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:2409.17185

Characterizing the set of quantum correlations in prepare-and-measure quantum chain-shaped networks

Ya Jia, Fen-Zhuo Guo, Yukun Wang, Haifeng Dong, Fei Gao

Published Sep 25, 2024• 0 citations
arXivHTMLPDF

Abstract

We introduce a hierarchy of tests satisfied by any probability distribution $P$ that represents the quantum correlations generated in prepare-and-measure (P\&M) quantum chain-shaped networks, assuming only the inner-product information of the non-orthogonal quantum states. The P\&M quantum chain-shaped networks involve multiple measurement parties, each measurement party potentially having multiple sequential receivers. Specifically, we adapt the original NPA-hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P\&M quantum chain-shaped networks. These constraints in each hierarchy are derived from sequential measurement operators and the inner-product matrix of the non-orthogonal quantum states. We apply the adapted NPA-hierarchy to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the $2 \to 1$ sequential QRACs. Furthermore, we have investigated semi-device-independent randomness certification in the double violation region of $2 \to 1$ sequential QRACs. Second, considering the presence of eavesdropper (Eve) in actual communication, we show how much global and local randomness can be certified using the optimal trade-off of $2 \to 1$ sequential QRACs. Additionally, we quantify the amount of local and global randomness that can be certified from the complete probabilities generated by the two sequential receivers. We conclude that utilizing the complete set of probabilities certifies more local and global randomness than relying solely on the optimal trade-off relationship.

DOI
10.48550/arxiv.2409.17185

Related papers

Characterizing the set of quantum correlations in prepare-and-measure quantum multichain-shaped networks

Ya Jia, Fen-Zhuo Guo, Yukun Wang +2 more

We introduce a hierarchy of tests satisfied by any probability distribution $P$ that represents the quantum correlations generated in prepare-and-measure (P) quantum multichain-shaped networks, assuming only the inner-product information of prepared states. The P quantum multichain-shaped networks involve multiple measurement parties, with each measurement party potentially having multiple sequential receivers. We adapt the original Navascu\'es, Pironio, and Ac\'{\i}n (NPA) hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P quantum multichain-shaped networks. These constraints in each hierarchy are derived from sequential measurements and the inner-product matrix of prepared states. The adapted NPA hierarchy is further applied to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and semi-device-independent randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the $2\ensuremath{\rightarrow}1$ sequential QRACs, and investigate randomness certification in its double violation region. Second, considering the presence of an eavesdropper in actual communication, we show how much local and global randomness can be certified using the optimal trade-off of $2\ensuremath{\rightarrow}1$ sequential QRACs. We also quantify the amount of local and global randomness that can be certified from the complete set of probabilities generated by the two sequential receivers. Our conclusion is that utilizing the full set of probabilities certifies more randomness than relying solely on the optimal trade-off relationship.

Physical Review A•Feb 24, 2025•3 citations

Sequential random access codes and self-testing of quantum measurement instruments

Karthik Mohan, Armin Tavakoli, Nicolas Brunner

Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

•Jan 1, 2019•22 citations

Sequential random access codes and self-testing of quantum measurement instruments

Karthik Mohan, Armin Tavakoli, Nicolas Brunner

Abstract Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

arXiv:1905.06726•New Journal of Physics•Jul 31, 2019•85 citations

Randomness Certification and Trade-offs in the Prepare-and-Broadcast Scenario

Tailan S. Sarubi, Moisés Alves, Vinícius F. Alves +4 more

We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.

quant-pharXiv:2608.08329•Aug 11, 2026•0 citations

Bounding sets of sequential quantum correlations and device-independent randomness certification

Joseph Bowles, Flavio Baccari, Alexia Salavrakos

An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.

arXiv:1911.11056•Quantum•Oct 19, 2020•36 citations

Sequential random access codes and self-testing of quantum instruments

Karthik Mohan, Armin Tavakoli, Nicolas Brunner

Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.

•May 16, 2019•0 citations
We introduce a hierarchy of tests satisfied by any probability distribution PPP that represents the quantum correlations generated in prepare-and-measure (P&M) quantum chain-shaped networks, assuming only the inner-product information of the non-orthogonal quantum states. The P&M quantum chain-shaped networks involve multiple measurement parties, each measurement party potentially having multiple sequential receivers. Specifically, we adapt the original NPA-hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P&M quantum chain-shaped networks. These constraints in each hierarchy are derived from sequential measurement operators and the inner-product matrix of the non-orthogonal quantum states. We apply the adapted NPA-hierarchy to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the 2→12 \to 12→1 sequential QRACs. Furthermore, we have investigated semi-device-independent randomness certification in the double violation region of 2→12 \to 12→1 sequential QRACs. Second, considering the presence of eavesdropper (Eve) in actual communication, we show how much global and local randomness can be certified using the optimal trade-off of 2→12 \to 12→1 sequential QRACs. Additionally, we quantify the amount of local and global randomness that can be certified from the complete probabilities generated by the two sequential receivers. We conclude that utilizing the complete set of probabilities certifies more local and global randomness than relying solely on the optimal trade-off relationship.
We introduce a hierarchy of tests satisfied by any probability distribution PPP that represents the quantum correlations generated in prepare-and-measure (P) quantum multichain-shaped networks, assuming only the inner-product information of prepared states. The P quantum multichain-shaped networks involve multiple measurement parties, with each measurement party potentially having multiple sequential receivers. We adapt the original Navascu\'es, Pironio, and Ac\'{\i}n (NPA) hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P quantum multichain-shaped networks. These constraints in each hierarchy are derived from sequential measurements and the inner-product matrix of prepared states. The adapted NPA hierarchy is further applied to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and semi-device-independent randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the $2\ensuremath{\rightarrow}1$ sequential QRACs, and investigate randomness certification in its double violation region. Second, considering the presence of an eavesdropper in actual communication, we show how much local and global randomness can be certified using the optimal trade-off of $2\ensuremath{\rightarrow}1$ sequential QRACs. We also quantify the amount of local and global randomness that can be certified from the complete set of probabilities generated by the two sequential receivers. Our conclusion is that utilizing the full set of probabilities certifies more randomness than relying solely on the optimal trade-off relationship.
Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.
Abstract Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.
We investigate the prepare-and-broadcast scenario, a multipartite extension of dimension-constrained prepare-and-measure experiments in which a quantum system is distributed to multiple receivers. We derive fundamental trade-offs between prepare-and-measure witnesses, Bell nonlocality, and quantum random access code performance. We further develop a semi-device-independent randomness certification framework based on prepare-and-broadcast witnesses, showing that the maximal quantum violation certifies two bits of joint randomness, exceeding the limit achievable from the CHSH inequality while remaining robust to noise. Finally, we show that the prepare-and-broadcast scenario naturally accommodates stronger adversarial models in which the eavesdropper retains a quantum system correlated with the measurement device, providing a natural framework for semi-device-independent randomness certification against quantum side information.
An important problem in quantum information theory is that of bounding sets of correlations that arise from making local measurements on entangled states of arbitrary dimension. Currently, the best-known method to tackle this problem is the NPA hierarchy; an infinite sequence of semidefinite programs that provides increasingly tighter outer approximations to the desired set of correlations. In this work we consider a more general scenario in which one performs sequences of local measurements on an entangled state of arbitrary dimension. We show that a simple adaptation of the original NPA hierarchy provides an analogous hierarchy for this scenario, with comparable resource requirements and convergence properties. We then use the method to tackle some problems in device-independent quantum information. First, we show how one can robustly certify over 2.3 bits of device-independent local randomness from a two-quibt state using a sequence of measurements, going beyond the theoretical maximum of two bits that can be achieved with non-sequential measurements. Finally, we show tight upper bounds to two previously defined tasks in sequential Bell test scenarios.
Quantum Random Access Codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.