Optimal Decompositions with Respect to Entropy and Symmetries
نویسنده
چکیده
The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for N-level systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mixed quantum states singled out by the entropy of Abelian subalgebras correspond to optimal detection schemes at the receiving end of a quantum channel. It is then worthwhile studying in some detail the structure of the convex hull of quantum states brought about by the variational definition of the entropy of a subalgebra. In this Letter, we extend previous results on the optimal decompositions for 3-level systems. Mathematical Subject Classifications (1991): 81S99, 94A17.
منابع مشابه
Broken Symmetries in the Entanglement of Formation
We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We show that both functionals are strongly related for some highly symmetric density matrices. Indeed, for certain interesting regions the entanglement of formatio...
متن کاملOptimal Decompositions of Quantum States with Respect to Entropy
Any non-pure quantum state admits an infinity of non-trivial decompositions. A recent proposal how to measure the information content of a quantum state with reference to a given subalgebra of operators, singles out some of them, called optimal decompositions, which depend both on the state and on the subalgebra. In this paper we start exploring their main features.
متن کاملEntropy and optimal decompositions of states relative to a maximal commutative subalgebra 1
To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra is a subfactor. I consider some general properties, valid for these definitions in finite dimensions, and apply them to a maximal commutative subalgebra of a...
متن کاملConcurrence and Foliations Induced by Some 1-Qubit Channels
We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of anti-linear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length two, getting the induced foliations of the state space, the optimal decompositions, and the entropy of a state with r...
متن کاملMaximum Entropy Approach to Optimal Sensor Placement for Aerospace Non-destructive Testing
The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault...
متن کامل