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Annalen der Physik

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

Priya Malpani, Kishore Thapliyal, J. Banerji, Anirban Pathak

Published Nov 20, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.1002/andp.202200261

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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.
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.
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.
ABSTRACT In this paper, we study new non‐Gaussian states known as superpositions of photon‐added and photon‐subtracted displaced Fock states (SPA‐PS‐DFSs). We express the SPA‐PS‐DFSs in terms of displaced Fock states (DFSs) and investigate their Wigner function and nonclassical properties. The obtained results of the Wigner function show that the superposition of photon addition and subtraction can enhance the non‐Gaussian and nonclassical properties of the SPA‐PS‐DFSs. Furthermore, the SPA‐PS‐DFSs exhibit nonclassical features, including higher‐order squeezing and higher‐order antibunching. Notably, these nonclassical characteristics are more enhanced than those of previous states generated solely by adding or subtracting photons to DFSs without superposition. These findings underscore the effectiveness of the superposition technique in enhancing the non‐Gaussian and nonclassical properties of the states.
Abstract Non-Gaussianity inducing operations are studied in the recent past from different perspectives. Here, we study the role of photon addition, a non-Gaussianity inducing operation, in the enhancement of nonclassicality in a finite dimensional quantum state, namely hypergeometric state with the help of some quantifiers and measures of nonclassicality. We observed that measures to characterize the quality of single photon source and anticlassicality lead to the similar conclusion, i.e. to obtain the desired quantum features one has to choose all the state parameters such that average photon numbers remains low. Wigner logarithmic negativity of the photon added hypergeometric state and concurrence of the two-mode entangled state generated at the output of a beamsplitter from this state show that nonclassicality can be enhanced by increasing the state parameter and photon number addition but decreasing the dimension of the state. In principle, decreasing the dimension of the state is analogous to holeburning and is thus expected to increase nonclassicality. Further, the variation of Wigner function not only qualitatively illustrates the same features as observed quantitatively through concurrence potential and Wigner logarithimic negativity, but illustrate non-Gaussianity of the quantum state as well.
ABSTRACT In this paper, we study the effects of additive Gaussian noise on Fock states. We put forth a simple analytical formula for the resulting output states. Additionally, we conduct numerical analysis into several key properties of noisy Fock states, including their purity, nonclassicality and non‐Gaussianness, with respect to the noise parameter. Finally, we examine the impact of noise on entangled N00N states, focusing on its entanglement‐breaking effects, which we quantify using the logarithmic negativity measure. Regarding purity, we observe that for a fixed noise level, the purity of a noisy Fock state decreases as the number of photons increases. In terms of non‐Gaussianity, we show that at any given noise level, higher Fock states exhibit higher non‐Gaussianity compared to lower ones. Although all noisy Fock states eventually lose their nonclassical characteristics under sufficient noise, higher Fock states exhibit more pronounced nonclassical features in low‐noise conditions, whereas lower Fock states show greater nonclassicality in high‐noise environments. We quantitatively show that the state is the most robust against additive Gaussian noise among the N00N states.
Abstract Nonclassical properties of photon added and subtracted displaced Fock states are studied using various witnesses of lower‐ and higher‐order nonclassicality. Compact analytic expressions are obtained for the nonclassicality witnesses. Using those expressions, it is established that these states and the states that can be obtained as their limiting cases (except coherent states) are highly nonclassical as they show the existence of lower‐ and higher‐order antibunching and sub‐Poissonian photon statistics, in addition to the nonclassical features revealed through the Mandel parameter, zeros of Q function, Klyshko's criterion, and Agarwal–Tara criterion. Further, some comparison between the nonclassicality of photon added and subtracted displaced Fock states have been performed using witnesses of nonclassicality. This has established that between the two types of non‐Gaussianity inducing operations (i.e., photon addition and subtraction) used here, photon addition influences the nonclassical properties more strongly. Further, optical designs for the generation of photon added and subtracted displaced Fock states from squeezed vacuum state have also been proposed.