A. T. Avelar, B. Baseia, J. M. C. Malbouisson
We consider experimental routes to determine the nonclassical degree of states of a field mode. We adopt a distance-type criterium based on the Hilbert-Schmidt metric to quantify the nonclassicality. The concept of nonclassical degree is extended for states of bipartite systems, allowing us to discuss a possible connection between nonclassicality and entanglement measures.
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Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, non-negative polynomials, the matrix approach, as well as the Cauchy-Schwarz inequality. Different approaches for deriving these inequalities are compared. Using the experimental photocount histogram generated by a weak noisy twin beam monitored by a photon-number-resolving iCCD camera the performance of the derived inequalities is compared. A basic set of ten inequalities suitable for monitoring the entanglement…
Simulating quantum nonlocality and steering requires augmenting pre-shared randomness with non-vanishing communication cost. This prompts the question of how one may provide such an operational characterization for the quantumness of correlations due even to unentangled states. Here we show that for a certain class of states, such quantumness can be pointed out by superlocality, the requirement for a larger dimension of the pre-shared randomness to simulate the correlations than that of the quantum state that generates them. This provides an approach to define the nonclassicality of local mult…
Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord implies the existence of nonclassical correlation. It is known that only the matrix transposition is nontrivial among Hermiticity-preserving (HP) linear EnCE maps when we use the changes in the eigenvalues of a density matrix due to a partial map for the purpose. In this paper, we prove that this is true even among not-necessarily HP (nnHP) linear EnCE maps. Th…
In quantum resource theory (QRT), asymmetry recognized as a valid resource for the advantage of various quantum information processing. In this paper, we establish the resource theory of asymmetry using quantum Fisher information (QFI). By defining the average Fisher information as a measure of asymmetry, it is shown that the discrepancy of bipartite global and local asymmetries naturally induces the nonclassical correlation between the subsystems. This measure satisfies all the necessary axioms of a faithful measure of bipartite quantum correlation. As an illustration, we have studied the pro…
A bipartite state is classical with respect to party $A$ if and only if party $A$ can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten $p$-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert-Schmidt norm, i.e. $p=2$, a closed formula is available for an arbitrary bipartite state.…
Several nonclassical effects displayed by wave packets subject to generic nonlinear Hamiltonians can be identified and assessed directly from tomograms without attempting to reconstruct the Wigner function or the density matrix explicitly. We have demonstrated this for both single-mode and bipartite systems. We have shown that a wide spectrum of effects such as the revival phenomena, quadrature squeezing and Hong-Mandel and Hillery type higher-order squeezing in both the single-mode system and the double-well Bose-Einstein condensate can be obtained from appropriate tomograms in a straightforw…
Recent progress in theories of quantum information has determined nonclassical correlation defined differently from widely-used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasib…
Singularity or negativity of Glauber P-function is a widespread notion of nonclassicality, with important implications in quantum optics and with the character of an irreducible resource. Here we explore how P-nonclassicality may be generated by conditional Gaussian measurements on bipartite Gaussian states. This nonclassical steering may occur in a weak form, which does not imply entanglement, and in a strong form that implies EPR-steerability and thus entanglement. We show that field quadratures are the best measurements to remotely generate nonclassicality, and exploit this result to derive…
We introduce an experimentally accessible method to measure a unique degree of nonclassicality, based on the quantum superposition principle, for arbitrary quantum states. We formulate witnesses and test a given state for any particular value of this measure. The construction of optimal tests is presented as well as the general numerical implementation. We apply this approach on examples such as squeezed states, and we show how to formulate conditions to certify a particular degree of nonclassicality for single- and multimode radiation fields.
In this paper, we use the characteristic function, i.e., the Fourier transform of the Glauber-Sudarshan phase-space distribution, to find the degree of nonclassicality of a given state. This degree of nonclassicality quantifies the nonclassicality in terms of quantum superpositions. We demonstrate two ways to determine or to estimate the degree of nonclassicality by studying the properties of the characteristic functions. The developed criteria are applied to two examples of squeezed states undergoing a classical mixing or a nonclassical superposition with vacuum.
Geometric discord, a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. Original version of this measure is suffered by the local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all criteria of a good measure of quantum correlation of the bipartite system and resolves local ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically the proposed quantity for both pure and mixed states. For an arbi…
A bipartite quantum system in a mixed state can exhibit nonclassical correlations, which can go beyond quantum entanglement. While quantum discord is the standard measure of quantifying such general quantum correlations, the nonclassicality can be determined by simpler means via the measurement of witness operators. We experimentally construct a positive map to witness nonclassicality of two qubits in an NMR system. The map can be decomposed so that a single run of an experiment on an ensemble of spins suffices to detect the nonclassicality in the state, if present. We let the state evolve in …
Several definitions of classicality are considered, such as P-representability, generalized coherent states and separable states. These notions are treated under a simple and general definition based on convex sets, which enables the use of the Hahn-Banach theorem to separate classical states from nonclassical ones. Nonclassicality linear witnesses are constructed, based on the observables available in a given physical situation. Some examples of nonclassical states are considered, with detection schemes available nowadays. Reviewing the concept of entanglement potential from a different persp…
We investigate the performance of a certain nonclassicality identifier, expressed via integrated second-order intensity moments of optical fields, in revealing bipartite entanglement of quantum-optical frequency combs (QOFCs), which are generated in both spontaneous and stimulated parametric down-conversion processes. We show that, by utilizing that nonclassicality identifier, one can well identify the entanglement of the QOFC directly from the experimentally measured intensity moments without invoking any state reconstruction techniques or homodyne detection. Moreover, we demonstrate that the…
We find a sufficient condition to imprint the single-mode bosonic phase-space nonclassicality onto a bipartite state as modal entanglement and vice versa using an arbitrary beam splitter. Surprisingly, the entanglement produced or detected in this way depends only on the nonclassicality of the marginal input or output states, regardless of their purity and separability. In this way, our result provides a sufficient condition for generating entangled states of arbitrary high temperature and arbitrary large number of particles. We also study the evolution of the entanglement within a lossy Mach-…
The degree of nonclassicality of states of a field mode is analysed considering both phase-space and distance-type measures of nonclassicality. By working out some general examples, it is shown explicitly that the phase-space measure is rather sensitive to superposition of states, with finite superpositions possessing maximum nonclassical depth (the highest degree of nonclassicality) irrespective to the nature of the component states. Mixed states are also discussed and examples with nonclassical depth varying between the minimum and the maximum allowed values are exhibited. For pure Gaussian …
We explore the dynamics of two atoms interacting with a cavity field via deformed operators. Properties of the asymptotic regularization of entanglement measures proving, for example, purity cost, regularized fidelity and accuracy of information transfer are analyzed. We show that the robustness of a bipartite system having a finite number of quantum states vanishes at finite photon numbers, for arbitrary interactions between its constituents and with cavity field. Finally it is shown that the stability of the purity and the fidelity is improved in the absence of the deformation parameters.
Classical-Nonclassical Polarity of Gaussian States
本文引入“经典-非经典极性”统一量化高斯态的非经典性，揭示其在多模系统中的守恒关系，为单模非经典性与纠缠的联系提供新视角。
We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations, and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also pr…
Nonlinear displaced Kerr state and its nonclassical properties
本文构造了非线性位移克尔态，研究其光子统计、压缩等非经典性质，并通过低克尔参数近似将其非经典性转化为双模纠缠。
We present the full experimental reconstruction of Gaussian entangled states generated by a type--II optical parametric oscillator (OPO) below threshold. Our scheme provides the entire covariance matrix using a single homodyne detector and allows for the complete characterization of bipartite Gaussian states, including the evaluation of purity, entanglement and nonclassical photon correlations, without a priori assumptions on the state under investigation. Our results show that single homodyne schemes are convenient and robust setups for the full characterization of OPO signals and represent a…
Nonclassical states of light induced via measurement in a bimodalsystem
本文研究双模耦合波导中通过条件投影测量从双模压缩态产生非经典光子态，利用Wigner负性和Mandel参数表征非经典性，并表明可通过调节相互作用强度与时间控制测量后态的非经典性质。
Experimental investigation of nonclassicality in the simplest scenario via the degrees of freedom of light
通过光的自由度在最简单场景中实验研究非经典性，验证经典光模拟与非经典性理论的一致性，为量子随机访问码等应用提供基础。
We evaluate a Gaussian distance-type degree of nonclassicality for a single-mode Gaussian state of the quantum radiation field by use of the recently discovered quantum Chernoff bound. The general properties of the quantum Chernoff overlap and its relation to the Uhlmann fidelity are interestingly illustrated by our approach.
The significance of photon addition in engineering the single- and two-mode (bipartite correlations) nonclassical properties of a quantum state is investigated. Specifically, we analyzed the behavior of the Wigner function of two quasi-Werner states theoretically constructed by superposing two normalized bipartite $m$-photon added coherent states. This allowed us to quantify the amount of nonclassicality present in the quantum states using Wigner logarithmic negativity (WLN), while quantum correlations are measured in terms of concurrence, entanglement of formation, and quantum discord. The WL…
Ergodiscord: An Operational and Distinct Notion of Quantumness of Correlations
本文提出操作性非经典性量化器 ergodiscord，用于刻画多体量子态中的关联量子性，并揭示非局域能量锁定及其超可加性现象，为量子储能装置设计提供新思路。
Quantum mechanics predicts that measurements of incompatible observables carry a minimum uncertainty which is independent of technical deficiencies of the measurement apparatus or incomplete knowledge of the state of the system. Nothing yet seems to prevent a single physical quantity, such as one spin component, from being measured with arbitrary precision. Here we show that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations. When revealed on local observables of a bipartite system, such uncertainty defines an entire class of bona fide meas…
This paper has been withdrawn.
A three level atom in $Λ$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a beam-splitter type of interaction, it provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well known measures of nonclassical correlations like the measurement induced disturbance, concurrence and negativity. The nonclassical features are found …
Quantum speedup from nonclassical polarization
提出框架识别极化系统中的非经典加速，通过对比角动量相干态经典极限与无限制量子速度极限，定量分析非经典性带来的加速，并在交叉Kerr相互作用中展示随光子数N的√N加速及奇偶效应。
We report the experimental realization and tomographic analysis of novel quantum light states obtained by exciting a classical thermal field by a single photon. Such states, although completely incoherent, possess a tunable degree of quantumness which is here exploited to put to a stringent experimental test some of the criteria proposed for the proof and the measurement of state non-classicality. The quantum character of the states is also given in quantum information terms by evaluating the amount of entanglement that they can produce.
A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulas describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon corr…
Nonclassicality in Two-Mode Stabilized Squeezed Coherent State: Quantum-to-Classical transition
本文提出一种新的非经典性度量$\Pi_{\rm N}$，用于分析双模稳定压缩相干态中的非经典性，揭示最优相位及两个新现象，并推动量子到经典转变的研究。
It has been recently shown (Bartlett et al. 2003) that information encoded into relative degrees of freedom enables communication without a common reference frame using entangled bipartite states. In this case the relative information stored in the two-qubit system is shared between the polarization degrees of freedom and the degree of entanglement. In the present article a specific state discrimination problem is envisioned where the degree of entanglement carries the only relative parameter, so that certain maximally entangled states are perfectly distinguishable, while discrimination of pro…
The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
We investigate the problem of finding the optimal convex decomposition of a bipartite quantum state into a separable part and a positive remainder, in which the weight of the separable part is maximal. This weight is naturally identified with the degree of separability of the state. In a recent work, the problem was solved for two-qubit states using semidefinite programming. In this paper, we describe a procedure to obtain the optimal decomposition of a bipartite state of any finite dimension via a sequence of semidefinite relaxations. The sequence of decompositions thus obtained is shown to c…
In this paper, we show that coherence witness for a single qubit itself yields conditions for nonlocality and entanglement inequalities for multiqubit systems. It also yields a condition for quantum discord in two--qubit systems. It is shown by employing homomorphism among the stabiliser group of a single qubit and those of multi--qubit states. Interestingly, globally commuting homomorphic images of single qubit stabilisers do not allow for consistent assignments of outcomes of local observables. As an application, we show that CHSH inequality can be straightforwardly generalised to nonlocalit…
Quantum discord (QD) reveals the nonclassical nature of correlations in bipartite quantum states, going beyond the entanglement-separability paradigm. In this article we discuss the suitability of QD in what concern its possible asymmetry with relation to the bipartition we choose to compute it. We obtain an analytical formula for a symmetrized version of QD (SQD) in Bell-diagonal states. We observe that if correlation is regarded as a shared property, then the SQD could be a convenient quantifier for asymmetric states.
We study an experimental scheme to generate Gaussian two-mode entangled states via beam splitter. Specifically, we consider a nonclassical Gaussian state (squeezed state) and a thermal state as two input modes, and evaluate the degree of entanglement at the output. Experimental conditions to generate entangled outputs are completely identified and the critical thermal noise to destroy entanglement is analytically obtained. By doing so, we discuss the possibility to link the resistance to noise in entanglement generation with the degree of single-mode nonclassicality.
The interaction between a $\diamondsuit$-type four-level atom and a single-mode field in the presence of Kerr medium with intensity-dependent coupling involving multi-photon processes has been studied. Using the generalized (nonlinear) Jaynes-Cummings model, the exact analytical solution of the wave function for the considered system under particular condition, has been obtained when the atom is initially excited to the topmost level and the field is in a coherent state. Some physical properties of the atom-field entangled state such as linear entropy showing the entanglement degree, Mandel pa…
We consider an experimentally realizable scheme for manipulating quantum states using a general superposition of products of field annihilation ($\hat{a}$) and creation ($\hat{a}^†$) operators of the type ($s \hat{a}\hat{a}^†+ t \hat{a}^†\hat{a}$), with $s^2 + t^2 = 1$. Such an operation, when applied on states with classical features, is shown to introduce strong nonclassicality. We quantify the generated degree of nonclassicality by the negative volume of Wigner distribution in the phase space and investigate two other observable nonclassical features, sub-Poissonian statistics and squeezing…
Harmonic oscillator coherent states are well known to be the analogue of classical states. On the other hand, nonlinear and generalised coherent states may possess nonclassical properties. In this article, we study the nonclassical behaviour of nonlinear coherent states for generalised classes of models corresponding to the generalised ladder operators. A comparative analysis among them indicates that the models with quadratic spectrum are more nonclassical than the others. Our central result is further underpinned by the comparison of the degree of nonclassicality of squeezed states of the co…
We study the open system dynamics of a circuit QED model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system.…
Proposal for Observing Nonclassicality in Highly Excited Mechanical Oscillators by Single Photon Detection
本文提出一种腔光力学态制备协议，通过相干态制备与单拉曼散射光子投影测量，使任意大相干振幅的机械振子进入非经典态，并借助拉曼边带光子统计观测其亚泊松声子分布。
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