguishability of single-photon states. It allows to verify quantum interference of light from single-photon emitters more sensitively than in the traditional Hong-Ou-Mandel test. Besides quantum optics, the multi-copy quantifiers can be also applied to experiments with atomic memories and mechanical oscillators.

Gary E. Bowman

Robert Lynch

Lina Yan, Jin-wei Hu, Guo-hui Yang +1 more

We propose a convenient and easily computable nonclassicality quantifier for bosonic field states based on the Wigner-Yanase skew information. The proposed nonclassicality quantifier is reflected by the quantum interaction between the maximum phase angle of the homodyne rotated quadrature operator and the bosonic field states. If the value of the nonclassical quantifier is greater than one-half, the state is nonclassical, and the quantifier is one-half for the pure classical. It is worth mentioning that an increase in the strength of nonclassicality inducing operations, such as squeezing and photon addition, leads to an enhancement of the nonclassicality in the quantum state. By computing some well-known nonclassical states and summarizing their existence features, we have confirmed the validity of our proposed nonclassicality quantifier. We have shown that in a range of values of the nonclassicality of the Gaussian state, revealing the sufficiency of the quantifier. We also compare it with two common nonclassical quantifiers to illustrate its advantages.