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Journal of Physics A Mathematical and General

A quasiprobability based criterion for classifying the states ofNspin-s as classical or non-classical

Ravinder Rupchand Puri

Published Sep 7, 1996• 6 citations
Publisher

Abstract

Based on the concept of joint quasiprobability of the eigenstates of non-commuting components of a spin, a criterion is proposed to characterize the states of a system of N spin- s as classical or non-classical. That criterion characterizes any state of a spin- and a factorizable state of N spin- s as classical. It correctly identifies any pure entangled state of two spin- s, an entangled eigenstate of any component of exchange symmetric spin system and squeezed spin states as non-classical.

DOI
10.1088/0305-4470/29/17/041

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Based on the concept of joint quasiprobability of the eigenstates of non-commuting components of a spin, a criterion is proposed to characterize the states of a system of N spin- s as classical or non-classical. That criterion characterizes any state of a spin- and a factorizable state of N spin- s as classical. It correctly identifies any pure entangled state of two spin- s, an entangled eigenstate of any component of exchange symmetric spin system and squeezed spin states as non-classical.
A sufficient condition for a quantum state of a system of spin-1/2 particles to admit a local hidden variable description, i.e., to be classical, is the separability of the density matrix characterizing its state, but not all classical states are separable. This leads one to infer that separability and classicality are two different concepts. These concepts are examined here in the framework of a criterion for identifying the classicality of a system of spin-1/2 particles based on the concept of joint quasiprobability (JQP) for the eigenvalues of spin components [Puri, J. Phys. A 29, 5719 (1996)]. The said criterion identifies a state as classical if a suitably defined JQP of the eigenvalues of spin components in three suitably chosen orthogonal directions is non-negative. In agreement with other approaches, the JQP-based criterion also leads to the result that all nonfactorizable pure states of two spin-1/2 particles are nonclassical. In this paper it is shown that the application of the said criterion to mixed states suggests that the states it identifies as classical are also separable and that there exist states which, identified as classical by other methods, may not be identified as classical by the criterion as it stands. However, results in agreement with the known ones are obtained if the criterion is modified to identify as classical also those states for which the JQP of the eigenvalues of the spin components in two of the three prescribed orthogonal directions is non-negative. The validity of the modified criterion is confirmed by comparing its predictions with those arrived at by other methods when applied to several mixed states of two spin-1/2 particles and the Werner-like state of three spin-1/2 particles [T\`oth and Ac\`{\i}n, Phys. Rev. A 74, 030306(R) (2006)]. The JQP-based approach, formulated as it is along the lines of the PPP-function approach for identifying classical states of the electromagnetic field, offers a unified approach for systems of an arbitrary number of spin-1/2 particles and the possibility of linking classicality with the nature of the measurement process.
We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a complete set of pure orthogonal product states. A constructive distinguishing procedure to obtain the concrete local measurements and classical communications is given. The non-commutativity of ensembles can be also used to characterize the quantumness for classical-quantum or quantum-classical correlated states.
PACS number: O3.65.Bz Abstract: Two or more quantum systems are said to be in an entangled or nonfactorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product states. It is only when the systems are in a factorisable state that they can be considered to be separated (in the sense of Bell). We show that whenever two quantum systems interact with each other, it is impossible that all factorisable states remain factorisable during the interaction unless the full Hamiltonian does not couple these systems so to say unless they do not really interact. We also present certain conditions under which particular factorisable states remain factorisable although they represent a bipartite system whose components mutually interact. We identify certain quasi-classical regimes that satisfy these conditions and show that they correspond to classical, pre-quantum, paradigms associated to the concept of particle
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a non-negative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement.
The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the latter decomposition property has been studied less frequently. In this contribution, we introduce a method for the generalized expansion of quantum states in terms of so-called quasistates. In contrast to the quasiprobability decomposition through nonclassical distributions and pure-state operators, our technique results in classical probabilities and nonpositive semidefinite operators, defining the notion of quasistates, that carry the information about the nonclassical characteristics of the system. Therefore, our method presents a complementary approach to prominent quasiprobability representations. We explore the usefulness of our technique with several examples, including applications for quantum state reconstruction and the representation of nonclassical light. In addition, using our framework, we also demonstrate that inseparable quantum correlations can be described in terms of classical joint probabilities and tensor-product quasistates for an unambiguous identification of quantum entanglement.
Abstract We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner–Yanase skew information. The variances in this uncertainty relation do not involve any classical mixing uncertainty, and is therefore purely of quantum mechanical nature. We show that a large class of mixed entangled states can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including two-qubit and two-qutrit Werner states and it turns out, for the states discussed in this paper, to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The relevant uncertainty relation reduces to the Schrodinger–Robertson inequality for pure states.