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

The intercept/resend attack and the collective attack on the six-state protocol of the quantum key distribution

In this paper, we discuss security of the six-state quantum key distribution protocol against intercept/resend attacks and collective attacks. For the intercept/resend attacks, we evaluate a probability that the legitimate users, Alice and Bob, do not notice interference caused by the eavesdropper Eve and a probability that Eve obtains a secret bit sent by Alice. For the collective attacks, we estimate not only the above two probabilities but also Eve's Shannon information. In the assessment of the security against the collective attacks, imposing looser constraints upon Eve's strategies than Bechmann-Pasquinucci and Gisin, we reach substantially the same result as their study. In other words, although we let Eve's strategies satisfy lower symmetry than Bechmann-Pasquinucci and Gisin, both their work and ours attain the same conclusion, i.e. the identical, unique, and optimum strategy. This implies that we obtain Eve's best tactic by applying simpler conditions to it than Bechmann-Pasquinucci and Gisin, so that this result is novel. Finally, we consider a relation between the six-state protocol and the E91 scheme. We show that the intercept/resend attacks can always be described by hidden variable models. In contrast, we demonstrate that we cannot regard the collective attacks as the hidden variable theories if the disturbance is smaller than $1/3$.Comment: 24 pages, 2 eps figures, latex2