Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

Rodríguez, Ernesto Benítez; Aguilar, L. M. Arévalo

doi:10.1038/s41598-018-22336-3

Cited by 22 publications

(21 citation statements)

References 68 publications

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“…As we can note from the previous quotation, the stated article [ 5 ] gives us an estimate of the interference that is found in the uncertainty of the observable B due to a previous measurement of A , as shown in Equation ( 25 ). This main idea has some similarities to what has been discussed in recent works about disturbance, for instance [ 21 ], where the comparison between the values that a measure of disturbance takes in two different moments is applied. However, quantifying the uncertainty in consecutive measurements was what Srinivas was really interested in; that is, when the measurement of an observable A is followed by the measurement of another observable B .…”

Section: Disturbance In the Noise–disturbance Trade-off (Ndt)mentioning

confidence: 87%

“…It is important to remember that the uncertainty principles and uncertainty relations have been the topic of many research articles. In particular, the area of Entropic Uncertainty Relations (EUR) is a leading branch in the study of uncertainty relations [ 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ]. The study of EUR has given rise to current definitions of uncertainty and disturbance in quantum mechanics.…”

Section: Definitionsmentioning

confidence: 99%

See 1 more Smart Citation

A Survey of the Concept of Disturbance in Quantum Mechanics

Rodríguez

Aguilar

2019

Entropy

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The concept of disturbance is of transcendental importance in Quantum Mechanics (QM). This key concept has been described in two different ways, the first one considering that the disturbance affects observables like x and p, as in the Heisenberg’s analysis of the measurement process and the other one takes into consideration that disturbance affects the state of the system instead. Entropic information measures have provided a path for studying disturbance in these both approaches; in fact, we found that initially it was studied by employing these entropic measures. In addition, in the last decade, there was an extensive amount of analyses and several new definitions of the disturbance concept emerged. Many crucial factors like this have inspired this concise paper which gathers the different concepts and definitions that have emerged through time for the better understanding of this topic.

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Section: Disturbance In the Noise–disturbance Trade-off (Ndt)mentioning

confidence: 87%

Section: Definitionsmentioning

confidence: 99%

A Survey of the Concept of Disturbance in Quantum Mechanics

Rodríguez

Aguilar

2019

Entropy

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“…Quantum mechanics is a fascinating field; nonetheless, the core ideas, like quantum nonlocality and “disturbance”, are difficult concepts to grasp. In fact, the concept of disturbance, caused by the measurement process, which is responsible for one of the interpretations of the Heisenberg uncertainty principle, is not fully understood yet, and it is under investigation, as well [ 88 ]. In this case, disturbance refers to the change and perturbation produced by the measurement process; see [ 88 ] and the references therein.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, the concept of disturbance, caused by the measurement process, which is responsible for one of the interpretations of the Heisenberg uncertainty principle, is not fully understood yet, and it is under investigation, as well [ 88 ]. In this case, disturbance refers to the change and perturbation produced by the measurement process; see [ 88 ] and the references therein. Quantum nonlocality is captivating, as well, and the fact of analyzing nonlocality by using the highly significant SGE could lead to understanding this concept better.…”

Section: Discussionmentioning

confidence: 99%

Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

Martínez

Rodríguez

Fierro

et al. 2018

Entropy

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Abstract:The Stern-Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z, θ) by redefining the Banaszek-Wódkiewicz correlation in terms of the Wigner operator, that is C(z, θ) = Ψ|Ŵ(z, p z )σ(θ)|Ψ , whereŴ(z, p z ) is the Wigner operator,σ(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser-Horne-Shimony-Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.

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“…This impression was strengthened by the state-dependent analysis of measurement uncertainties introduced by Ozawa [8], resulting in yet another round of criticisms and controversy [9][10][11][12][13][14]. At the same time, measurement theories attained new relevance in the context of quantum information, where the focus shifted from uncertainties towards quantum state discrimination [15][16][17][18][19]. As a result of all of these developments, there is now an abundance of methods and approaches to quantum measurement that has made it even more difficult to find any common ground on fundamental questions regarding the role and the significance of the measurement process in quantum theory.…”

Section: Introductionmentioning

confidence: 99%

The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements

Patekar

Hofmann

2019

New J. Phys.

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Measurement processes can be separated into an entangling interaction between the system and a meter and a subsequent readout of the meter state that does not involve any further interactions with the system. In the interval between these two stages, the system and the meter are in an entangled state that encodes all possible effects of the readout in the form of non-local quantum correlations between the system and the meter. Here, we show that the entanglement generated in the system-meter interaction expresses a fundamental relation between the amount of decoherence and the conditional probabilities that describe the resolution of the measurement. Specifically, the entanglement generated by the measurement interaction correlates both the target observable and the back-action effects on the system with sets of non-commuting physical properties in the meter. The choice of readout in the meter determines the trade-off between irreversible decoherence and measurement information by steering the system into a corresponding set of conditional output states. The Hilbert space algebra of entanglement ensures that the irreversible part of the decoherence is exactly equal to the Hellinger distance describing the resolution achieved in the measurement. We can thus demonstrate that the trade-off between measurement resolution and back-action is a fundamental property of the entanglement generated in measurement interactions.

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Disturbance-Disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance

Cited by 22 publications

References 68 publications

A Survey of the Concept of Disturbance in Quantum Mechanics

A Survey of the Concept of Disturbance in Quantum Mechanics

Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

The role of system–meter entanglement in controlling the resolution and decoherence of quantum measurements

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