Can Decay Be Ascribed to Classical Noise?

Burgarth, Daniel; Facchi, Paolo; Garnero, Giancarlo; Nakazato, Hiromichi; Pascazio, Saverio; Yuasa, Kazuya

doi:10.1142/s1230161217500019

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…By averaging over the stochastic process, one obtains the unconditional dephasing dynamics, while a continuous observation in time of the classical stochastic process allows to obtain the conditional states. It is in fact well known that Markovian dephasing is equivalent to the average dynamics obtained by putting a stochastic term in the system Hamiltonian [65][66][67][68][69]. Remarkably, we have derived the same results starting from a fully quantum approach, that is, considering the interaction of the system with a quantum environment, represented by trains of incoming bosonic input modes, with the classical stochastic terms appearing because of the measurement performed on the environment.…”

Section: Photo-detectionmentioning

confidence: 66%

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Albarelli

Rossi

Genoni

2020

Int. J. Quantum Inform.

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We discuss the problem of estimating a frequency via N -qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

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Section: Photo-detectionmentioning

confidence: 66%

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Albarelli

Rossi

Genoni

2020

Int. J. Quantum Inform.

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“…Roughly, the reason why decoupling works is that the clock state does not change the dynamics, and that the singularity at t = 0 in (2) integrates to something continuous. This is suprising, because previous studies [24,9,15] seemed to indicate that dilations of amplitude damping might be particularly bity. 3) dilating the single-qubit amplitude damping model.…”

Section: Physical Summary and Single-qubit Illustrationmentioning

confidence: 95%

“…Since [3] works in the framework of constant Hamiltonian whereas here H(t) is not constant, we would like to relate the two frameworks. Choose m ∈ N and a piece-wise constant (step function) approximation H m of H with m equal length steps on (0, t] such that (15)…”

Section: The Dilation and Dynamical Decouplingmentioning

confidence: 99%

Control of quantum noise: on the role of dilations

Burgarth,

Facchi,

Hillier

2020

Preprint

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We show that every finite-dimensional quantum system with Markovian time evolution has an autonomous unitary dilation which can be dynamically decoupled. Since there is also always an autonomous unitary dilation which cannot be dynamically decoupled, this highlights the role of dilations in the control of quantum noise. We construct our dilation via a time-dependent version of Stinespring in combination with Howland's clock Hamiltonian and certain point-localised states, which may be regarded as a C*-algebraic analogue of improper bra-ket position eigenstates and which are hence of independent mathematical and physical interest.

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“…Yet another definition of dephasing has been put forward, more recently, by Burgarth et al [30]. For the case where the Lindbladian is pure, namely, if L = L (L,0) for a single L, the QMS is (maximally) dephasing if it admits a stable basis or, equivalently, if L is a normal operator.…”

Section: Comparison With Other Definitions Of Dephasingmentioning

confidence: 99%

Mathematical models of Markovian dephasing

Fagnola

Gough

Nurdin

et al. 2019

J. Phys. A: Math. Theor.

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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, the Hamiltonian obstruction, which vanishes if and only if the latter admits a self-adjoint representation and quantifies the hindrance to having a classical diffusive noise model.

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Can Decay Be Ascribed to Classical Noise?

Cited by 12 publications

References 17 publications

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

Control of quantum noise: on the role of dilations

Mathematical models of Markovian dephasing

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