Decoherence for Quantum Markov Semi-Groups on Matrix Algebras

Carbone, Raffaella; Sasso, Emanuela; Umanità, Veronica

doi:10.1007/s00023-012-0199-3

Cited by 29 publications

(27 citation statements)

References 16 publications

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“….g., [11]) and so that there exists a self-adjoint operator H such that, Φ t • E N (ρ) = e iHt E N (ρ)e −iHt . In words, the evolution asymptotically behaves like a unitary evolution.…”

Section: Quantum Channels Markovian Evolutions and Their Spectrum Nementioning

confidence: 99%

Eventually Entanglement Breaking Markovian Dynamics: Structure and Characteristic Times

Hanson

Rouzé

França

2020

Ann. Henri Poincaré

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We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete-time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT 2 conjecture is that every PPT quantum channel has an entanglement breaking index of at most 2; we prove that every faithful PPT quantum channel has a finite entanglement breaking index, and more generally, any faithful PPT CP map whose Hilbert-Schmidt adjoint is also faithful is eventually entanglement breaking. We also provide a method to obtain concrete bounds on this index for any faithful quantum channel. To obtain these estimates, we use a notion of robustness of separability to obtain bounds on the radius of the largest separable ball around faithful product states. We also extend the framework of Poincaré inequalities for non-primitive semigroups to the discrete setting to quantify the convergence of quantum semigroups in discrete time, which is of independent interest.

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Section: Quantum Channels Markovian Evolutions and Their Spectrum Nementioning

confidence: 99%

Eventually Entanglement Breaking Markovian Dynamics: Structure and Characteristic Times

Hanson

Rouzé

França

2020

Ann. Henri Poincaré

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“…The following example shows that F(T ), unlike N (T ), may not be an algebra. We refer to [12], section 4, for additional examples.…”

Section: Propositionmentioning

confidence: 99%

“…In recent years, there has been a growing interest in the use of QMSs to model open quantum systems having subsystems which are not affected by decoherence (see Lidar and Whaley [27], Knill and Laflamme [29], Olkiewicz [8,30,31], Ticozzi and Viola [35], see also [12,13,14] and the references therein). In these applications the QMS (in the Heisenberg picture) acts as a semigroup of automorphisms of a von Neumann subalgebra N (T ) of B(h), called the decoherence-free subalgebra.…”

Section: Introductionmentioning

confidence: 99%

Structure of uniformly continuous quantum Markov semigroups

et al. 2016

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The structure of uniformly continuous quantum Markov semigroups with atomic decoherence-free subalgebra is established providing a natural decomposition of a Markovian open quantum system into its noiseless (decoherencefree) and irreducible (ergodic) components. This leads to a new characterisation of the structure of invariant states and a new method for finding decoherence-free subsystems and subspaces. Examples are presented to illustrate these results.

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“…6) and the initial state ω loses its quantum features (see Refs. 2,6,7,10,13,19,23,24, and 26 for a dual approach based on observables rather than states and references therein).…”

Section: Decoherence-free Subspacesmentioning

confidence: 99%