Phase-space contraction and quantum operations

Abstract

We give a criterion to differentiate between dissipative and diffusive quantum operations. It is based on the classical idea that dissipative processes contract volumes in phase space. We define a quantity that can be regarded as "quantum phase space contraction rate" and which is related to a fundamental property of quantum channels: non-unitality. We relate it to other properties of the channel and also show a simple example of dissipative noise composed with a chaotic map. The emergence of attaractor-like structures is displayed.

Spectral behavior of contractive noise

“…In the classical case the dissipation parameter determines the dimension of the attractor, d = 1 + ln(2)/[ln(2) − ln( )] [21]. In the quantum case is related to the quantum phase space contraction rate [9]. We have verified that, as N increases, the phase space representation of ψ R 0 reveals finer details of the attractor, reflecting the quantum-to-classical correspondence.…”

“…[9], quantum dissipative processes can be described by nonunital quantum operations. In this work the dissipative noise is implemented by an N 2 × N 2 Kraus superoperator of the form…”

Simulation of n-qubit quantum systems. III. Quantum operations

“…("phase-space contraction", qoperation E ) Phase-space contraction as a consequence of the dissipation process E(ρ); this is essentially a measure of the channel's nonunitality given by η = N Tr[(E(ρ I ) − ρ I ) 2 ], where N = dim H and ρ I = I/N is the maximally mixed state [38]. archive includes several example worksheets (see the next section) and a Read.me file to briefly explain the installation of the program package.…”

“…A well-known exception is the amplitude damping channel which describes a dissipative, nonunital process. In general, the nonunitality of a quantum operation can be measured by means of the 'phase-space contraction' (measure) [38], which has been implemented also in the FEYNMAN program (see Table 4). …”

Normalization procedure for relaxation studies in NMR quantum information processing

“…This shows that the process S is not generally linear in σ. The linearity of S with respect to σ is only obtained if S is a unital process (S(1) = 1), for instance, unitary transformations, which is not the case for most relaxation phenomena [14]. Trace-preserving unital processes are the quantum analogs of the classical doubly stochastic processes, which can only increase the von-Neumann entropy of a state (defined to be −Tr{ρlogρ}).…”