Quantum chaos and physical distance between quantum states

Physical transformations between quantum states

Given two sets of quantum states {A1, . . . , Ak} and {B1, . . . , Bk}, represented as sets as density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T , represented as a trace-preserving completely positive map, such that T (Ai) = Bi for i = 1, . . . , k. General completely positive maps without the trace-preserving requirement, and un...

Relations Between Quantum Maps and Quantum States

The relation between completely positive maps and compound states is investigated in terms of the notion of quantum conditional probability.

Quantum Instantons and Quantum Chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential. ∗Corresponding author, Email: [email protected]

Discriminating quantum states: the multiple Chernoff distance

We consider the problem of testing multiple quantum hypotheses {ρ 1 , . . . , ρ r }, where an arbitrary prior distribution is given and each of the r hypotheses is n copies of a quantum state. It is known that the minimal average error probability Pe decays exponentially to zero, that is, Pe = exp{−ξn+ o(n)}. However, this error exponent ξ is generally unknown, except for the case that r = 2. I...

Quantum Chaos and Quantum Ergodi ityx