Protecting a quantum state from environmental noise by an incompatible finite-time measurement

Brasil, Carlos Alexandre; Castro, Leonardo Andreta de; Napolitano, Reginaldo de Jesus

doi:10.1103/physreva.84.022112

Cited by 11 publications

(46 citation statements)

References 33 publications

(61 reference statements)

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“…There is, however, works on quantum measurement theory where the condition (1) is not obeyed [56,57,58].…”

Section: Pointer Basismentioning

confidence: 99%

Understanding the pointer states

Brasil¹,

Castro²

2015

Eur. J. Phys.

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In quantum mechanics, pointer states are eigenstates of the observable of the measurement apparatus that represent the possible positions of the display pointer of the equipment. The origin of this concept lies in attempts to fill the blanks in the Everett's relative-state interpretation, and to make it a fully valid description of physical reality. To achieve this, it was necessary to consider not only the main system interacting with the measurement apparatus (like von Neumann and Everett did) but also the role of the environment in eliminating correlations between different possible measurements when interacting with the measurement apparatus. The interaction of the environment with the main system (and the measurement apparatus) is the core of the decoherence theory, which followed Everett's thesis. In this article, we review the measurement process according to von Neumann, Everett's relative state interpretation, the purpose of decoherence and some of its follow-up until Wojciech Zurek's primordial paper that consolidated the concept of pointer state, previously presented by Heinz Dieter Zeh. Employing a simple physical model consisting of a pair of two-level systems -one representing the main system, the other the measurement apparatus -and a thermal bath -representing the environment -we show how pointer states emerge, explaining its contributions to the question of measurement in quantum mechanics, as well as its limitations. Finally, we briefly show some of its consequences. This paper is accessible to readers with elementary knowledge about quantum mechanics, on the level of graduate courses.

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“…There is, however, works on quantum measurement theory where the condition (1) is not obeyed [56,57,58].…”

Section: Pointer Basismentioning

confidence: 99%

Understanding the pointer states

Brasil¹,

Castro²

2015

Eur. J. Phys.

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show abstract

“…In this section, we overview the model of noisy finite-time measurement that was developed and employed in our previous works [24,25]. This model assumes that the system interacts with the measurement apparatus through a Markovian interaction.…”

Section: The Model Of Finite-time Measurementmentioning

confidence: 99%

“…II briefly explains the method that can be found, with greater details, on [18] and solutions for the Lindblad equation for x -component measurement without environment found on [24]; Sec. III shows the zcomponent solution and the simplified (T = 0 and ω 0 = 0) x -component solutions found on [24] for the phase-damping interaction; finally, on Sec. V we show the formula for upper limit for the measurement duration found on [25].…”

Section: I+ii) Measmentioning

confidence: 99%

“…In previous papers [18,24,25], our formalism was applied to a two-state system in contact with an environment via phase-damping interaction, in the case of an Ohmic spectral density. Under some restrictions -both the natural system frequency and the environmental temperature set to zero -chosen to simplify the problem and allow analytical solutions, we verified that [24], when the measurement does not commute with the system-environment interaction, (i) the more intense the system-environment interaction, the more marked is the decrease of the population -i.e., the larger is the measurement error -and (ii) the more intense the system-measurement apparatus interaction, the less marked is the rate of change of the populations.…”

Section: I+ii) Measmentioning

confidence: 99%

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Efficient finite-time measurements under thermal regimes

2014

Self Cite

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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.

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“…In the following, we will use the approximate method presented in Ref. [44] to solve the master equation (5) and to obtain the density matrix of the open system. This method has been proved to be valid by exact numerical calculations based on the superoperator-splitting method [45] for weak coupling between the system and its environment.…”

Section: The Model and Solutionmentioning

confidence: 99%

Measurement-based direct quantum feedback control in an open quantum system

Yan¹,

Zou²,

Xu³

et al. 2013

Phys. Rev. A

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We consider a general quantum system interacting with a bath and derive a master equation in the Lindblad form describing the evolution of the whole quantum system subjected to a measurementbased direct quantum feedback control (MDFC). As an example, we consider a qubit coupled with a dephasing environment under the MDFC. We show that for any given pure target state we can always find the corresponding MDFC scheme which can effectively drive any initial state into this target state. And by using appropriate MDFC scheme with weak measurement we can stabilize a single qubit initially prepared in one of two nonorthogonal states against dephasing noise. Furthermore, we can effectively protect a kind of known mixed states composed of two nonorthogonal states by using the corresponding MDFC scheme.

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Protecting a quantum state from environmental noise by an incompatible finite-time measurement

Cited by 11 publications

References 33 publications

Understanding the pointer states

Understanding the pointer states

Efficient finite-time measurements under thermal regimes

Measurement-based direct quantum feedback control in an open quantum system

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