Fundamentals of quantum mechanics in Liouville space

Gyamfi, Jerryman A.

doi:10.1088/1361-6404/ab9fdd

Cited by 45 publications

(40 citation statements)

References 62 publications

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“…In the derivation of the moment evolution equations below, it will be useful to have the adjoint of the mas-ter equation in generalized Lindblad form, which is defined according to Tr[(L † Ô)ρ] = Tr[ Ô(Lρ)] for an arbitrary operator Ô, such that L † correspond to the adjoint of L with respect to the Hilbert-Schmidt inner product [31,32]. Thus, if L is time-independent, the adjoint master equation takes the form…”

Section: A Adjoint Master Equationmentioning

confidence: 99%

Generalized Lindblad master equations in quantum reservoir engineering

Bernal-García¹,

Huang²,

Miroshnichenko³

et al. 2021

Preprint

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Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by making an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the well-known Gorini-Kossakowski-Lindblad-Sudarshan form (here called standard Lindblad form). Instead, it has a more general structure (here called generalized Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear systems, bosonic and fermionic, described by master equations in a generalized Lindblad form. Our method is efficient and allows one to obtain analytical solutions for the steady state. Further, we include as a review some covariance matrix methods for which our results are particularly relevant, paying special attention to those related to the measurement of entanglement. Finally, we prove that the Duan criterion for entanglement is also applicable to fermionic systems.

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Section: A Adjoint Master Equationmentioning

confidence: 99%

Generalized Lindblad master equations in quantum reservoir engineering

Bernal-García¹,

Huang²,

Miroshnichenko³

et al. 2021

Preprint

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“…where L represents the Liouvillian superoperator describing the open system dynamics and |ρ is the vectorised form of density matrix in Liouville space. The mathematical form of L can be obtained by applying the transformation BρC → C * ⊗ B|ρ to the master equation where |ρ is obtained by vertically stacking the columns of density matrix [15,[40][41][42].…”

Section: B Steady State Dynamicsmentioning

confidence: 99%

Observation of quantum phase-synchronization in a nuclear spin-system

Krithika,

Solanki,

Vinjanampathy

et al. 2021

Preprint

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We report an experimental study of phase-synchronization in a pair of interacting nuclear spins subjected to an external drive in nuclear magnetic resonance architecture. A weak transitionselective radio-frequency field applied on one of the spins is observed to cause phase-localization, which is experimentally established by measuring the Husimi distribution function under various drive conditions. To this end, we have developed a general interferometric technique to directly extract values of the Husimi function via the transverse magnetization of the undriven nuclear spin. We further verify the robustness of synchronization to detuning in the system by studying the Arnold tongue behaviour.

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“…Here we present an alternative approach, using multiple time scale perturbation theory [92], for deriving the reduced master equation ( 2) of the main text. We analyze the problem in Fock-Liouville space, where density matrices are converted to column vectors and superoperators become matrices [93,94]. When we apply this formalism to a classical model in Sec.…”

Section: Threshold Feedbackmentioning

confidence: 99%

“…Equation ( 1) of the main text can be rewritten by introducing a vectorized form of the density matrix |ρ , containing the entries of the original matrix stacked in a single vector with N 2 elements, where N is the dimension of the Hilbert space [93,94]. The master equation (1) then becomes…”

Section: Extension To Fock-liouville Spacementioning

confidence: 99%

Quantum Fokker-Planck master equation for continuous feedback control

Annby-Andersson,

Bakhshinezhad,

Bhattacharyya

et al. 2021

Preprint

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Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical.

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Fundamentals of quantum mechanics in Liouville space

Cited by 45 publications

References 62 publications

Generalized Lindblad master equations in quantum reservoir engineering

Generalized Lindblad master equations in quantum reservoir engineering

Observation of quantum phase-synchronization in a nuclear spin-system

Quantum Fokker-Planck master equation for continuous feedback control

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