Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2209.14582 · Physical Review A

Measurement incompatibility and quantum advantage in communication

Debashis Saha, Debarshi Das, Arun Kumar Das, Bihalan Bhattacharya, A. S. Majumdar

Published Jun 12, 2023• 21 citations
arXivHTMLPDF

Abstract

Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from $d$-dimensional classical systems assisted with shared randomness is the same as the set obtained from $d$-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks---a general version of random access codes---to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on $d$-dimensional systems and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions---classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness---produced in communication scenarios.

DOI
10.1103/physreva.107.062210

Related papers

Certifying Measurement Incompatibility under Bounded Classical Communication

Oxana Shaya

Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most $k$ bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most $k$. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.

quant-pharXiv:2610.06722•Oct 6, 2026•0 citations

Quantum random access codes and incompatibility of measurements

Claudio Carmeli, Teiko Heinosaari, Alessandro Toigo

It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.

arXiv:1911.04360•Europhysics Letters (EPL)•Jun 26, 2020•45 citations

Genuine certification of incompatible quantum instruments through sequential communication tasks

Arindam Mitra, Satyaki Manna, Debashis Saha

Quantum instruments constitute the general description of quantum dynamics, encompassing both quantum measurements and quantum channels as special cases. Consequently, the incompatibility of quantum instruments represents a fundamental manifestation of nonclassicality in quantum theory. Here, we establish the operational significance of this notion by demonstrating communication tasks with classical inputs and outputs that enable the semi-device-independent certification of incompatible quantum instruments. We introduce a class of three-party communication tasks involving a sender, a relayer, and a receiver, and derive the tight upper bounds of the figure of merits of these tasks achievable by all compatible instruments implemented by the relayer. Furthermore, we show that these bounds coincide with the optimal performance attainable in a classical communication subject to the same dimensional constraints. Violation of this bound certifies the incompatibility of the pair of quantum instruments implemented by the relayer. This identifies certification of incompatible instruments as a manifestation of quantum advantage in communication. This certification protocol is genuine as it is able to certify the incompatibility of a pair of instruments where the set of induced measurements and the set of induced channels are compatible and, therefore it does not depend on the incompability of measurements and channels induced by the instruments. Finally, we identify the simplest instance of our communication scenario that enable the certification of incompatible quantum instruments.

quant-pharXiv:2606.23647•Jun 23, 2026•0 citations

Quantifying incompatibility of quantum measurements through non-commutativity

Krzysztof Mordasewicz, Jędrzej Kaniewski

Abstract The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While incompatibility might at first glance seem like an obstacle, it turns to be a necessary ingredient to achieve the so-called quantum advantage in various operational tasks like random access codes or key distribution. To improve our understanding of how to quantify incompatibility of quantum measurements, we define and explore a family of incompatibility measures based on non-commutativity. We investigate some basic properties of these measures, we show that they satisfy some natural information-processing requirements and we fully characterize the pairs which achieve the highest incompatibility (in a fixed dimension). We also consider the behavior of our measures under different types of compositions. Finally, to link our new measures to existing results, we relate them to a robustness-based incompatibility measure and two operational scenarios: random access codes and entropic uncertainty relations.

arXiv:2110.10646•Journal of Physics A Mathematical and Theoretical•May 20, 2022•12 citations

Distributed sampling, quantum communication witnesses, and measurement incompatibility

Leonardo Guerini, Marco Túlio Quintino, Leandro Aolita

We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully untrusted measurement device. A distributed-sampling task naturally arises in this scenario, where the goal is for Alice and Bob to reproduce the statistics of his measurements on her quantum inputs using a fixed communication channel. Their performance of this task can certify quantum communication (QC), and this is formalized by measurement-device-independent QC witnesses. Furthermore, we prove that QC can provide an advantage (over classical communication) for distributed sampling if and only if Bob's measurements are incompatible. This gives an operational interpretation to measurement incompatibility and motivates a generalized notion of it related to a subset of quantum states. Our findings have both fundamental and applied implications.

arXiv:1904.08435•Physical Review A•Oct 14, 2019•28 citations

Measurement-incompatibility constraints for maximal randomness

Tianqi Zheng, Yi Li, Yu Xiang +1 more

Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers, without relying on the Bell-inequality violations. By analyzing probability distributions directly, we identify a class of quantum states and projective measurements that achieve maximal randomness in bipartite and tripartite scenarios, ensuring practical feasibility. Further analysis reveals a counterintuitive trade-off governing measurement incompatibility among users: sufficient incompatibility for one user permits arbitrarily small incompatibility for others, defying conventional symmetry assumptions in the Bell test. This asymmetry provides a pathway to optimize device-independent protocols by strategically distributing quantum resources. Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.

arXiv:2505.17585•Physical Review A•Jan 5, 2026•0 citations
Measurement incompatibility stipulates the existence of quantum measurements that cannot be carried out simultaneously on single systems. We show that the set of input-output probabilities obtained from ddd-dimensional classical systems assisted with shared randomness is the same as the set obtained from ddd-dimensional quantum strategies restricted to compatible measurements with shared randomness in any communication scenario. Thus, measurement incompatibility is necessary for quantum advantage in communication, and any quantum advantage (with or without shared randomness) in communication acts as a witness to the incompatibility of the measurements at the receiver's end in a semi-device-independent way. We introduce a class of communication tasks---a general version of random access codes---to witness incompatibility of an arbitrary number of quantum measurements with arbitrary outcomes acting on ddd-dimensional systems and provide generic upper bounds on the success metric of these tasks for compatible measurements. We identify all sets of three incompatible rank-one projective qubit measurements that random access codes can witness. Finally, we present the generic relationship between different sets of probability distributions---classical, quantum with or without shared randomness, and quantum restricted to compatible measurements with or without shared randomness---produced in communication scenarios.
Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most kkk bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most kkk. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.
It is one of the peculiar features of quantum physics that some sets of measurements are incompatible in the sense that they cannot be performed simultaneously. Incompatibility is an important quantum resource as it enables Bell nonlocality and steering. Here we show that incompatibility is crucial also in certain communication tasks; we prove that quantum random access code performs better than its classical counterpart only when incompatible quantum measurements are used in the decoding task. As a consequence, evaluating the average success probability for quantum random access code provides a semi-device-independent test for the detection of quantum incompatibility. We further demonstrate that any incompatible pair of projective measurements gives an advantage over all classical strategies. Finally, we establish a connection between the maximal average success probability for quantum random access code and earlier quantities introduced to assess incompatibility.
Quantum instruments constitute the general description of quantum dynamics, encompassing both quantum measurements and quantum channels as special cases. Consequently, the incompatibility of quantum instruments represents a fundamental manifestation of nonclassicality in quantum theory. Here, we establish the operational significance of this notion by demonstrating communication tasks with classical inputs and outputs that enable the semi-device-independent certification of incompatible quantum instruments. We introduce a class of three-party communication tasks involving a sender, a relayer, and a receiver, and derive the tight upper bounds of the figure of merits of these tasks achievable by all compatible instruments implemented by the relayer. Furthermore, we show that these bounds coincide with the optimal performance attainable in a classical communication subject to the same dimensional constraints. Violation of this bound certifies the incompatibility of the pair of quantum instruments implemented by the relayer. This identifies certification of incompatible instruments as a manifestation of quantum advantage in communication. This certification protocol is genuine as it is able to certify the incompatibility of a pair of instruments where the set of induced measurements and the set of induced channels are compatible and, therefore it does not depend on the incompability of measurements and channels induced by the instruments. Finally, we identify the simplest instance of our communication scenario that enable the certification of incompatible quantum instruments.
Abstract The existence of incompatible measurements, i.e. measurements which cannot be performed simultaneously on a single copy of a quantum state, constitutes an important distinction between quantum mechanics and classical theories. While incompatibility might at first glance seem like an obstacle, it turns to be a necessary ingredient to achieve the so-called quantum advantage in various operational tasks like random access codes or key distribution. To improve our understanding of how to quantify incompatibility of quantum measurements, we define and explore a family of incompatibility measures based on non-commutativity. We investigate some basic properties of these measures, we show that they satisfy some natural information-processing requirements and we fully characterize the pairs which achieve the highest incompatibility (in a fixed dimension). We also consider the behavior of our measures under different types of compositions. Finally, to link our new measures to existing results, we relate them to a robustness-based incompatibility measure and two operational scenarios: random access codes and entropic uncertainty relations.
We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully untrusted measurement device. A distributed-sampling task naturally arises in this scenario, where the goal is for Alice and Bob to reproduce the statistics of his measurements on her quantum inputs using a fixed communication channel. Their performance of this task can certify quantum communication (QC), and this is formalized by measurement-device-independent QC witnesses. Furthermore, we prove that QC can provide an advantage (over classical communication) for distributed sampling if and only if Bob's measurements are incompatible. This gives an operational interpretation to measurement incompatibility and motivates a generalized notion of it related to a subset of quantum states. Our findings have both fundamental and applied implications.
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal randomness from observed probability distributions across systems with arbitrary user numbers, without relying on the Bell-inequality violations. By analyzing probability distributions directly, we identify a class of quantum states and projective measurements that achieve maximal randomness in bipartite and tripartite scenarios, ensuring practical feasibility. Further analysis reveals a counterintuitive trade-off governing measurement incompatibility among users: sufficient incompatibility for one user permits arbitrarily small incompatibility for others, defying conventional symmetry assumptions in the Bell test. This asymmetry provides a pathway to optimize device-independent protocols by strategically distributing quantum resources. Our results establish a versatile and experimentally accessible route to scalable randomness certification, with implications for quantum cryptography and the physics of nonlocal correlations.