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arXiv:2112.08408 · Quantum Science and Technology

Experimentally determining the incompatibility of two qubit measurements

Andrea Smirne, S. Cialdi, Daniele Cipriani, Claudio Carmeli, Alessandro Toigo, Bassano Vacchini

Published Jan 24, 2022• 3 citations
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Abstract

Abstract We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons’ polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.

DOI
10.1088/2058-9565/ac4e6f

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Abstract We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons’ polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.
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.
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.
The existence of incompatible measurement setups is one of the distinctive features of quantum theory. Here we extend the notion of incompatibility from measurements that test preparations to measurements that test dynamical processes. Such measurements, known as testers, consist of the preparation of an input state, the application of the tested process, and a measurement on the output. Mathematically, testers are described by a suitable generalization of the notion of positive operator-valued measure (POVM). Unlike in the case of POVMs, however, testers that commute are not necessarily compatible, and testers that are compatible do not necessarily commute. Given a set of testers, we define the robustness of incompatibility as the minimum amount of mixing needed to make the testers compatible. We show that (i) the robustness is lower bounded by the distinguishability of the input states prepared by the different testers, and (ii) maximum robustness is attained when the input states are orthogonal. An extensive analysis of incompatibility is provided for factorized qubit testers with two outcomes. All our results can be extended to measurements that test quantum processes consisting of multiple time steps.
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.
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.