Quantum steering—a strong correlation to be verified even when one party or its measuring device is fully untrusted—not only provides a profound insight into quantum physics but also offers a crucial basis for practical applications. For continuous-variable (CV) systems, Gaussian states among others have been extensively studied, however, mostly confined to Gaussian measurements. While the fulfilment of Gaussian criterion is sufficient to detect CV steering, whether it is also necessary for Gaussian states is a question of fundamental importance in many contexts. This critically questions the validity of characterizations established only under Gaussian measurements like the quantification of steering and the monogamy relations. Here, we introduce a formalism based on local uncertainty relations of non-Gaussian measurements, which is shown to manifest quantum steering of some Gaussian states that Gaussian criterion fails to detect. To this aim, we look into Gaussian states of practical relevance, i.e. two-mode squeezed states under a lossy and an amplifying Gaussian channel. Our finding significantly modifies the characteristics of Gaussian-state steering so far established such as monogamy relations and one-way steering under Gaussian measurements, thus opening a new direction for critical studies beyond Gaussian regime.

We theoretically propose and experimentally demonstrate a nonclassicality test of single-mode field in phase space, which has an analogy with the nonlocality test proposed by Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.PACS numbers: 03.65. Ta, 42.50.Dv, 42.50.Ar Introduction-Nonclassicality of a quantum state is a topic of crucial importance that has attracted a lot of theoretical and experimental efforts for long. It provides not only a profound conceptual framework to distinguish quantum phenomena from classical ones, but also an essential practical basis for numerous applications, e.g. in quantum information processing. An important approach to studying quantum mechanics in comparison with classical mechanics is to adopt a phase-space description of a quantum state [1]. A wide variety of quantum systems of continuous variables (CVs) can be addressed in phase space, including quadrature amplitudes of light fields, collective spin states of atomic ensembles, and motional states of trapped ions, Bose-Einstein condensate, or mechanical oscillators, etc. [2]. Investigating quantum dynamics in phase space has yielded a great deal of intuition to quantum-to-classical transition [3]. It also offers a powerful tool to treat problems in quantum optics [4] and CV quantum informatics [5].A clear signature of nonclassicality is the negativity of phase-space distribution, which does not exist in classical probability distributions. However, its demonstration typically requires a full reconstruction of Wigner function [6] and it is of fundamental and practical significance to have a simpler set of measurements manifesting nonclassicality [7,8], desirably even when the Wigner function is non-negative. For instance, every Gaussian state possesses a positive-definite Wigner function, which restricts a possible set of nonclassicality tests. To manifest the Bell nonlocality, e.g., by employing homodyne detections, a Gaussian state must be transformed to a non-Gaussian state having a non-positive Wigner function to rule out hidden-variable models [9,10]. Banaszek and Wódkiewicz (BW) introduced a different seminal approach to manifesting CV ...

We examine nonclassical properties of the field states generated by applying the photon annihilation-then-creation operation (AC) and creation-thenannihilation operation (CA) to the thermal and coherent states. Effects of repeated applications of AC and of CA are also studied. We also discuss experimental schemes to realize AC and CA with a cavity system using atom-field interactions.

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurementaxis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine nonGaussianity under a CV measurement.N onclassicality is a fundamentally profound concept to identify quantum phenomena inaccessible from classical physics. It also provides a practically useful resource, for example, entanglement, making possible a lot of applications in quantum information processing beyond classical counterparts (1-3). A wide range of quantum systems, for example, field amplitudes of light, collective spins of atomic ensembles, motional modes of trapped ions, and Bose-Einstein condensate and mechanical oscillators, can be used for quantum information processing based on continuous variables (CVs) (2). It is of crucial importance to establish efficient and reliable criteria of nonclassicality for CV systems, desirably testable with fewer experimental resources, for example, fewer measurement settings (4-8) and with the capability of detecting a broad class of nonclassical states. In this paper, in view of the Glauber-Sudarshan P function (9, 10), those states that cannot be represented as a convex mixture of coherent states are referred to as nonclassical.A standard method to obtain information on a CV quantum state is to measure marginal distributions along many different axes in phase space constituting quantum-state tomography (11).This tomographic reconstruction may r...

We show that the coherent superposition tâ râ † of photon subtraction and addition applied to each local mode of a two-mode entangled state can enhance the nonlocality manifested by the violation of a Bell inequality. A twomode squeezed state is used as an input state for this demonstration with four different Bell inequalities employed: Bell inequalities adopting displaced parity operator, pseudospin operator, homodyne measurement, and conditional entropy, respectively. We find that the coherent operation significantly enhances the nonlocality remarkably in the weak squeezing limit, compared with other possible non-Gaussian operations. It can also give a maximal Bell violation with a very small squeezing for the inequalities with pseudospin operator and conditional entropy.