Detecting nonclassicality of light via Lieb's concavity

Nonclassical light states are important for both conceptual and practical reasons: they are basic ingredients in testing and exploring quantum foundations, and are crucial resources in quantum technologies. Various useful criteria have been developed to detect nonclassicality in the literature, and several meaningful measures of nonclassicality have been introduced and measured experimentally. In this work, by use of a non-Hermitian generalization of the Wigner-Yanase-Dyson skew information and playing with operator ordering in evaluating average photon number, we develop a novel family of criteria for detecting nonclassicality of light based on Lieb's concavity, which is a deep and powerful result concerning interaction between quantum states and observables. We elucidate the information-theoretic as well as the physical meaning of the criteria, and illustrate their effectiveness in capturing and quantifying nonclassicality of various important light states.     

Manipulating Nonclassicality via Quantum State Engineering Processes: Vacuum Filtration and Single Photon Addition

The effect of two quantum state engineering processes that can be used to burn a hole at vacuum in the photon number distribution of quantum states of radiation field is compared using various witnesses of lower- and higher-order nonclassicality as well as a measure of nonclassicality. Specifically, the modification in nonclassical properties due to vacuum state filtration and a single photon addition on an even coherent state, binomial state, and Kerr state are investigated using the criteria of lower- and higher-order antibunching, squeezing, and sub-Poissonian photon statistics. Further, the amount of nonclassicality present in these engineered quantum states having enormous applications in continuous variable quantum communication is quantified and analyzed by using an linear entropy-based entanglement potential. It is observed that all the quantum states studied here are highly nonclassical, and the hole-burning processes can introduce/enhance nonclassical features. However, it is not true in general. A hole at vacuum implies a maximally nonclassical state (as far as Lee's nonclassical depth is concerned), but a particular process of hole burning at vacuum does not ensure the existence of any particular nonclassical feature. Specifically, lower- and higher-order squeezing are not observed for photon-added and vacuum filtered even coherent states.     

Decoherence in phase-preserving linear dissipative processes

Decoherence of nonclassicality and entanglement of bosonic states in phase-preserving linear dissipative processes is investigated by means of the time-convolutionless quantum master equation. It is shown that the sufficient condition for phase-preserving linear dissipative processes to completely destruct nonclassicality and entanglement is that the average value of the noise photon number per unit gain is no less than unity.     

Direct sampling of negative quasiprobabilities of a squeezed state

Although squeezed states are nonclassical states, so far, their nonclassicality could not be demonstrated by negative quasiprobabilities. In this work we derive pattern functions for the direct experimental determination of so-called nonclassicality quasiprobabilities. The negativities of these quantities turn out to be necessary and sufficient for the nonclassicality of an arbitrary quantum state and are therefore suitable for a direct and general test of nonclassicality. We apply the method to a squeezed vacuum state of light that was generated by parametric down-conversion in a second-order nonlinear crystal.     

Quantifying nonclassicality of one-mode Gaussian states of the radiation field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.     

Computable measure of nonclassicality for light

We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These three properties together make it stand out from previously proposed nonclassicality measures. We derive closed expressions for the EP of important classes of states and analyze as an example of the degradation of nonclassicality in lossy channels.     

Output nonlocality and nonclassicality in a two-mode entanglement laser

Output nonlocality and nonclassicality for the two modes are investigated in an entanglement laser sys-tem. Within the framework of a quantum theory of multiwave mixing,nonlocality and nonclassicality are discussed according to the violations of Bell inequality and Cauchy-Schwarz inequality. It is found that both nonlocality and nonclassicality can be fulfilled in the outside cavity fields under certain conditions. It is also shown that there are some nonclassical states that do not show nonlocality.     

Enhancement of Non-Gaussianity and Nonclassicality of Photon-Added Displaced Fock State: A Quantitative Approach

Non-Gaussian and nonclassical states and processes are already found to be important resources for performing various tasks related to quantum gravity and quantum information processing. Considering these facts, a quantitative analysis of the nonclassical and non-Gaussian features is performed here for photon added displaced Fock state, as a test case, using a set of measures, namely entanglement potential, Wigner–Yanese skew information, Wigner logarithmic negativity, and relative entropy of non-Gaussianity. It is observed that Fock parameter always increases the amount of nonclassicality and non-Gaussianity, while photon addition is effective only for small values of the displacement parameter. Further, the nonclassical and non-Gaussian effects decrease initially with an increase in the displacement parameter before increasing for the large displacement to saturate to the corresponding Fock state (equivalently displaced Fock state) value. Finally, dynamics of the Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.     

The effect of atomic spontaneous decay on the dynamics of the negativity of the Wigner function of radiation

The exact solution of the master equation for the case of a high-Q cavity with atomic decay is found. We use the negativity of the Wigner function (WF) as an indicator of nonclassicality. It is found that the negative values of the field WF are very sensitive to any change in the damping parameter. The atomic spontaneous decay leads to the simultaneous disappearance of both entanglement and nonclassicality of quantum states. Moreover, the purity of the field states is completely lost.     

Wigner distribution,nonclassicality and decoherence of generalized and reciprocal binomial states

There are quantum states of light that can be expressed as finite superpositions of Fock states (FSFS). We demonstrate the nonclassicality of an arbitrary FSFS by means of its phase space distributions such as the Wigner function and the Q-function. The decoherence of the FSFS is studied by considering the time evolution of its Wigner function in amplitude decay and phase damping channels. As examples, we determine the nonclassicality and decoherence of generalized and reciprocal binomial states.     

Long-time death of nonclassicality of a cavity field interacting with a charge qubit and its own reservoir

A measure of nonclassicality of quantum states based on the negative values of the Wigner function (WF) of a charge qubit-field system is proposed. It is found that, the negative values of the field WF are very sensitive to any change in dissipation parameter. The dissipation leads to a long-time death for both entanglement and nonclassicality, and also the coherence of the cavity state is lost completely.     

Discord and nonclassicality in probabilistic theories

Quantum discord quantifies nonclassical correlations in quantum states. We introduce discord for states in causal probabilistic theories, inspired by the original definition proposed by H. Ollivier and W.?H. Zurek [Phys. Rev. Lett. 88, 017901 (2001)]. We show that the only probabilistic theory in which all states have null discord is classical probability theory. Non-null discord is then not just a quantum feature, but a generic signature of nonclassicality.     

Maximizing the Hilbert space for a finite number of distinguishable quantum states

Given a particular quantum computing architecture, how might one optimize its resources to maximize its computing power? We consider quantum computers with a number of distinguishable quantum states, and entangled particles shared between those states. Hilbert-space dimensionality is linked to nonclassicality and, hence, quantum computing power. We find that qutrit-based quantum computers optimize the Hilbert-space dimensionality and so are expected to be more powerful than other qudit implementations. In going beyond qudits, we identify structures with much higher Hilbert-space dimensionalities.     

Characterizing quantum properties of a measurement apparatus: insights from the retrodictive approach

Using the retrodictive approach of quantum physics, we show that the state retrodicted from the response of a measurement apparatus is a convenient tool to fully characterize its quantum properties. We translate in terms of this state some interesting aspects of the quantum behavior of a detector, such as the nonclassicality or the non-gaussian character of its measurements. We also introduce estimators--the projectivity, the ideality, the fidelity, or the detectivity of measurements performed by the apparatus--which directly follow from the retrodictive approach. Beyond their fundamental significance for describing general quantum measurements, these properties are crucial in several protocols, in particular, in the conditional preparation of nonclassical states of light or in measurement-driven quantum information processing.     

Generalized coherent states for solvable quantum systems with degenerate discrete spectra and their nonclassical properties

In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are studied. Finally, using the Gazeau-Klauder coherent states approach, the time evolution of some of the nonclassical properties of the coherent states corresponding to the considered physical systems are discussed.     

Generalized Photon Added and Subtracted f-Deformed Displaced Fock States

In this paper, by making use of the nonlinear coherent states approach, the generalized photon added and subtracted f-deformed displaced Fock states are introduced. In other words, a natural link between photon added and subtracted displaced Fock states and nonlinear coherent states associated with nonlinear oscillator algebra is obtained. It is found that various kinds of nonclassical states can be generated by adopting appropriately controlling parameters in both linear and nonlinear regimes. Moreover, examining some of the most nonclassical properties such as Mandel's Q parameter, different types of squeezing, namely, quadrature, amplitude–squared and phase entropic squeezing, and Vogel's characteristic function, the nonclassicality features of the considered quantum states of interest are studied. Furthermore, to obtain the degree of quantum coherence, the relative entropy of coherence is investigated. Indeed, the nonclassicality aspects of the states obtained have been numerically studied to understand the roles of deformation functions, photons added and subtracted, and photon number occupied in the Fock state on physical properties. It is demonstrated that the depth and the domain of the nonclassicality features of the system can properly be controlled by selecting the suitable parameters.     

Fisher information,nonclassicality and quantum revivals

Wave packet revivals and fractional revivals are studied by means of a measure of nonclassicality based on the Fisher information. In particular, we show that the spreading and the regeneration of initially Gaussian wave packets in a quantum bouncer and in the infinite square-well correspond, respectively, to high and low nonclassicality values. This result is in accordance with the physical expectations that at a quantum revival wave packets almost recover their initial shape and the classical motion revives temporarily afterward.     

Decoherence and Fidelity in Teleportation of Coherent Photon-Added Two-Mode Squeezed Thermal States

We theoretically introduce a kind of non-Gaussian entangled resources, i.e., coherent photon-added two-mode squeezed thermal states (CPA-TMSTS), by successively performing coherent photon addition operation to the two-mode squeezed thermal states. The normalization factor related to bivariate Hermite polynomials is obtained. Based upon it, the nonclassicality and decoherence process are analyzed by virtue of the Wigner function. It is shown that the coherent photon addition operation is an effective way in generating partial negative values of Wigner function, which clearly manifests the nonclassicality and non-Gaussianity of the target states. Additionally, the fidelity in teleporting coherent states using CPA-TMSTS as entangled resource is quantified both analytically and numerically. It is found that the CPA-TMSTS is an entangled resource of high-efficiency and high-fidelity in quantum teleportation.     

Generalized squeezed states

Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is yet inadequate in the literature. In this article, we propose a method for the generalization of such states, which can be utilized to construct the squeezed states for any kind of quantum models. Our protocol works accurately for the case of the trigonometric Rosen–Morse potential, which we have considered as an example. Presumably, the scheme should also work for any other quantum mechanical model. In order to verify our results, we have studied the nonclassicality of the given system using several standard mechanisms. Among them, the Wigner function turns out to be the most challenging from the computational point of view. We, thus, also explore a generalization of the Wigner function and indicate how to compute it for a general system like the trigonometric Rosen–Morse potential with a reduced computation time.     

Nonclassicality and information exchange in deterministic entanglement formation

We discuss the role of nonclassicality of quantum states as a necessary resource in deterministic generation of multipartite entangled states. In particular for three bilinearly coupled modes of the electromagnetic field, tuning of the coupling constants between the parties allows the total system to evolve into both Bell and GHZ states only when one of the parties is initially prepared in a nonclassical state. A superposition resource is then converted into an entanglement resource.