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 ...
Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α| ≫ d 2π , as a qudit -a d-level quantum system -in a state that is an even superposition of d pseudo-number states. A pair of such coherent-state qudits can be prepared in maximally entangled state by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.
We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.
We derive steerability criteria applicable for both finite and infinite dimensional quantum systems using covariance matrices of local observables. We show that these criteria are useful to detect a wide range of entangled states particularly in high dimensional systems and that the Gaussian steering criteria for general M × N -modes of continuous variables are obtained as a special case. Extending from the approach of entanglement detection via covariance matrices, our criteria are based on the local uncertainty principles incorporating the asymmetric nature of steering scenario. Specifically, we apply the formulation to the case of local orthogonal observables and obtain some useful criteria that can be straightforwardly computable, and testable in experiment, with no need for numerical optimization.In quantum world, there exist some strong correlations that cannot be described in classical ways providing thereby a crucial basis for applications, e.g. in quantum information processing. Among different forms of quantum correlations, the most well studied are quantum entanglement [1] and nonlocality [2]. Nonlocality is the strongest correlation that does not admit any local realistic models [3], in which the joint probability for the outcomes a and b of local measurements A and B, respectively, are explained bywhere a hidden-variable λ is chosen according to the distribution p λ . On the other hand, quantum entanglement is the correlation distinguished from classical correlation within the framework of quantum mechanics. That is, if a quantum state shows correlation that cannot be explained by the formwhere the superscript Q refers to the restriction to quantum statistics only, it is called quantum entangled.Recently, an intermediate form of correlation between quantum entanglement and nonlocality was rigorously defined in [4]-quantum steering-and it has attracted a great deal of interest during the past decade. The concept of quantum steering envisions a situation where Alice performs a local measurement on her system, which makes it possible to steer Bob's local state depending on her choice of measurement setting [5,6]. This notion is practically relevant when Bob wants to confirm quantum correlation although he cannot trust Alice or her devices at all [4], leading to some applications, e.g. one-sided device-independent cryptography [7] and subchannel discrimination [8]. In view of joint probability distribution, steering is the quantum correlation that can rule out the local hidden state (LHS) models,where Alice's statistics P λ (a|A) is unrestricted while Bob' statistics P Q λ (b|B) obeys quantum principles. P LHS is obviously a subset of P LHV as seen from its construction, which makes EPR steering more accessible in experiment than nonlocality [9]. There have been other remarkable works on quantum steering including its connection to measurement incompatibility [10] and the phenomenon of one-way steering [11,12], etc.. However, we need to have a more comprehensive set of steering criteria readily testable...
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