Abstract In this paper, we investigate the nonclassicality and non-Gaussianity of a coherent superposed quantum state (CSQS) which is obtained by applying a coherent superposition of field annihilation (a) and creation ( a † ) operators, N ( t a + r a † ) to a classical coherent state | α ⟩ , where t and r are scalars with t 2 + r 2 = 1 . Such an operation, when applied on states having classical characters, introduces strong nonclassicality. We use different criteria to check the nonclassicality and non-Gaussianity of the considered quantum state. We first compute the Wigner function of CSQS. To study the nonclassicality of the considered state we further use (a) linear entropy (b) Wigner logarithmic negativity and (c) skew information based measure. Relative entropy based measure is considered to analyze the variation in non-Gaussianity of CSQS. Finally, the dynamics of the Wigner function evolving under the photon loss channel is addressed to probe the effect of noise on nonclassicality as well as non-Gaussianity of CSQS.
Abstract In this paper, we investigate the nonclassicality and non-Gaussianity of a coherent superposed quantum state (CSQS) which is obtained by applying a coherent superposition of field annihilation (a) and creation ( a † ) operators, N ( t a + r a † ) to a classical coherent state | α ⟩ , where t and r are scalars with t 2 + r 2 = 1 . Such an operation, when applied on states having classical characters, introduces strong nonclassicality. We use different criteria to check the nonclassicality and non-Gaussianity of the considered quantum state. We first compute the Wigner function of CSQS. To study the nonclassicality of the considered state we further use (a) linear entropy (b) Wigner logarithmic negativity and (c) skew information based measure. Relative entropy based measure is considered to analyze the variation in non-Gaussianity of CSQS. Finally, the dynamics of the Wigner function evolving under the photon loss channel is addressed to probe the effect of noise on nonclassicality as well as non-Gaussianity of CSQS.
In this paper, a quantitative investigation of the non-classical and quantum non-Gaussian characters of the photon-subtracted displaced Fock state [Formula: see text], where k is the number of photons subtracted and n is Fock parameter, is performed by using a collection of measures like Wigner logarithmic negativity, linear entropy potential, skew information-based measure, and relative entropy of quantum non-Gaussianity. It is noticed that the number of photons subtracted ( k) changes the nonclassicality and quantum non-Gaussianity in a significant amount in the regime of small values of the displacement parameter, whereas the Fock parameter ( n) presents a notable change in the large regime of the displacement parameter. In this respect, the role of the Fock parameter is found to be stronger as compared to the photon subtraction number. Finally, the Wigner function dynamics considering the effects of photon loss channel is used to show that the Wigner negativity can only be detected by highly efficient detectors.
A coherent state is defined conventionally in different ways such as a displaced vacuum state, an eigenket of an annihilation operator, or as an infinite dimensional Poissonian superposition of Fock states. In this work, we describe a superposition ( t a + r a † ) of field annihilation and creation operators acting on a continuous variable coherent state | α ⟩ and specify it by | ψ ⟩ . We analyze the lower- as well as higher-order nonclassical properties of | ψ ⟩ . The comparison is performed by using a set of nonclassicality witnesses (e.g., higher-order photon statistics, higher-order antibunching, higher-order sub-Poissonian statistics, higher-order squeezing, Agarwal–Tara parameter, Klyshko’s condition, and a relatively new concept, matrix of phase-space distribution). It is found that the higher-order criteria are much more efficient to detect the presence of nonclassicality as compared to lower-order conditions except squeezing, where the lower-order one is more competent than its higher-order counterpart.
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. The effect of non-Gaussianity inducing operators on the nonclassicality of quantum states has also been studied rigorously. 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 like entanglement potential, Wigner Yanese skew information, Wigner logarithmic negativity and relative entropy of non-Gaussianity. It is observed that photon addition (Fock parameter) significantly increases the amount of nonclassicalty and non-Gaussianity for small (large) values of the displacement parameter, which decreases both the quantum features monotonically. In this respect, the role of Fock parameter is found to be more prominent and stronger compared to photon addition. Finally, the dynamics of Wigner function under the effect of photon loss channel is used to show that only highly efficient detectors are able to detect Wigner negativity.
Abstract 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.
Glauber's coherent state is denoted by ∣α⟩ and its two-mode extension is represented by ∣α,β⟩. In this work, we introduce a two-mode superposition operator A=tab+ra†b†, whose action on the two-mode coherent state produces the two-mode coherent superposed quantum state ∣ψ⟩=(tab+ra†b†)∣α,β⟩. We investigate the nonclassicality and quantum non-Gaussianity of this state by means of the Wigner distribution and Wigner logarithmic negativity. Once its intrinsic nonclassical and non-Gaussian structure is established, the state is employed as the entangled resource in the Braunstein-Kimble continuous-variable (CV) teleportation protocol. We compute the ideal teleportation fidelity for coherent and squeezed inputs and analyze how the strengths of nonclassicality and non-Gaussianity influence the teleportation efficiency. Our results identify specific parameter regimes where enhanced non-Gaussian features or increased nonclassicality enable fidelities beyond the classical threshold, thereby revealing the operational significance of engineered two-mode quantum states in CV quantum information processing.
Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.