Dynamics of incompatibility of quantum measurements in open systems

Addis, Carole; Heinosaari, Teiko; Kiukas, Jukka; Laine, Elsi-Mari; Maniscalco, Sabrina

doi:10.1103/physreva.93.022114

Cited by 10 publications

(20 citation statements)

References 45 publications

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“…where p a a { } and q b b { } are probability distributions. This measure has been investigated in many works [12,16,29,31,34,35,[42][43][44][45], and also in the framework of general probabilistic theories [46,47].…”

Section: Incompatibility Probabilistic Robustness 331 Definition Amentioning

confidence: 99%

Incompatibility robustness of quantum measurements: a unified framework

2019

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In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e. measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not well-understood. In this work, we develop a general framework that encompasses all the commonly used measures of incompatibility based on robustness to noise. Moreover, we propose several conditions that a measure of incompatibility should satisfy, and investigate whether the existing measures comply with them. We find that some of the widely used measures do not fulfil these basic requirements. We also show that when looking for the most incompatible pairs of measurements, we obtain different answers depending on the exact measure. For one of the measures, we analytically prove that projective measurements onto two mutually unbiased bases are among the most incompatible pairs in every dimension. However, for some of the remaining measures we find that some peculiar measurements turn out to be even more incompatible.performed simultaneously by performing the parent measurement. If such a parent measurement does not exist, we say that the measurements are incompatible (or not jointly measurable). We remark here that other notions of compatibility, such as commutativity, non-disturbance and coexistence, are also used in the literature [1,3]; let us for completeness briefly explain how they are related. Commutativity of a measurement pair implies nondisturbance, which in turn implies joint measurability, which then implies coexistence. Moreover, it is known that none of the converse implications hold in general, therefore these notions are strictly distinct [4]. In this work we focus solely on the notion of joint measurability, because the existence (or not) of a parent measurement has a clear operational meaning. Therefore, throughout the present paper we use the terms '(in) compatibility' and '(non-)joint measurability' interchangeably. It is important to notice that whenever two measurements are compatible, they cannot be used to produce quantum advantage in tasks like Bell nonlocality [5] or Einstein-Podolsky-Rosen steering [6,7]. Moreover, it was recently shown that joint measurability is equivalent to a specific notion of classicality, namely, preparation non-contextuality [8,9]. Hence, one may think of compatible measurements as 'classical' , and incompatible measurements as a resource for the above tasks. Therefore, it is of fundamental importance to characterise and understand the structure of incompatible measurements.What is particularly important is to go beyond the dichotomy of compatible and incompatible measurements, and quantify to what extent a pair of measurements is incompatible. A natural framework for this qua...

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Section: Incompatibility Probabilistic Robustness 331 Definition Amentioning

confidence: 99%

Incompatibility robustness of quantum measurements: a unified framework

2019

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“…In order to quantify this loss, we need a numerical incompatibility monotone; they can be constructed [16,26] using the noise-robustness idea from general quantum resource theories [1,[27][28][29][30][31]. The dynamics of incompatibility has recently been studied using these monotones [32].…”

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confidence: 99%

“…Good operational incompatibility monotones describe convex-geometric noise-robustness [1, 16, 26, 31]: we mix classical noise with distribution p = (p i ) into measurements via A → (1−λ)A+λp1, and define I to be the minimal λ for which the resource is lost, i.e. measurements become jointly measurable (see [26,32] for discussion).…”

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Quantum resource control for noisy Einstein-Podolsky-Rosen steering with qubit measurements

Kiukas

Burgarth

2016

Phys. Rev. A

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We demonstrate how quantum optimal control can be used to enhance quantum resources for bipartite one-way protocols, specifically EPR-steering with qubit measurements. Steering is relevant for one-sided device-independent key distribution, the realistic implementations of which necessitate the study of noisy scenarios. So far mainly the case of imperfect detection efficiency has been considered; here we look at the effect of dynamical noise responsible for decoherence and dissipation. In order to set up the optimisation, we map the steering problem into the equivalent joint measurability problem, and employ quantum resource-theoretic robustness monotones from that context. The advantage is that incompatibility (hence steerability) with arbitrary pairs of noisy qubit measurements has been completely characterised through an analytical expression, which can be turned into a computable cost function with exact gradient. Furthermore, dynamical loss of incompatibility has recently been illustrated using these monotones. We demonstrate resource control numerically using a special gradient-based software, showing, in particular, the advantage over naive control with cost function chosen as a fidelity in relation to a specific target. We subsequently illustrate the complexity of the control landscapes with a simplified two-variable scheme. The results contribute to the theoretical understanding of the limitations in realistic implementations of quantum information protocols, also paving way to practical use of the rather abstract quantum resource theories.

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“…The range of approaches to defining and quantifying non-Markovian behavior as well as applications in quantum information and simulation protocols [20][21][22], foundational issues of quantum mechanics, [23] and even studies in condensed matter is incredibly vast [24][25][26][27][28][29][30]. Although no unique answer regarding the physical nature of non-Markovianity is currently available, its intrinsic multifaceted aspect has surely sparked interest in a plethora of different fields.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits

et al. 2018

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The exploitation and characterization of memory effects arising from the interaction between system and environment is a key prerequisite for quantum reservoir engineering beyond the standard Markovian limit. In this paper we investigate a prototype of non-Markovian dynamics experimentally implementable with superconducting qubits. We rigorously quantify non-Markovianity, highlighting the effects of the environmental temperature on the Markovian to non-Markovian crossover. We investigate how memory effects influence, and specifically suppress, the ability to perform work on the driven qubit. We show that the average work performed on the qubit can be used as a diagnostic tool to detect the presence or absence of memory effects.

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Dynamics of incompatibility of quantum measurements in open systems

Cited by 10 publications

References 45 publications

Incompatibility robustness of quantum measurements: a unified framework

Incompatibility robustness of quantum measurements: a unified framework

Quantum resource control for noisy Einstein-Podolsky-Rosen steering with qubit measurements

Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits

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