Quantifying nonclassicality of multimode bosonic fields via skew information

We quantify the nonclassicality of multimode bosonic field states by adopting an information-theoretic approach involving the Wigner-Yanase skew information. The fundamental properties of the quantifier such as convexity, superadditivity, monotonicity, and conservation relations are revealed. The quantifier is illustrated by a variety of typical examples, and applications to the quantification of nonclassical correlations are discussed. Various extensions are indicated.     

Generalized structure of higher order nonclassicality

A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering theorem introduced by us in [A. Pathak, J. Phys. A 33 (2000) 5607]. It is also generalized for multi-photon Bose operators of Brandt and Greenberg. Similarly, condition for higher order subpoissonian photon statistics is derived by normal ordering of higher powers of number operator. Further, with the help of simple density matrices, it is shown that the higher order antibunching (HOA) and higher order subpoissonian photon statistics (HOSPS) are not the manifestation of the same phenomenon and consequently it is incorrect to use the condition of HOA as a test of HOSPS. It is also shown that the HOA and HOSPS may exist even in absence of the corresponding lower order phenomenon. Binomial state, nonlinear first order excited squeezed state (NLESS) and nonlinear vacuum squeezed state (NLVSS) are used as examples of quantum state and it is shown that these states may show higher order nonclassical characteristics. It is observed that the Binomial state which is always antibunched, is not always higher order squeezed and NLVSS which shows higher order squeezing does not show HOSPS and HOA. The opposite is observed in NLESS and consequently it is established that the HOSPS and HOS are two independent signatures of higher order nonclassicality.     

Quantum Phase Properties of Photon Added and Subtracted Displaced Fock States

Quantum phase properties of photon added and subtracted displaced Fock states (and their limiting cases) are investigated from a number of perspectives, and it is shown that the quantum phase properties are dependent on the quantum state engineering operations performed. Specifically, the analytic expressions for quantum phase distributions and angular Q distribution as well as measures of quantum phase fluctuation and phase dispersion are obtained. The uniform phase distribution of the initial Fock states is observed to be transformed by the unitary operation (i.e., displacement operator) into non‐Gaussian shape, except for the initial vacuum state. It is observed that the phase distribution is symmetric with respect to the phase of the displacement parameter and becomes progressively narrower as its amplitude increases. The non‐unitary (photon addition/subtraction) operations make it even narrower in contrast to the Fock parameter, which leads to broadness. The photon subtraction is observed to be a more powerful quantum state engineering tool in comparison to the photon addition. Further, one of the quantum phase fluctuation parameters is found to reveal the existence of antibunching in both the engineered quantum states under consideration. Finally, the relevance of the engineered quantum states in the quantum phase estimation is also discussed.     

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states:Non-classical and non-Gaussian properties

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation(AC) and creation-then-annihilation operation(CA) to the thermal state(TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number,Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.     

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.     

Entangling two single-mode Gaussian states by use of a beam splitter

Considering two light beams which are in general single-mode Gaussian states and incident on input ports of an ideal beam splitter, respectively, this paper investigates how separability and entanglement of the output lights depend on degrees of nonclassicality and purities of the input states. The minimum and maximum amounts of attainable entanglement in the output state are found.     

Nonclassicality of a two-variable Hermite polynomial state

The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied.     

Multiple-Photon-Added and -Subtracted Two-Mode Binomial States:Nonclassicality and Entanglement *

We theoretically analyze the nonclassicality and entanglement of two new non-Gaussian entangled states generated by applying multiple-photon addition and subtraction to a two-mode binomial state. The nonclassical properties are investigated in terms of the partial negativity of the Wigner functions, whose results show that their nonclassicality can be enhanced via one-mode even-number photon operations and two-mode symmetrical operations for the initial two-mode binomial state. We also find that there exists some enhancement in the entanglement properties in certain parameter ranges via one-mode photon-addition and two-mode symmetrical operations.