Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur

Influence of refrigeration and ageing time on textural characteristics of fresh meat

Research of the textural characteristics of pork, beef and baby beef meat samples was conducted. Hardness and adhesivity of the meat was measured immediately after slaughtering, then after 24, 48 and 72 hours. Half of the samples were kept at room temperature, while the other half were refrigerated at 4 C. The results showed that the hardness and adhesivity suddenly dropped during the first 24 hours (up to 345 N, or 41.7 %). After next 48 hours of storage, the values of measured textural properties showed a slight decrease (only additional 15.6 %). The refrigerated samples retained their textural properties a lot better (31 % decrease in hardness during first 24 h, additional 7.4 % in the next 48 hours) than the non-refrigerated ones. In correlation with consumer and industry experience with the texture of cooked or fried meat, refrigeration is a better choice after 48 hours, while after that period, meat at room temperature, is too soft for further processing

Quantum inference of states and processes

The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that measurements on probe and transformed probe states are available. Drawbacks of various approximate treatments are considered.Comment: 7 pages, 4 figure

Iterative algorithm for reconstruction of entangled states

An iterative algorithm for the reconstruction of an unknown quantum state from the results of incompatible measurements is proposed. It consists of Expectation-Maximization step followed by a unitary transformation of the eigenbasis of the density matrix. The procedure has been applied to the reconstruction of the entangled pair of photons.Comment: 4 pages, no figures, some formulations changed, a minor mistake correcte

Finding optimal strategies for minimum-error quantum-state discrimination

We propose a numerical algorithm for finding optimal measurements for quantum-state discrimination. The theory of the semidefinite programming provides a simple check of the optimality of the numerically obtained results.Comment: 4 pages, 2 figure

Mixed quantum state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.