Quantum vs Noncontextual Semi-Device-Independent Randomness Certification

We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterized. We study randomness certification based on state discrimination and take noncontextuality as the notion of classicality. A contextual advantage was recently shown to exist for state discrimination. Here, we develop quantum and noncontextual semi-device independent protocols for random-number generation based on maximum-confidence discrimination, which generalizes unambiguous and minimum-error state discrimination. We show that, for quantum eavesdroppers, quantum devices can certify more randomness than noncontextual ones whenever none of the input states are unambiguously identified. That is, a quantum-over-classical advantage exists.We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterized. We study randomness certification based on state discrimination and take noncontextuality as the notion of classicality. A contextual advantage was recently shown to exist for state discrimination. Here, we develop quantum and noncontextual semi-device independent protocols for random-number generation based on maximum-confidence discrimination, which generalizes unambiguous and minimum-error state discrimination. We show that, for quantum eavesdroppers, quantum devices can certify more randomness than noncontextual ones whenever none of the input states are unambiguously identified. That is, a quantum-over-classical advantage exists.

arXiv:2112.09678Physical Review LettersJul 25, 20220 citations

Contextual advantages across two-state discrimination strategies

Kieran Flatt, Joonwoo Bae

Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum-error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum-confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results show that contextual advantages are observed across all two-state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over noncontextual theories.Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive outcomes across various guessing strategies. For minimum-error discrimination, the advantage is in terms of the confidences of individual outcomes, while for unambiguous state discrimination, it is in terms of the average guessing probability. For maximum-confidence discrimination, we show that contextual advantages occur not only for the confidence but also their average, the guessing probability, as well as the inconclusive outcome rate. Our results show that contextual advantages are observed across all two-state discrimination schemes and figures of merit. We envisage that various quantum information applications based on state discrimination may offer advantages over noncontextual theories.

quant-pharXiv:2511.04100New Journal of PhysicsNov 7, 20252 citations

Contextual Advantages and Certification for Maximum-Confidence Discrimination

Kieran Flatt, Hanwool Lee, Carles Roch i Carceller +2 more

One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal quantum states.In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination.We first show that maximum-confidence discrimination, as well as unambiguous discrimination, contains contextual advantages.We then consider a semi-device-independent scenario of certifying maximum-confidence measurement.The scenario naturally contains undetected events, making it a natural setting to explore maximum-confidence measurements.We show that the certified maximum confidence in quantum theory also contains contextual advantages.Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.One of the most fundamental results in quantum information theory is that no measurement can perfectly discriminate between nonorthogonal quantum states.In this work, we investigate quantum advantages for discrimination tasks over noncontextual theories by considering a maximum-confidence measurement that unifies different strategies of quantum state discrimination, including minimum-error and unambiguous discrimination.We first show that maximum-confidence discrimination, as well as unambiguous discrimination, contains contextual advantages.We then consider a semi-device-independent scenario of certifying maximum-confidence measurement.The scenario naturally contains undetected events, making it a natural setting to explore maximum-confidence measurements.We show that the certified maximum confidence in quantum theory also contains contextual advantages.Our results establish how the advantages of quantum theory over a classical model may appear in a realistic scenario of a discrimination task.

arXiv:2112.09626PRX QuantumSep 13, 202246 citations

Optimal and Feasible Contextuality-Based Randomness Generation

Yuan Liu, Ravishankar Ramanathan

Semi-device-independent randomness generation protocols based on Kochen-Specker contextuality offer the attractive features of compact devices, high rates, and ease of experimental implementation over fully device-independent (DI) protocols. Here, we investigate this paradigm and derive four results to improve the state of the art. Firstly, we introduce a family of simple, experimentally feasible orthogonality graphs (measurement compatibility structures) for which the maximum violation of the corresponding noncontextuality inequalities allows the certification of the maximum amount of log_{2}d bits of randomness from a qudit system with projective measurements for d≥3. We analytically derive the Lovász theta and fractional packing number for this graph family, and thereby prove their utility for optimal randomness generation in both randomness expansion and amplification tasks. Secondly, a central additional assumption in contextuality-based protocols over fully DI ones is that the measurements are repeatable and satisfy an intended compatibility structure. We frame a relaxation of this condition in terms of ϵ-orthogonality graphs for a parameter ϵ>0, and derive quantum correlations that allow the certification of randomness for arbitrary relaxation ϵ∈[0,1). Thirdly, it is well-known that a single qubit is noncontextual, i.e., the qubit correlations can be explained by a noncontextual hidden variable model. We show however that a single qubit is almost contextual in that there exist qubit correlations that cannot be explained by ϵ-faithful noncontextual hidden variable models for small ϵ>0. Finally, we point out possible attacks by quantum and general consistent (nonsignaling) adversaries for certain classes of contextuality tests over and above those considered in DI scenarios.Semi-device-independent randomness generation protocols based on Kochen-Specker contextuality offer the attractive features of compact devices, high rates, and ease of experimental implementation over fully device-independent (DI) protocols. Here, we investigate this paradigm and derive four results to improve the state of the art. Firstly, we introduce a family of simple, experimentally feasible orthogonality graphs (measurement compatibility structures) for which the maximum violation of the corresponding noncontextuality inequalities allows the certification of the maximum amount of log_{2}d bits of randomness from a qudit system with projective measurements for d≥3. We analytically derive the Lovász theta and fractional packing number for this graph family, and thereby prove their utility for optimal randomness generation in both randomness expansion and amplification tasks. Secondly, a central additional assumption in contextuality-based protocols over fully DI ones is that the measurements are repeatable and satisfy an intended compatibility structure. We frame a relaxation of this condition in terms of ϵ-orthogonality graphs for a parameter ϵ>0, and derive quantum correlations that allow the certification of randomness for arbitrary relaxation ϵ∈[0,1). Thirdly, it is well-known that a single qubit is noncontextual, i.e., the qubit correlations can be explained by a noncontextual hidden variable model. We show however that a single qubit is almost contextual in that there exist qubit correlations that cannot be explained by ϵ-faithful noncontextual hidden variable models for small ϵ>0. Finally, we point out possible attacks by quantum and general consistent (nonsignaling) adversaries for certain classes of contextuality tests over and above those considered in DI scenarios.

arXiv:2412.20126Physical Review LettersOct 3, 20251 citation

Sequential semi-device-independent quantum randomness certification

Carles Roch i Carceller, Hanwool Lee, Jonatan Bohr Brask +2 more

Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the context of semi-device-independent randomness certification using sequential maximum-confidence measurements. We develop a general framework and versatile numerical methods to bound the amount of certifiable randomness in such scenarios. We further introduce a technique to compute min-tradeoff functions via semidefinite programming duality, thus making the framework suitable for bounding the certifiable randomness against adaptive attacking strategies through entropy accumulation. Our results establish sufficient criteria showing that maximum-confidence measurements enable the distribution and certification of randomness across a sequential measurement chain in single-party systems.Quantum measurements under realistic conditions reveal only partial information about a system. Yet, by performing sequential measurements on the same system, additional information can be accessed. We investigate this problem in the context of semi-device-independent randomness certification using sequential maximum-confidence measurements. We develop a general framework and versatile numerical methods to bound the amount of certifiable randomness in such scenarios. We further introduce a technique to compute min-tradeoff functions via semidefinite programming duality, thus making the framework suitable for bounding the certifiable randomness against adaptive attacking strategies through entropy accumulation. Our results establish sufficient criteria showing that maximum-confidence measurements enable the distribution and certification of randomness across a sequential measurement chain in single-party systems.

arXiv:2510.19445Physical Review ResearchApr 25, 20260 citations

Semi-device-independent randomness certification using n→1 quantum random access codes

Hong-Wei Li, Marcin Pawłowski, Zhen−Qiang Yin +2 more

We study random-number-expansion protocols based on the $n\ensuremath{\rightarrow}1$ quantum random access codes (QRACs). We consider them in the semi-device-independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions of the systems being communicated. This approach does not require the use of entanglement and makes the physical realization of these protocols much easier than in the standard device-independent scenario. In our work, we propose a protocol for randomness expansion, compute min-entropy for the semi-device-independent protocol, and investigate $n\ensuremath{\rightarrow}1$ QRACs with a view to their use in randomness-expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on $n$ and find it optimal for $n=3$ , and provide the explanation for this fact.We study random-number-expansion protocols based on the $n\ensuremath{\rightarrow}1$ quantum random access codes (QRACs). We consider them in the semi-device-independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions of the systems being communicated. This approach does not require the use of entanglement and makes the physical realization of these protocols much easier than in the standard device-independent scenario. In our work, we propose a protocol for randomness expansion, compute min-entropy for the semi-device-independent protocol, and investigate $n\ensuremath{\rightarrow}1$ QRACs with a view to their use in randomness-expansion protocols. We also calculate the dependence of the effectiveness of the randomness generation on $n$ and find it optimal for $n=3$, and provide the explanation for this fact.

arXiv:1109.5259Physical Review AMay 11, 2012111 citations

n

and find it optimal for

n=3

, and provide the explanation for this fact.