94 research outputs found
Optimal parameter estimation of a depolarizing channel
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
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
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
and the cat state . For the
evaluation of the inequality, we choose the displaced parity operators
characterized by a complex number . We look for the optimum parameter
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 ). Moreover, as we let approach zero, the optimized
parameter 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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