Engineering topics

Guta, Madalin

Publications and source records attributed to Guta, Madalin.

4 records

DOE OSTI2011

Asymptotically optimal purification and dilution of mixed qubit and Gaussian states

Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, produces a larger ensemble, while reducing the purity level of the systems. In this paper we find asymptotically optimal procedures for purification and dilution of an ensemble of independently and identically distributed mixed qubit states, for some given input and output purities and an asymptotic output rate. Our solution involves using the statistical tool of local asymptotic normality, which recasts the qubit problem in terms of attenuation and amplification of a single-mode displaced Gaussian state. Therefore, to obtain the qubit solutions, we must first solve the analogous problems in the Gaussian setup. We provide full solutions to all of the above for the (global) trace-norm figure of merit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolute bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Quantum U-statistics

The notion of a U-statistic for an n-tuple of identical quantum systems is introduced in analogy to the classical (commutative) case: given a self-adjoint 'kernel' K acting on (C{sup d}){sup '}x{sup r} with r<n, we define the symmetric operator U{sub n}=((n/r)){Sigma}{sub {beta}K}{sup ({beta})} with K{sup ({beta})} being the kernel acting on the subset {beta} of {l_brace}1,...,n{r_brace}. If the systems are prepared in the product state {rho}{sup xn}, it is shown that the sequence of properly normalized U-statistics converges in moments to a linear combination of Hermite polynomials in canonical variables of a canonical commutation relation algebra defined through the quantum central limit theorem. In the special cases of nondegenerate kernels and kernels of order of 2, it is shown that the convergence holds in the stronger distribution sense. Two types of applications in quantum statistics are described: testing beyond the two simple hypotheses scenario and quantum metrology with interacting Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2010

Quantum-teleportation benchmarks for independent and identically distributed spin states and displaced thermal states

A successful state-transfer (or teleportation) experiment must perform better than the benchmark set by the 'best' measure and prepare procedure. We consider the benchmark problem for the following families of states: (i) displaced thermal equilibrium states of a given temperature; (ii) independent identically prepared qubits with a completely unknown state. For the first family we show that the optimal procedure is heterodyne measurement followed by the preparation of a coherent state. This procedure was known to be optimal for coherent states and for squeezed states with the 'overlap fidelity' as the figure of merit. Here, we prove its optimality with respect to the trace norm distance and supremum risk. For the second problem we consider n independent and identically distributed (i.i.d.) spin-(1/2) systems in an arbitrary unknown state {rho} and look for the measurement-preparation pair (M{sub n},P{sub n}) for which the reconstructed state {omega}{sub n}:=P{sub n} circle M{sub n}({rho}{sup xn}) is as close as possible to the input state (i.e., parallel {omega}{sub n}-{rho}{sup xn} parallel {sub 1} is small). The figure of merit is based on the trace norm distance between the input and output states. We show that asymptotically with n this problem is equivalent to the first one. The proof and construction of (M{sub n},P{sub n}) uses the theory of local asymptotic normality developed for state estimation which shows that i.i.d. quantum models can be approximated in a strong sense by quantum Gaussian models. The measurement part is identical to 'optimal estimation', showing that 'benchmarking' and estimation are closely related problems in the asymptotic set up.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗