94 research outputs found

    Weak Values Influenced by Environment

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    Optimal parameter estimation of a depolarizing channel

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    We investigate strategies for estimating a depolarizing channel for a finite dimensional system. Our analysis addresses the double optimization problem of selecting the best input probe state and the measurement strategy that minimizes the Bayes cost of a quadratic function. In the qubit case, we derive the Bayes optimal strategy for any finite number of input probe particles when bipartite entanglement can be formed in the probe particles

    Another convex combination of product states for the separable Werner state

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    In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained by Wootters' method. The Werner state in a two-qubit system has a single real parameter and varies from inseparable state to separable state according to the value of its parameter. We derive a hidden variable model that is induced by our decomposed form for the separable Werner state. From our explicit form of the convex combination of product states, we understand the following: The critical point of the parameter for separability of the Werner state comes from positivity of local density operators of the qubits.Comment: 7 pages, Latex2e; v2: 9 pages, title changed, an appendix and a reference added, minor correction

    Violations of the Leggett-Garg inequality for coherent and cat states

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    We show that in some cases the coherent state can have a larger violation of the Leggett-Garg inequality (LGI) than the cat state by numerical calculations. To achieve this result, we consider the LGI of the cavity mode weakly coupled to a zero-temperature environment as a practical instance of the physical system. We assume that the bosonic mode undergoes dissipation because of an interaction with the environment but is not affected by dephasing. Solving the master equation exactly, we derive an explicit form of the violation of the inequality for both systems prepared initially in the coherent state ∣α⟩|\alpha\rangle and the cat state (∣α⟩+∣−α⟩)(|\alpha\rangle+|-\alpha\rangle). For the evaluation of the inequality, we choose the displaced parity operators characterized by a complex number β\beta. We look for the optimum parameter β\beta that lets the upper bound of the inequality be maximum numerically. Contrary to our expectations, the coherent state occasionally exhibits quantum quality more strongly than the cat state for the upper bound of the violation of the LGI in a specific range of three equally spaced measurement times (spacing τ\tau). Moreover, as we let τ\tau approach zero, the optimized parameter β\beta diverges and the LGI reveals intense singularity.Comment: 29 pages, 14 eps figures, latex2e; v2: The title has been changed. We have improved Sect. 8 and added many references; v3: Equation (57) has been modifie
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