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In this paper, we address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator potentials share the equally spaced energy levels of the shifted harmonic oscillator but differ significantly in that they are nonharmonic. Consequently, their ground states and thermal equilibrium states are no longer Gaussian and exhibit nonclassical properties. We quantify their non-Gaussianity and evaluate their nonclassicality using various measures, including quadrature squeezing, photon number squeezing, Wigner function negativity, and quadrature coherence scale. Additionally, we employ quantum estimation theory to identify optimal measurement strategies and establish ultimate precision bounds for inferring the deformation parameter. Our findings prove that quantum systems isospectral to the harmonic oscillator may represent promising platforms for quantum information with continuous variables. In turn, non-Gaussian and nonclassical stationary states may be obtained and these features persist at nonzero temperature.

By using Wigner–Heisenberg algebra (WHA) and its Fock representation, even and odd Wigner negative binomial states (WNBSs) $|M,\xi ,\nu {〉}_{\pm }^W$ ($\nu =0$ corresponds to the ordinary even and odd negative binomial states (NBSs)) are introduced. These states can be reduced to the Wigner cat states in special limit. We establish the resolution of identity property for them through a positive definite measure on the unit disc. Some of their nonclassical properties, such as Mandel’s parameter and quadrature squeezing have been investigated numerically. We show that in contrast with the even NBSs, even WNBSs may exhibit sub-Poissonian statistics. Also squeezing in the field quadratures appears for both even and odd WNBSs. It is found that the deformation parameter $\nu$ plays an essential role in displaying highly nonclassical behaviors.

We have discussed the time evolution along with the nonclassicality phenomena of a system containing a vee-type three-level atom interacting with a bimodal electromagnetic field. A general expression for the atomic inversion is presented. It is found that the model undergoes Rabi oscillation. The total noise of the output state is measured.

In this paper, we investigate the possibility to use the Wigner function to detect and quantify quantum correlations in general. We study these quantum correlations for two quasi-Werner states formed with two general bipartite superposed squeezed states. We find then that the Wigner function is not sensitive to all kinds of quantum correlations but it only witnesses entanglement.

Nonclassicality is an interesting property of light having applications in many different contexts of quantum optics, quantum information and computation. Nonclassical states produce substantial amount of reduced noise in optical communications. Furthermore, they often behave as sources of entangled quantum states, which are the most elementary requirement for quantum teleportation. We study various nonclassical properties of coherent states and Schrödinger cat states in a setting of noncommutative space resulting from the generalized uncertainty relation, first, in a complete analytical fashion and, later, by computing their entanglement entropies, which in turn provide supporting arguments behind our analytical results. By using standard theoretical frameworks, they are shown to produce considerably improved squeezing and nonclassicality and, hence, significantly higher amount of entanglement in comparison to the usual quantum mechanical models. Both the nonclassicality and the entanglement can be enhanced further by increasing the noncommutativity of the underlying space. In addition, we find as a by-product some rare explicit minimum uncertainty quadrature and number squeezed states, i.e., ideal squeezed states.

We investigate nonclassical properties of a state generated by the interaction of a three-level atom with a quantized cavity field and an external classical driving field. In this study, the fields being degenerate in frequency are highly detuned from the atom. The atom interacts with the quantized field in a dispersive manner. The experimental setup involves a three-level atom passing through a cavity and interacting dispersively with the cavity field mode. Simultaneously, the atom interacts with an external classical field that is in resonance with the cavity field. The three-level atom can enter the cavity in one of the bare states $|e〉$, $|f〉$ or $|g〉$ or in a superposition of two of these states. In this paper, we consider superposition of $|e〉$ and $|f〉$. In our analysis, we focus on the statistical properties of the cavity field after interacting with the atom. The state vector $|\psi (t)〉$ describes the entire atom–field system but we analyze the properties of the cavity field independently neglecting the atomic component of the system. For this the atom part is traced out from $|\psi (t)〉$ to acquire the cavity field state only, denoted by $|{\psi }_f(t)〉$. We evaluate different nonclassical measures including photon number distribution, Mandel’s $Q_M$ parameter, squeezing properties $S_x$ and $S_p$, Wigner distribution, $Q_f$ function, second-order correlation function $g^2(0)$, etc. for the obtained cavity field state.

The Wigner functions of the Fock states and their superposition states have negative value clearly. We focus on discussing the time evolution of the Fock states and their superposition states by the Wigner function under the coherent drive (pumping laser) and dissipation channels (cavity radiation). The results show that the negative region of their Wigner function gradually diminishes as the time kt or the gain coefficient g increasing. In addition, the disappearing time is related to the value of g - k. The loss of non-classical features becomes slower when g increases with the k > g; there is the "frozen zone" when k = g; then the loss of non-classical features becomes faster when g increases with k < g.

An orthogonal state of coherent state is produced by applying an orthogonalizer related with Hermite-excited superposition operator $H_m(x{a}^{†}+ya)$. Using some technique, we cleverly deal with the normalization and discuss the nonclassical and non-Gaussian characters of the orthogonal state. The analytical expressions for the Wigner functions of the orthogonal state are derived in detail. Numerical results show that the orthogonal state will exhibit its richly nonclassical and non-Gaussian character by changing the interaction parameters.

I theoretically construct a kind of new angular momentum coherent states by virtue of the nonlinear Bose SU(2) generators, and investigate their nonclassicality by analyzing the sub-Poissonian distributions, photon number distributions, entanglement entropy and Wigner phase-space distributions. The results show that the new states always have the sub-Poissonian distributions for all of the photon number sum $n_a+n_b=q$ of two modes, the photon number distributions are subjected to the parameter q, and the entanglement always increases quickly and then decreases slowly with increasing $\varsigma$, and the new states for odd q possess more stronger nonclassicality than for even q.

Using the normally ordered form of thermal state characteristic of average photon number n_c, we introduce the photon-added thermal state (PATS) and investigate its statistical properties, such as Mandel's Q-parameter, photon number distribution (PND), and Wigner function (WF). We then study its decoherence in a thermal environment with average thermal photon number and dissipative coefficient κ by deriving analytical expressions of the WF. The nonclassicality is discussed in terms of the negativity of the WF. It is found that the WF is always positive when for any number PATS. The expression for time evolution of the PND and the tomogram of PATS are also derived analytically, which are related to hypergeometric function and single variable Hermite polynomials.

The quantum backflow effect is a counterintuitive behavior of the probability current of a free particle, which may be negative even for states with vanishing negative momentum component. Here, we address the notion of nonclassicality arising from the backflow effect, i.e. from the negativity of the probability current, and analyze its relationships with the notion of nonclassicality based on the negativity of the Wigner function. Our results show that backflow is linked to a different, and in fact more restrictive, notion of nonclassicality, the negativity of the Wigner function being only a necessary prerequisite for its occurrence. This hierarchical structure may be confirmed by looking at the addition of thermal noise, which more easily destroys the negativity of the probability current than the negativity of the Wigner function itself.

Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. Central to this capacity is their role as tomographically complete measurements with the fewest possible number of outcomes for a given finite dimension. Despite their advantages, little is known about them. We establish general properties of MICs, explore constructions of several classes of them, and make some developments to the theory of MIC Gram matrices. These Gram matrices turn out to be a rich subject of inquiry, relating linear algebra, number theory and probability. Among our results are some equivalent conditions for unbiased MICs, a characterization of rank-1 MICs through the Hadamard product, several ways in which immediate properties of MICs capture the abandonment of classical phase space intuitions, and a numerical study of MIC Gram matrix spectra. We also present, to our knowledge, the first example of an unbiased rank-1 MIC which is not group covariant. This work provides further context to the discovery that the symmetric informationally complete quantum measurements (SICs) are in many ways optimal among MICs. In a deep sense, the ideal measurements of quantum physics are not orthogonal bases.

Quantum non-Gaussian states are considered a useful resource for many tasks in quantum information processing, from quantum metrology and quantum sensing to quantum communication and quantum key distribution. Another useful tool that is gaining attention is the newly constructed quantum switch. Its applications in many tasks in quantum information have been proved to outperform many existing schemes in quantum communication and quantum thermometry. In this contribution, we demonstrate this to be very useful for engineering highly non-Gaussian states from Gaussian operations whose order is controlled by degrees of freedom of a control qubit. The nonconvexity of the set of Gaussian states and the set of Gaussian operations guarantees the emergence of non-Gaussianity after post-selection on the control qubit deterministically, in contrast to existing protocols in the literature. The nonclassicality of the resulting states is discussed accordingly.