Negativity Of Wigner Function Research Articles

Magnon statistical properties in multiphoton-catalyzed optomagnonics

Generating magnon states with the nonclassical behavior is a key step of implementing quantum magnonic technologies for applications. We proposed a strategy of magnonic state production by using the conditional measurement, derived from the jointed action of a cavity optomagnonics device and a beam splitter. At the case of the quantum catalysis applying to the optical field of optomagnonic system, the characters of yielding catalyzed state rely not only upon the parameters of optomechanic system but also upon the catalysis photon number and the beam splitter angle. We theoretically create a kind of the catalyzed photon–magnon entangled state and examine the statistical properties of the magnon mode of two mode optomagnonic states in the fields of the mean magnon number, the magnon number distribution, the Mandel Q parameter, the second-order autocorrelation function and the Wigner function. We demonstrate that the sub-Poisson distribution, the antibunching effect and the Wigner function negativity in the magnons can be realized via multiphoton catalysis. We also find that the magnon nonclassical statistical feature may be regulated by adjusting parameters of photon catalysis. Our work will provide a good reference for producing magnonic nonclassical state.

The failure of Wigner function negativity to detect quantum dissonance in an open bipartite system

We study the dynamics of Wigner function, quantum discord, entanglement and quantum dissonance for bipartite Bell-diagonal states independently interacting with dephasing reservoirs. We analyze comparatively their behavior under the decoherence effect. Our main goal is to test the ability of Wigner function negativity to measure all kinds of quantum correlations in such system. Particularly, we find that this negativity can only capture entanglement and discord. Of course it succeeded in predicting the behavior of quantum dissonance, but nevertheless, it failed to detect its presence. As a matter of fact, we conclude that Wigner function negativity cannot be used as measure of quantum dissonance in the two qubit open system.

Anomalous energy exchanges and Wigner-function negativities in a single-qubit gate

Anomalous weak values and the Wigner function's negativity are well-known witnesses of quantum contextuality. We show that these effects occur when analyzing the energetics of a single-qubit gate generated by a resonant coherent field traveling in a waveguide. The buildup of correlations between the qubit and the field is responsible for bounds on the gate fidelity, but also for a nontrivial energy balance recently observed in a superconducting setup. In the experimental scheme, the field is continuously monitored through heterodyne detection and then postselected over the outcomes of a final qubit's measurement. The postselected data can be interpreted as the field's weak values and can show anomalous values in the variation of the field's energy. We model the joint system dynamics with a collision model, gaining access to the qubit-field entangled state at any time. We find an analytical expression of the quasiprobability distribution of the postselected heterodyne signal, i.e., the conditional Husimi-Q function. The latter grants access to all the field's weak values: we use it to obtain that of the field's energy change and display its anomalous behavior. Finally, we derive the field's conditional Wigner function and show that anomalous weak values and Wigner function negativities arise for the same values of the gate's angle.

Nonlinear quantum behavior of ultrashort-pulse optical parametric oscillators

The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.

Hybrid communication assisted by coherent oscillator using resonant excitation of Nitrogen–vacancy center in diamond

We propose the multi-channel hybrid communication assisted by a coherent oscillator, by configuring the diamond Nitrogen–vacancy center using spontaneous parametric four-wave mixing. For one-channel hybrid communication, composite signal of fluorescence (information) and Stokes (carrier) is sent to the receiver; information is recovered by subtracting intensities of composite signal and reference coherent signal (from coherent oscillator) at demodulator. Further, we achieved two-channel and three-channel hybrid communication through two-mode and three-mode intensity–noise correlation, respectively. Two-mode correlation of hybrid signal (produced through photon subtraction) and anti-Stokes demonstrates the nonclassical behavior by violating Cauchy–Schwarz inequality, verified through corresponding squeezing (−5 dB). Such phenomenon of non-classical behavior was also verified by non-Gaussian negativity of Wigner function. Our hybrid communication model is based on temporal width- and coherence time-contrast, which can be controlled by wavelength (power) of input beams. The coherence time-contrast is about 90%.

Quantifying quantum coherence of optical cat states

The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l 1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.

Robustness of Wigner function negativity under the exciton-exciton interaction effects inside two coupled semiconductor quantum dots

We analyze theoretically the Wigner function negativity for thermal density matrix of analogous and equidistant two coupled semiconductor quantum dots at different temperatures. In this respect, we explore the quantum influences of the temperature, the external electric field, the Forster interaction and the exciton-exciton dipole interaction energy on its behavior. In particular, we show that the negativity of wigner function still survives for large values of temperature ensuring that the non-classicality of the two coupled semiconductor quantum dots system does not get lost under thermal effect. Moreover, we show that this negativity is hypersensitive to the external electric field effect, nevertheless, its sensitivity to this effect is extensively perturbed for higher values of Forster interaction, temperature and exciton-exciton dipole interaction energy. Further, we show that increasing this latter enhances the quantumness of system as the negativity of wigner function also increases.

Generating new nonclassical state by repeatedly operating number operator on coherent state

In this paper, using the principle of quantum state superposition, we report a nonclassical quantum state which is constructed by repeatedly operating the number operator on the coherent state. Nonclassical effects of this state are discussed by photon-number distribution, sub-Poissonian statistics, anti-bunching and negativity of Wigner function and squeezing effect. Our work provides an important nonclassical resource, which may be used in quantum communication and quantum optics.

Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors.

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.

Quantum phase diagrams of matter-field Hamiltonians II: Wigner function analysis

Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. We show that the surfaces of minimum fidelity or maximum Bures distance constitute a signature of quantum phase transitions. Additionally the behaviour of the Wigner function associated to the field modes carry the information of both, the entanglement properties between matter and field sectors, and the regions of the parameter space where the quantum phase transitions take place. A finer classification for the continuous phase transitions is obtained through the computation of the surface of maximum Bures distance.

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

AbstractThe 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.

Enhancing nonclassical and entanglement properties of trio coherent states by photon-addition

Trio coherent states as a kind of three-mode entangled state were introduced and studied. Some nonclassical characteristics of them such as higher-order antibunching, three-mode sum-squeezing and intermodal entanglement have been well revealed. In this paper, we further confirm their nonclassicality by examining negativity of Wigner function and non-Gaussian feature. However, our main purpose is to show that all the above-mentioned quantum properties of the trio coherent state can be enhanced by simultaneously adding photons to each mode of the state. In particular, we demonstrate that such so-called photon-added trio coherent states can possess three-mode sum-squeezing while the original trio coherent state (without photon-addition) cannot. In general, we show analytically and graphically how the degree of nonclassicality and/or entanglement depends on the number of added photons. Furthermore, we also consider a beamsplitter-based scheme for generation of the photon-added trio coherent states and evaluate the fidelity as well as the success probability as functions of the beamsplitter's parameter and the number of added photons.

Symmetric informationally complete measurements identify the irreducible difference between classical and quantum systems

We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule. Such representations are motivated by QBism, where the Born Rule is understood as a consistency condition between probabilities assigned to the outcomes of one experiment in terms of the probabilities assigned to the outcomes of other experiments. In this setting, the difference between quantum and classical physics is the way their physical assumptions augment bare probability theory: Classical physics corresponds to a trivial augmentation---one just applies the Law of Total Probability (LTP) between the scenarios---while quantum theory makes use of the Born Rule expressed in one or another of the forms of our general procedure. To mark the irreducible difference between quantum and classical, one should seek the representations that minimize the disparity between the expressions. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses---the first to do with unitarily invariant distance measures between the rules, and the second to do with available volume in a reference probability simplex (roughly speaking a new kind of uncertainty principle). Both of these arise from a significant majorization result. This work complements recent studies in quantum computation where the deviation of the Born Rule from the LTP is measured in terms of negativity of Wigner functions.

Construction of Laguerre polynomial’s photon-added squeezing vacuum state and its quantum properties**Project supported by the Natural Science Foundation of Fujian Province of China (Grant No. 2015J01020).

Laguerre polynomial’s photon-added squeezing vacuum state is constructed by operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state. By making use of the technique of integration within an ordered product of operators, we derive the normalization coefficient and the calculation expression of 〈ala†〉. Its statistical properties, such as squeezing, the anti-bunching effect, the sub-Poissonian distribution property, the negativity of Wigner function, etc., are investigated. The influences of the squeezing parameter on quantum properties are discussed. Numerical results show that, firstly, the squeezing effect of the 1-order Laguerre polynomial’s photon-added operator exciting squeezing vacuum state is strengthened, but its anti-bunching effect and sub-Poissonian statistical property are weakened with increasing squeezing parameter; secondly, its squeezing effect is similar to that of squeezing vacuum state, but its anti-bunching effect and sub-Poissonian distribution property are stronger than that of squeezing vacuum state. These results show that the operation of Laguerre polynomial’s photon-added operator on squeezing vacuum state can enhance its non-classical properties.

Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states

We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.

A class of nonlinear coherent states attached to Tsallis q-exponential

We construct a new class of nonlinear coherent states (NCS's) based on Tsallis q -exponential with $1 < q\leq 2$ . The special cases q = 2 and $ q\rightarrow 1$ recover the well-known harmonious states and canonical coherent states, respectively. Some non-classical properties are then studied. It has been found that this class of NCS's exhibits quadrature squeezing in the p component, amplitude squared squeezing in the Y component and negativity of Wigner function, however, it obeys a super-Poissonian statistics and exhibits a bunching behavior. In addition, we introduce nonlinear two-mode squeezed vacuum states (NTSVSs) attached to Tsallis q-exponential. These states are reduced to the well-known two-mode squeezed vacuum states (TSVSs) and pair coherent states (PCSs) when $ q\rightarrow 1$ and q = 2, respectively. Furthermore, the entanglement of the NTSVSs is examined by evaluating the linear entropy. Finally, we investigate the quantum teleportation of a coherent state using a NTSVS as a shared entangled resource instead of a TSVS. It is shown that the fidelity of teleportation depends on the nonlinearity function f(n) and recovers its standard expression in the linear limit $f(n)=1$ .

The negativity of partial transpose versus the negativity of Wigner function

We investigate the multipartite entanglement in the phase space using the negativity of Wigner function (NWF) and in the Hilbert space using the negativity of partial transpose (NPT). We analyze comparatively these quantities and the different types of entanglements that are present in two major classes — GHZ and [Formula: see text] — made of coherent states. We show that the negativity of Wigner function can be used as a good measure of genuine entanglement in multipartite systems. However, the negativity of partial transpose is a good quantifier for only the bipartite entanglement in tripartite systems.

Negativity of Wigner function and phase sensitivity of an SU(1,1) interferometer**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574092, 61775062, 61378012, 91121023, and 60978009), the National Basic Research Program of China (Grant No. 2013CB921804), and the Innovation Project of Graduate School of South China Normal University (Grant No. 2017LKXM088).

Both the negativity of Wigner function and the phase sensitivity of an SU(1,1) interferometer are investigated in this paper. In the case that the even coherent state and squeezed vacuum state are input into the interferometer, the Heisenberg limit can be approached with parity detection. At the same time, the negativity volume of Wigner function of detection mode comes entirely from the input state and varies periodically with the encoding phase. In addition, the negativity volume of Wigner function is positively correlated with the phase sensitivity of the SU(1,1) interferometer. The positive correlation may mean that the non-classicality indicated by negative Wigner function is a kind of resource that can verify some related research results of phase estimation.

A new nonclassicality measure for the quantum states of a bosonic field

We review a recently proposed measure of the nonclassicality of a bosonic field, based on the sensitivity of its quasi-probability distributions to ordering of the creation and annihilation operators. We illustrate the new measure by several concrete examples and show its advantages compared to other measures of nonclassicality such as the Wigner function negativity and the entanglement potential.

Markovian and Non-Markovian Dynamics of Non-classical Correlations and Wigner Function for GHZ-Type Coherent States

We process comparatively the time evolution of quantum discord, quantum entanglement and Wigner function for GHZ-type coherent states independently interacting with dephasing reservoirs and we address the influence of both Markovian and non-Markovian environments on their evolution. As a matter of fact, we show that in open multipartite systems negativity of Wigner function is sensitive not only to quantum entanglement but also to quantum discord. Indeed, we deem that the Wigner function can be used to capture and quantify general quantum correlations in open multipartite systems.