Mathematical Models of Markovian Dephasing

Abstract

We develop a notion of dephasing under the action of a quantum Markov semigroup in terms of convergence of operators to a block-diagonal form determined by irreducible invariant subspaces. If the latter are all one-dimensional, we say the dephasing is maximal. With this definition, we show that a key necessary requirement on the Lindblad generator is bistochasticity, and focus on characterizing whether a maximally dephasing evolution may be described in terms of a unitary dilation with only classical noise, as opposed to a genuine non-commutative Hudson-Parthasarathy dilation. To this end, we make use of a seminal result of Kümmerer and Maassen on the class of commutative dilations of quantum Markov semigroups. In particular, we introduce an intrinsic quantity constructed from the generator, which vanishes if and only if the latter admits a self-adjoint representation and which quantifies the degree of obstruction to having a classical diffusive noise model.

submitted 12 November to AHP

References in corpus (6)

• Quantum Feedback Networks: Hamiltonian Formulation
• The structure of preserved information in quantum processes
• Simulating Open Quantum Systems with Hamiltonian Ensembles and the Nonclassicality of the Dynamics
• Quantum Decoherence of Two Qubits
• Decoherence of spin registers revisited
• Effective description of the short-time dynamics in open quantum systems

Cited by in corpus (8)

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• Quantum nonreciprocal interactions via dissipative gauge symmetry
• Distinguishing between quantum and classical Markovian dephasing dissipation
• Frequency estimation under non-Markovian spatially correlated quantum noise: Restoring superclassical precision scaling
• Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels
• Quantifying environment non-classicality in dissipative open quantum dynamics
• The decoherence-free subalgebra of Gaussian Quantum Markov Semigroups
• Decoherence, Perturbations and Symmetry in Lindblad Dynamics -- Implications for Diffractive Dissociation