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Nonclassicality of noisy quantum states

А. А. Семенов, Dmytro Vasylyev, Bohdan I. Lev

Published Jan 1, 2005• 11 citations
OpenAlex

Abstract

Abstract. Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case affection of the thermal noise can be compensated via transformation of an observable, which tests the nonclassicality (witness function). Possibilities for experimental implementations based on unbalanced homodyning are discussed. At the same time we demonstrate that the scheme based on balanced homodyning cannot be improved for noisy states with proposed technique and should be applied directly. PACS numbers: 03.65.Yz, 42.50.-p Submitted to: J. Phys. B: At. Mol. Phys. Nonclassicality of noisy quantum states 2

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Nonclassicality of noisy quantum states

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Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case, affection of the thermal noise can be compensated via transformation of an observable, which tests the nonclassicality (witness function). Possibilities for experimental implementations based on unbalanced homodyning are discussed. At the same time, we demonstrate that the scheme based on balanced homodyning cannot be improved for noisy states with the proposed technique and should be applied directly.

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Abstract. Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case affection of the thermal noise can be compensated via transformation of an observable, which tests the nonclassicality (witness function). Possibilities for experimental implementations based on unbalanced homodyning are discussed. At the same time we demonstrate that the scheme based on balanced homodyning cannot be improved for noisy states with proposed technique and should be applied directly. PACS numbers: 03.65.Yz, 42.50.-p Submitted to: J. Phys. B: At. Mol. Phys. Nonclassicality of noisy quantum states 2
Nonclassicality conditions for an oscillator-like system interacting with a hot thermal bath are considered. Nonclassical properties of quantum states can be conserved up to a certain temperature threshold only. In this case, affection of the thermal noise can be compensated via transformation of an observable, which tests the nonclassicality (witness function). Possibilities for experimental implementations based on unbalanced homodyning are discussed. At the same time, we demonstrate that the scheme based on balanced homodyning cannot be improved for noisy states with the proposed technique and should be applied directly.
In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi Q functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.
Necessary and sufficient conditions are derived that allow one to completely characterize the nonclassicality of an arbitrary quantum state of a harmonic oscillator. Starting from a theorem by Bochner we derive an infinite hierarchy of conditions for the characteristic functions of the quantum state. Following the hierarchy step by step, the nonclassicality can be classified with respect to increasing orders. The full hierarchy of conditions is completely equivalent to the most commonly accepted criterion for nonclassicality: the failure of the Glauber–Sudarshan P -function to be a probability density. Our reformulated version of the criterion is directly related to measurable quantities that can be observed in phase-sensitive measurements such as homodyne detection. It directly generalizes a criterion for nonclassicality (Vogel 2000 Phys. Rev. Lett. 84 1849) that has already been applied in experiments (Lvovsky and Shapiro 2002 Phys. Rev. A 65 033830). Examples of phase-insensitive quantum states are considered that exhibit no first-order nonclassical effects, but that are nonclassical in second order.
Coupling an oscillator to a single two-level system is one of the most fundamental interactions in quantum physics. We report on a dynamical effect during which a thermal state of an oscillator is unconditionally transformed to a highly nonclassical state with negative Wigner function values by mere absorbtion by a single uncontrolled two-level system. This complements the traditional test of Rabi oscillations and it serves as a simply measurable witness that the process in question is highly nonclassical. The process is experimentally feasible with possible experimental implementation in a number of experimental platforms with intrinsic Jaynes-Cummings interaction and it has the potential of enabling deterministic generation of nonclassical quantum states.
Nonclassicality in bosonic systems can be certified directly from occupation probabilities without full state reconstruction. To complete a library of such criteria we introduce a numerical framework that constructs optimal linear nonclassicality witnesses from arbitrary subsets of measured occupation probabilities by solving a semi-infinite linear program. The method contains known analytical criteria as special cases while generally detecting substantially larger nonclassical regions. We provide an open-source implementation of the numerical optimization together with the analytical criteria discussed here, enabling direct application of the framework to measured occupation statistics across bosonic platforms. As a case study, we apply it to the resonant Jaynes--Cummings model with thermal states and reveal nonclassicality at short interaction times and close to thermal balance, where detection of nonclassicality is otherwise challenging.
A unified characterization of continuous-variable quantum states is presented that gives general insight in their nonclassical features and, in particular, in their entanglement properties. Nonclassicality is characterized in terms of observable characteristic functions. Equivalently, the nonclassicality conditions are reformulated in terms of moments. The latter approach turns out to be a powerful tool for deriving a complete set of entanglement conditions for bipartite quantum systems, which are fully equivalent to the nonpositivity of the partially transposed density operator. The possibilities of observing the needed moments by balanced homodyne correlation measurements are analyzed.