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Using the thermal-entangled state representations, we obtain the analytical evolution of quantum states simultaneously undergoing two kinds of quantum noises that can be represented as the infinitive Kraus operator-sum representation. We also prove the normalization and trace preservation of Kraus operators. Besides, we obtain the evolutions of Wigner distribution and photon number distribution of any quantum state when simultaneously passing through two kinds of quantum noises.

Phase space analysis of quantum states is a newly developed topic in quantum optics. In this work we present Wigner phase space distributions for the two-mode binomial state produced by quantum entanglement between a vacuum state and a number state in a beamsplitter. By using two new binomial formulas involving two-variable Hermite polynomials and the so-called entangled Wigner operator, we find that the analytical Wigner function for the binomial state |ξ〉q ≡ D(ξ) |q, 0〉 is related to a Laguerre polynomial, i.e., $ W\left (\sigma _{,}\gamma \right ) =\frac {(-1)^{q}e^{-\left \vert \gamma \right \vert ^{2}-\left \vert \sigma \right \vert ^{2}}}{\pi ^{2}}L_{q}\left (\left \vert \frac {-\varsigma (\sigma -\gamma )+\sigma ^{\ast }+\gamma ^{\ast }} {\sqrt {1+|\varsigma |^{2}}}\right \vert ^{2}\right ) $ and its marginal distributions are proportional to the module-square of a single-variable Hermite polynomial. Also, the numerical results show that the larger number sum q of two modes lead to the stronger interference effect and the nonclassicality of the states |ξ〉q is stronger for odd q than for even q.

Three classes of quantum states are induced from coherent state (CS) based on three operations associated with the photon creation operator. One class is the famous photon-added coherent state (PACS) introduced by Agarwal and Tara (Phys. Rev. A 43, 492–497, 1991). The other two classes are the orthogonal states of the CS (Here we abbreviate them as OCS1 and OCS2). Indeed, the OCS1 is just the displacement Fock state, and the OCS2 is constructed by orthogonalizer proposed by Kim group (Phys. Rev. Lett. 116, 110501, 2016). In contrast to the original CS, the three induced states can exhibit their respective nonclassical properties. We study and compare some properties for these four quantum states (CS, PACS, OCS1, OCS2). The studied properties include the mean number of photons, the sub-Poissonian character, the squeezing effect in the field quadrature, and the quasi-probability distributions including the Husimi Q function and the Wigner function. Besides, their fidelities between each two of them are also discussed.

The nonclassical and non-Gaussian quantum states—photon-added two-mode squeezed coherent states have been theoretically introduced by adding multiple photons to each mode of the two-mode squeezed coherent states. Starting from the new expression of two-mode squeezing operator in entangled states representation, the normalization factor is obtained, which is directly related to bivariate Hermite polynomials. The sub-Poissonian photon statistics, cross-correlation between two modes, partial negative Wigner function are observed, which fully reflect the nonclassicality of the target states. The negative Wigner function often display non-Gaussian distribution meanwhile. The investigations may provide experimentalists with some better references in quantum engineering.

Exploiting the thermo entangled state approach, we successfully solve the master equation for describing the single-mode cavity driven by an oscillating external field in the heat reservoir and then get the analytical time-evolution rule for the density operator in the infinitive Kraus operator-sum representation. It is worth noting that the Kraus operator Ml, m is proved to be a trace-preserving quantum operation. As an application, the time-evolution for an initial coherent state ρ|β〉 = |β〉〈β| in such an environment is investigated, which shows that the initial coherent state decays to a new mixed state as a result of thermal noise, however the coherence can still be reserved for amplitude damping.

Different from the previous methods of obtaining optical tomography of quantum states, in this paper we use the Radon transform between the single- (two-)mode Wigner operator and the pure-state density operator |q〉 f,g f,g 〈q| (|η,τ 1,τ 2〉〈η,τ 1,τ 2|) to analytically obtain optical tomograms for single- (two-)mode squeezed chaotic fields, where the states |q〉 f,g (|η,τ 1,τ 2〉) refer to the newly introduced intermediate coordinate-momentum (entangled) states. More interestingly, we find that the tomograms of squeezed chaotic fields and those of coherent states are related by a integration. Thus, we establish a new convenient approach of obtaining tomograms for quantum states.

By virtue of the thermal entangled state representation, we analytically study time-dependent evolution of photon-number distribution and density operator of squeezed thermal state (STS) in the thermal environment. It is found that the initial density operator of STS still keeps squeezing and thermal within the thermal environment. At long times, such a state decays to thermal, a Gaussian classical state, as a result of decoherence. Moreover, the oscillations of photon-number distribution slowly disappear with increasing t, but the change of oscillations is completely different from that of STS in amplitude dissipative channel.

We analytically study the Wigner function (WF) for the two-variable Hermite polynomial state (TVHPS) and the effect of decoherence on the TVHPS in thermal environment. The nonclassicality of the TVHPS is investigated in terms of the partial negativity of the WF which depends on the polynomial orders m,n and the squeezing parameter r. We also investigate how the WF for the TVHPS evolves in the thermal environment. At long times, the TVHPS decays to thermal, a mixed Gaussian state, within the thermal environment.

Based on EPR’s idea of quantum entanglement, new parameterized coherent-entangled states |α,p〉 μ,ν are introduced in two-mode Fock space, which can be implemented by using a beam splitter. Possible superpositions of |α,p〉 μ,ν result in some new entangled states. The asymmetric ket-bra integration from |α,p〉 μ,ν leads to a new one- and two-mode combinatorial squeezing operator with stronger squeezing, which clearly shows the intrinsic relationship between squeezing mechanism and quantum entanglement.

Using the technique of integration within an ordered product (IWOP) of operators we derive a new kind of bipartite entangled state |β 1,β 2〉, which is perfectly different from the preceding entangled states in construction. We also present main properties, generation scheme of |β 1,β 2〉, superposition of |β 1,β 2〉, Wigner function and some applications of |β 1,β 2〉 in quantum optics.

A new kind of bipartite coherent-entangled state (CES) is introduced in the two-mode Fock space which exhibits the properties of both coherent state and entangled state. The set of CESs make up a complete and partly nonorthogonal representation. A simple experimental scheme to produce the CES is proposed by using a beam splitter. Some applications of the CES are also presented in quantum optics.

This paper examines the quantization for the capacitance coupling inductance-capacitance (LC) mesoscopic circuit. By virtue of the “invariant eigen-operator” (IEO) method, it deduces the selection rules of energy-level transition when the system is disturbed by the external electromagnetic field.

A new method of quantizing the mesoscopic RLC circuit is proposed, i.e., such a circuit can be equivalent to a changing mass simple harmonic oscillator. By virtue of the thermal entangled state representation and the generalized Hellmann-Feynman Theorem, the thermal effect for the system is investigated.

In this paper we obtain the Wigner functions of two-variable Hermite polynomial states (THPS) and their marginal distribution using the entangled state |ξ〉 representation. Also we obtain tomogram of THPS by virtue of the Radon transformation between the Wigner operator and the projection operator of another entangled state |η,τ1,τ2〉.

Using the entangled state representation of Wigner operator and some formulae related to the two-variable Hermite polynomials, the Wigner function of the squeezed pair coherent state (SPCS) and its two marginal distributions are derived. Based on the entangled Husimi operator introduced by Fan et al. (Phys. Lett. A 358:203, 2006) and the Weyl ordering invariance under similar transformations, we also obtain the Husimi function of the SPCS and its marginal distribution functions. The comparison between the two quasibability functions shows that, for the same amount of information included in two functions, the solving process of the Husimi function is simpler than that of the Wigner function.

The Hamilton operator for the mesoscopic LC circuits including complicated coupling is given. Because the practical circuits are inevitably influenced by the external environment, the effect of temperature on the quantum effects for the mesoscopic circuit must be taken into account. Then we discuss the thermal effect of the system by simulating it with the biphotonic process and the contribution of each process to the energy ensemble average by virtue of the generalized Hellmann-Feynman Theorem (GHFT).

Via the Hamilton dynamical approach we have constructed Hamiltonian for the mutual inductance coupling magnetic flux qubits. The entangled state representation is used to propose Cooper-pair number-phase quantization and the Hamiltonian operator for the whole system. The dynamical evolution of the phase difference operator and the Cooper-pairs number operator is investigated by virtue of Heisenberg equations.

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the even and odd negative binomial states (NBSs) are obtained. We concentrate our analysis on the fact that the even and odd NBSs interpolate between the even and odd coherent states and the even and odd quasi-thermal states depending on the values of the parameters involved. Moreover, the tomograms of the even and odd NBSs are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner functions of the Klauder-Perelomov coherent states (KP-CSs) for the pseudoharmonic oscillator (PHO) are obtained and the variations of the Wigner functions with the parameters k and z are discussed. Moreover, the tomograms of the KP-CSs for the PHO are calculated by virtue of intermediate coordinate-momentum representation in quantum optics.

The number-phase quantization scheme of the capacitance coupling double Josephson junction mesoscopic circuit is given. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can be prepared.

In this paper we shall introduce two q-analogues of the squeezed states in terms of the technique of integration within an ordered product of operators and the properties of the inverses of q-deformed annihilation and creation operators, and some nonclassical properties of the states are examined. Furthermore, we obtain some new completeness relations composed of the bra and ket which are not mutually Hermitian conjugate.

The quantization scheme of a single-qubit structure with Superconducting Quantum Interference Device (SQUID) is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. The eigenvalues and eigenstates of the system are discussed.