Computable measure of nonclassicality for light

We propose the entanglement potential (EP) as a measure of nonclassicality for quantum states of a single-mode electromagnetic field. It is the amount of two-mode entanglement that can be generated from the field using linear optics, auxiliary classical states, and ideal photodetectors. The EP detects nonclassicality, has a direct physical interpretation, and can be computed efficiently. These three properties together make it stand out from previously proposed nonclassicality measures. We derive closed expressions for the EP of important classes of states and analyze as an example of the degradation of nonclassicality in lossy channels.     

Entanglement of Photon-Subtracted Two-Mode Squeezed Thermal State and Its Decoherence in Thermal Environments

Using a non-Gaussian operation—photon subtraction from two-mode squeezed thermal state (PS-TMSTS), we construct a kind of entangled state. A Jacobi polynomial is found to be related to the normalization factor. The negativity of Wigner function (WF) is used to discuss its nonclassicality. The investigated entanglement properties turn out that the symmetrical PS-TMSTS may be more effective than the non-symmetric for quantum teleportation. Then the time evolution of WF is used to examine the decoherence effect, which indicates that the characteristic time of single PS-TMSTS depends not only on the average photon number of environment, but also on the average photon number of thermal state and the squeezing parameter.     

Single-mode quadrature-amplitude measurement for generalized two-mode squeezed states studied by virtue of the entangled state representation

The result of one-mode quadrature-amplitude measurement for some generalized two-mode squeezed states has been studied by virtue of the entangled state representation of the corresponding two-mode squeezing operators. We find that the remaining field-mode simultaneously collapses to the single-mode squeezed state with more stronger squeezing. The measurement result caused by a single-mode squeezed state projector is also calculated, which indicates quantum entanglement in squeezing.     

Continuous-Variable Entanglement and Wigner-Function Negativity via Adding or Subtracting Photons

The performance of adding or subtracting photons on two-mode squeezed thermal states via examining the Einstein–Podolsky–Rosen (EPR) correlation, the Hillery–Zubairy (HZ) correlation, the fidelity of teleportation, and the negativity of Wigner function is theoretically investigated. The normalization factors and the teleportation fidelity are related to Jacobi polynomials, and the (evolved) Wigner functions are simply associated with two-variable Hermite polynomials. Compared with the original squeezed thermal states, the EPR correlation and the teleportation fidelity can be enhanced by photon subtraction and basically weakened by photon addition symmetric operations, but they cannot be enhanced for both photon addition and subtraction asymmetric cases. Also, HZ correlation can provide a better option relative to the EPR correlation in detecting the entanglement, and the fidelity for teleporting a squeezed state with a large squeezing can also be enhanced via photon addition symmetric operations, in contrast to teleporting a coherent state. Additionally, the nonclassicality is discussed in terms of the negativity of the (evolved) Wigner functions, which shows that photon addition and subtraction and the squeezing cannot restrain the deteriorate of nonclassicality, and the evolved Wigner functions become Gaussian (corresponding to vacuum) with long decay times as a result of amplitude decay.     

Quantifying nonclassicality of one-mode Gaussian states of the radiation field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.     

Quantum teleportation of one－ and two－photon superposition states

Quantum teleportation of one- and two-photon superposition states based on EPR entanglement of continuous-wave two-mode squeezed state is discussed. The fidelities of teleportation axe deduced for two different input quantum states. The dependence of the fidelity on the parameters of EPR entanglement and the gain of the classical channels are shown numerically. Comparing with the teleportation of Fock state and coherent state, it is pointed out that for given EPR entanglement and classical gain, the higher the nonclassicality of the input state, the lower the accessible fidelity of teleportation.     

Preparation and control of entangled states in the two-mode coherent fields interacting with a moving atom via two-photon process

We investigate the preparation and the control of entangled states in a system with the two-mode coherent fields interacting with a moving two-level atom via the two-photon transition. We discuss entanglement properties between the two-mode coherent fields and a moving two-level atom by using the quantum reduced entropy, and those between the two-mode coherent fields by using the quantum relative entropy. In addition, we examine the influences of the atomic motion and field-mode structure parameter $p$ on the quantum entanglement of the system. Our results show that the period and the duration of the prepared maximal atom-field entangled states and the frequency of maximal two-mode field entangled states can be controlled, and that a sustained entangled state of the two-mode field, which is independent of atomic motion and the evolution time, can be obtained, by choosing appropriately the parameters of atomic motion, field-mode structure, initial state and interaction time of the system.     

Evolution of a two-mode squeezed vacuum for amplitude decay via continuous-variable entangled state approach

Extending the recent work completed by Fan et al. [Front. Phys. 9(1), 74 (2014)] to a two-mode case, we investigate how a two-mode squeezed vacuum evolves when it undergoes a two-mode amplitude dissipative channel, with the same decay rate κ, using the continuous-variable entangled state approach. Our analytical results show that the initial pure-squeezed vacuum state evolves into a definite mixed state with entanglement and squeezing, decaying over time as a result of amplitude decay. We also investigate the time evolutions of the photon number distribution, the Wigner function, and the optical tomogram in this channel. Our results indicate that the evolved photon number distribution is related to Jacobi polynomials, the Wigner function has a standard Gaussian distribution (corresponding to the vacuum) at long periods, losing its nonclassicality due to amplitude decay, and a larger squeezing leads to a longer decay time.     

Entanglement and nonclassicality evolution of the atom in a squeezed vacuum

As an important parameter, von Neumann entropy has been used to characterize the entanglement between atom and light field. We discussed the entanglement and nonclassicality evolution of an atom in a squeezed vacuum—a typical nonclassical field, and compare it with that of the coherent state. It shows that the atom-field entanglement in squeezed vacuum is much stronger and stabler than that in coherent state, whereas the nonclassicality of the light field depends on its initial status. This investigation is trying to find a new insight into the relation between entanglement of atom-field system and nonclassicality of light fields. The result shows that the entanglement between the atom and the field can be maintained well in the squeezed vacuum and this implies better control of atom and photon mutually.     

Entangled states in the two-mode coherent fields interacting with a two-level atom

We investigate the entanglement properties of the two-mode coherent fields interacting with a two-level atom via the two-photon transition. We discuss the quantum entanglement between the two-mode coherent fields and the two-level atom by using the quantum reduced entropy and that between the two-mode coherent fields by using the quantum relative entropy. We also examine the influences of the initial states of the atom and the two-mode coherent fields on the quantum entanglement of the system. Our results show that three types of entangled states can be prepared via the two-mode coherent fields interacting with a two-level atom and choosing appropriately the initial-state parameters of the system.     

Manipulating Nonclassicality via Quantum State Engineering Processes: Vacuum Filtration and Single Photon Addition

The effect of two quantum state engineering processes that can be used to burn a hole at vacuum in the photon number distribution of quantum states of radiation field is compared using various witnesses of lower- and higher-order nonclassicality as well as a measure of nonclassicality. Specifically, the modification in nonclassical properties due to vacuum state filtration and a single photon addition on an even coherent state, binomial state, and Kerr state are investigated using the criteria of lower- and higher-order antibunching, squeezing, and sub-Poissonian photon statistics. Further, the amount of nonclassicality present in these engineered quantum states having enormous applications in continuous variable quantum communication is quantified and analyzed by using an linear entropy-based entanglement potential. It is observed that all the quantum states studied here are highly nonclassical, and the hole-burning processes can introduce/enhance nonclassical features. However, it is not true in general. A hole at vacuum implies a maximally nonclassical state (as far as Lee's nonclassical depth is concerned), but a particular process of hole burning at vacuum does not ensure the existence of any particular nonclassical feature. Specifically, lower- and higher-order squeezing are not observed for photon-added and vacuum filtered even coherent states.     

Nonclassical state via superposition of two coherent states (π/2 out of phase) and related entangled states

Nonclassical features of the superposition of two coherent states which are π/2 out of phase are discussed, such as sub-Poissonian photon statistics and quadrature squeezing, as well as negativity of the Wigner function. Special nonclassicality is found in the special state where the relative phase of superposition has relationship with the average photon number. The analysis of the amount of entanglement is also presented for the related two-mode entangled coherent states.     

Gaussian transformations and distillation of entangled Gaussian states

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. More generally, we show that any hypothetical distillation protocol for Gaussian states involving only Gaussian operations would be a deterministic protocol. Finally, we argue that the protocol considered by Eisert et al. [preceding Letter, Phys. Rev. Lett. 89, 137903 ()]] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.     

Single-mode photon number measurement for the squeezed two-mode number state

Based on the fact that a two-mode squeezed number state is a two-variable Hermite polynomial excitation of the two-mode squeezed vacuum state, the result of one-mode l-photon measurement for the two-mode squeezed number state $S_2|m,n\rangle$ is discussed. It is found that a remaining field-mode simultaneously collapses into a number state $|n-m+l\rangle$ with the coefficient being a Jacobi polynomial of n, m and l, which manifestly exhibits the entanglement between the two modes, i.e. it depends on the number-difference between the two modes. The second mode collapses into an excited coherent state when the first mode is measured as a coherent state.     

High-fidelity teleportation beyond the no-cloning limit and entanglement swapping for continuous variables

We experimentally demonstrate continuous-variable quantum teleportation beyond the no-cloning limit. We teleport a coherent state and achieve the fidelity of 0.70 +/- 0.02 that surpasses the no-cloning limit of 2/3. Surpassing the limit is necessary to transfer the nonclassicality of an input quantum state. By using our high-fidelity teleporter, we demonstrate entanglement swapping, namely, teleportation of quantum entanglement, as an example of transfer of nonclassicality.     

Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement,polarization, and nonclassical properties

In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variabletype entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f-deformed creation operator A = f(n)aon the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the twomode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f-deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.     

Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately.Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion(which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than(but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.     

Optimal squeezing and entanglement from noisy Gaussian operations

We investigate the creation of squeezing via operations subject to noise and losses and ask for the optimal use of such devices when supplemented by noiseless passive operations. Both single and repeated uses of the device are optimized analytically and it is proven that in the latter case the squeezing converges exponentially fast to its asymptotic optimum, which we determine explicitly. For the case of multiple iterations we show that the optimum can be achieved with fixed intermediate passive operations. Finally, we relate the results to the generation of entanglement and derive the maximal two-mode entanglement achievable within the considered scenario.     

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.