Solution of the Lindblad equation in the Kraus representation

Nakazato, Hiromichi; Hida, Yuichiro; Yuasa, Kazuya; Militello, Benedetto; Napoli, A.; Messina, A.

doi:10.1103/physreva.74.062113

Cited by 37 publications

(27 citation statements)

References 53 publications

(62 reference statements)

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“…In Section III, the reduced density matrix of a two-level system interacting with a squeezed thermal bath via a dissipative system-bath interaction, resulting in a Lindblad form of evolution, was obtained, which reduces to the one found by Nakazato et al [59] for the case of a thermal bath without squeezing. This solution was used to study the phase distribution for the system, starting (1) in an atomic coherent state, and (2) in an atomic squeezed state.…”

Section: Discussionmentioning

confidence: 91%

Phase diffusion in quantum dissipative systems

Banerjee

Srikanth

2007

Phys. Rev. A

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We study the dynamics of the quantum phase distribution associated with the reduced density matrix of a system for a number of situations of practical importance, as the system evolves under the influence of its environment, interacting via a quantum nondemoliton type of coupling, such that there is decoherence without dissipation, as well as when it interacts via a dissipative interaction, resulting in decoherence as well as dissipation. The system is taken to be either a two-level atom (or equivalently, a spin-1/2 system) or a harmonic oscillator, and the environment is modeled as a bath of harmonic oscillators, starting out in a squeezed thermal state. The impact of the different environmental parameters on the dynamics of the quantum phase distribution for the system starting out in various initial states, is explicitly brought out. An interesting feature that emerges from our work is that the relationship between squeezing and temperature effects depends on the type of system-bath interaction. In the case of quantum nondemolition type of interaction, squeezing and temperature work in tandem, producing a diffusive effect on the phase distribution. In contrast, in case of a dissipative interaction, the influence of temperature can be counteracted by squeezing, which manifests as a resistence to randomization of phase. We make use of the phase distributions to bring out a notion of complementarity in atomic systems. We also study the dispersion of the phase using the phase distributions conditioned on particular initial states of the system.

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Section: Discussionmentioning

confidence: 91%

Phase diffusion in quantum dissipative systems

Banerjee

Srikanth

2007

Phys. Rev. A

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“…Most importantly, in this regime, we find as our second main result that the efficiency is enhanced by exploiting coherences. Specifically, it can overcome the quasi-classical value (44) and even approach its upper bound 1 in the limit 0 ω γ → ∞.…”

Section: Quasi-classical Versus Coherence-enhanced Regimementioning

confidence: 99%

Coherence-enhanced efficiency of feedback-driven quantum engines

et al. 2015

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A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that this additional energetic cost leads to a stronger bound on the work extractable after a single measurement from a system initially in thermal equilibrium (2009 Phys. Rev. A 80 012322). Here, we extend this bound to a large class of feedback-driven quantum engines operating periodically and in finite time. The bound thus implies a natural definition for the efficiency of information to work conversion in such devices. For a simple model consisting of a laser-driven two-level system, we maximize the efficiency with respect to the observable whose measurement is used to control the feedback operations. We find that the optimal observable typically does not commute with the Hamiltonian and hence would not be available in a classical two level system. This result reveals that periodic feedback engines operating in the quantum realm can exploit quantum coherences to enhance efficiency.

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“…An example of converting a widely used type of master equation -the Lindblad equation -into the operator sum representation has been provided in Ref. [26]. In this work we focus on the more general operator sum representation.…”

Section: Introductionmentioning

confidence: 99%

A quantum algorithm for evolving open quantum dynamics on quantum computing devices

Xia

Kais

2020

Sci Rep

123

138

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Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.

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Solution of the Lindblad equation in the Kraus representation

Cited by 37 publications

References 53 publications

Phase diffusion in quantum dissipative systems

Phase diffusion in quantum dissipative systems

Coherence-enhanced efficiency of feedback-driven quantum engines

A quantum algorithm for evolving open quantum dynamics on quantum computing devices

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