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arXiv:quant-ph/0308161

Nonclassical degree of states of single and bipartite systems

Ardiley Torres Avelar, B. Baseia, J. M. C. Malbouisson

Published Aug 28, 2003• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.quant-ph/0308161

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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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What is the most effective metric for quantifying the nonclassical characteristics of an individual quantum state? Our answer to this question is that it depends on what will be used for. Here we present some of the most widely used measures, as well as some promising ones. In this discussion, we analyze the question and ultimately determine that there is no singular superior metric. However, a mix of measures can provide a comprehensive understanding of the situation. Each measure has a potential application, some can be classified as a general nonclassicality measure, while others are dedicated measures. Some measures have a practical physical meaning, while others are justified by the results. We show that the negativity of the Wigner function, Mandel’s Q parameter and Hilbert–Schmidt distance are good dedicated measures, while Roughness is a general one, like Skewness in this case for pure states.
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 perspective, it is shown that in some contexts an arbitrary single-system nonclassical state can be converted into a bipartite entangled state, provided a generalized controlled-displacement (e.g., beam-splitter, CNOT gate) is available. Also, this entanglement can be detected in a simple way using the nonclassicality witness of the original single-system state. Finally, we extend the discussion to multipartite states, proposing alternative ways to generate and classify multipartite entanglement.
We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.
The state of a bipartite system may be changed by a cyclic operation applied on one of its subsystem. The change is a nonlocal effect, and can be detected only by measuring the two parts jointly. By employing the Hilbert-Schmidt metric, we can quantify such nonlocal effects via measuring the distance between initial and final state. By making use of the new nonlocal effect we can measure the entanglement of bipartite system. For qubit pair, we show that this measurement is equivalent to degree of entanglement and consists with the Bell inequality.