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Physical Review Research

Entanglement-free witnessing of quantum incompatibility in a high-dimensional system

Dian Wu, Qi Zhao, Yi-Han Luo, Han-Sen Zhong, Li-Chao Peng, Kai Chen, Peng Xue, Li Li, Nai-Le Liu, Chao‐Yang Lu, Jian-Wei Pan

Published Apr 6, 2021• 4 citations
Publisher

Abstract

Quantum incompatibility, as an important quantum resource, is believed to play a key role in quantum information processing tasks.In order to detect this property, an entanglement-free incompatibility witness is proposed via constructing a combined quantum state discrimination task with prior-measurement and postmeasurement information strategies.Here we experimentally implement the witness of the incompatibility of mutually unbiased measurements under different noise levels in a qutrit system.Moreover, we estimate the robustness of incompatibility using collected data.Our work paves the path for understanding quantum incompatibility and exploring the features of the quantum resource.

DOI
10.1103/physrevresearch.3.023017

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Quantum incompatibility, as an important quantum resource, is believed to play a key role in quantum information processing tasks.In order to detect this property, an entanglement-free incompatibility witness is proposed via constructing a combined quantum state discrimination task with prior-measurement and postmeasurement information strategies.Here we experimentally implement the witness of the incompatibility of mutually unbiased measurements under different noise levels in a qutrit system.Moreover, we estimate the robustness of incompatibility using collected data.Our work paves the path for understanding quantum incompatibility and exploring the features of the quantum resource.
We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases.
Incompatible measurements are of fundamental importance to revealing the peculiar features of quantum theory, and are also useful resources in various quantum information tasks. In this work, we investigate the quantum incompatibility of mutually unbiased bases (MUBs) within the operational framework of quantum resource theory, and report an experimental validation via the task of state discrimination. In particular, we construct an experimentally friendly witness to detect incompatible MUBs, based on the probability of correctly discriminating quantum states. Furthermore, we prove that the noise robustness of MUBs can be retrieved from violating the above witness. Finally, we experimentally test the incompatibility of MUBs of dimensionality ranging from 2 to 4, and demonstrate that it is more robust to noise, as either the dimensionality of measurements or the number of MUBs increases. Our results may aid the exploration of the essential roles of incompatible measurements in both theoretical and practical applications in quantum information.
We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination protocol according to this scheme. As an application, we characterize the joint measurability region of two noisy mutually unbiased bases.
Quantum incompatibility, referred as the phenomenon that some quantum measurements cannot be performed simultaneously, is necessary for various quantum information processing tasks, such as nonlocality and steering. When these applications come to high-dimensional multimeasurement scenarios, it is crucial and challenging to witness the incompatibility of measurements with complex structures. To address this problem, we propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pairwise ones and employs noise robustness to bound incompatibility structures. We then derive arithmetic bounds for arbitrary measurements and analytical bounds for mutually unbiased bases, and capture some quantum incompatibility structures where measurements are partly compatible and partly incompatible. Finally, we experimentally demonstrate our results and connect them with quantum steering, quantum simulability and quantum communications.
Abstract Quantum incompatibility is a fundamental property in quantum physics and is considered as a resource in quantum information processing tasks. Here, we construct a framework based on the incompatibility witness originated from quantum state discrimination. In this framework, we discuss the geometrical properties of the witnesses with noisy mutually unbiased bases and construct a quantifier of quantum incompatibility associated with geometrical information. Furthermore, we explore the incompatibility of a pair of positive operator valued measurements, which only depends on the information of measurements, and discuss the incompatibility of measurements which can be discriminated by mutually unbiased bases. Finally, if we take a resource-theory perspective, the new-defined quantifier can characterize the resource of incompatibility. This geometrical framework gives the evidence that vectors can be utilized to describe resourceful incompatibility and make a step to explore geometrical features of quantum resources.
Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource in tasks involving quantum state discrimination and quantum programmability. Here, we link quantum incompatibility with the amount of information that can be extracted from a system upon successive measurements of noncommuting observables, a scenario related to communication tasks. This approach leads us to characterize incompatibility as a resource encoded in a physical context, which involves both the quantum state and observables. Moreover, starting with a measure of context incompatibility we derive a measurement-incompatibility quantifier that is easily computable, admits a geometrical interpretation, and is maximum only if the eigenbases of the involved observables are mutually unbiased.