The master equation for the reduced open-system dynamics, including a Lindbladian description of finite-duration measurement

Brasil, Carlos Alexandre; Napolitano, Reginaldo de Jesus

doi:10.1140/epjp/i2011-11091-y

Cited by 5 publications

(17 citation statements)

References 28 publications

(41 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Here, the first term of the right-hand side, − i Ĥ ,ρ SB , is the Liouvillian and corresponds to unitary evolutions, while the second term, Here, we are only interested in the reduced density operatorρ S of S. In our formalism [18], this is done with the help of the Nakajima-Zwanzig projectors [19,20] that, for the general operatorX (t) and the initial instant t 0 , act aŝ…”

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…Both here and in our previous applications [18,24,25], we have considered S a 2-state system and B the environment, with corresponding Hamiltonianŝ…”

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…In our previous works [18,24,25], to obtain analytical solutions, we had considered only the system-environment interaction in the phase-damping format and, in the case when the Lindblad does not commute with that interaction, we had considered the particular situation when the frequency ω 0 and the environment temperature T are both zero. In the following sections, we will present numerical implementations without these restrictions and with the use of both kinds of interaction.…”

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…The partial trace for the environmental degrees of freedom, following the procedures already shown in [18,24], furnish:…”

Section: Amplitude-damping Interactionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient finite-time measurements under thermal regimes

2014

View full text Add to dashboard Cite

Contrary to conventional quantum mechanics, which treats measurement as instantaneous, here we explore a model for finite-time measurement. The main two-level system interacts with the measurement apparatus in a Markovian way described by the Lindblad equation, and with an environment, which does not include the measuring apparatus. To analyse the environmental effects on the final density operator, we use the Redfield approach, allowing us to consider a non-Markovian noise. In the present hybrid theory, to trace out the environmental degrees of freedom, we use a previously-developed analytic method based on superoperator algebra and Nakajima-Zwanzig superoperators. Here, we analyse two types of system-environment interaction, phase and amplitude damping, which allows us to conclude that, in general, a finite-time quantum measurement performed during a certain period is more efficient than an instantaneous measurement performed at the end of it, because the rate of change of the populations is attenuated by the system-measurement apparatus interaction.

show abstract

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…Both here and in our previous applications [18,24,25], we have considered S a 2-state system and B the environment, with corresponding Hamiltonianŝ…”

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…The partial trace for the environmental degrees of freedom, following the procedures already shown in [18,24], furnish:…”

Section: Amplitude-damping Interactionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient finite-time measurements under thermal regimes

2014

View full text Add to dashboard Cite

show abstract

“…A derivada temporal da matriz densidade reduzida é dada por: 20) o que, usando tanto a aproximação markoviana quanto a expressão em termos da base {F i }, torna-se:…”

Section: Equação De Lindbladunclassified

Teoria de correção de erros quânticos durante operações lógicas e medidas de diagnóstico de duração finita

Castro¹

View full text Add to dashboard Cite

How Much Time Does a Measurement Take?

2013

Self Cite

View full text Add to dashboard Cite

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction.Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.

show abstract

The master equation for the reduced open-system dynamics, including a Lindbladian description of finite-duration measurement

Cited by 5 publications

References 28 publications

Efficient finite-time measurements under thermal regimes

Efficient finite-time measurements under thermal regimes

Teoria de correção de erros quânticos durante operações lógicas e medidas de diagnóstico de duração finita

How Much Time Does a Measurement Take?

Contact Info

Product

Resources

About