Quantum System Fidelity Estimation

Advancement of estimation fidelity in continuous quantum measurement

We estimate an unknown qubit from the long sequence of n random polarization measurements of precision ∆. Using the standard Ito-stochastic equations of the aposteriori state in the continuous measurement limit we calculate the advancement of fidelity. We show that the standard optimum value 2/3 is achieved asymptotically for n ∆/96 1. We append a brief derivation of novel Ito-equations for the...

Sub- and super-fidelity as bounds for quantum fidelity

We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super–fidelity. It is analogous to another quantity called sub–fidelity. For any two states of a two– dimensional quantum system (N = 2) all three quantities coincide. We demonstrate that sub– and super–fidelity are concave functions. We ...

Semiclassical evaluation of quantum fidelity.

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it also gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov reg...

Rank penalized estimation of a quantum system

Quantum fidelity for degenerate ground states in quantum phase transitions.

Spontaneous symmetry breaking in quantum phase transitions leads to a system having degenerate ground states in its broken-symmetry phase. In order to detect all possible degenerate ground states for a broken-symmetry phase, we introduce a quantum fidelity defined as an overlap measurement between a system ground state and an arbitrary reference state. If a system has N-fold degenerate ground s...