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:2201.08649 · Entropy

Device-Independent Certification of Maximal Randomness from Pure Entangled Two-Qutrit States Using Non-Projective Measurements

Jakub J. Borkała, Chellasamy Jebarathinam, Shubhayan Sarkar, Remigiusz Augusiak

Published Feb 28, 2022• 14 citations
arXivHTMLPDF

Abstract

While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of 2log23 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl-Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.

DOI
10.3390/e24030350

Related papers

Optimal randomness certification from one entangled bit

Antonio Acín, Stefano Pironio, Tamás Vértesi +1 more

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.

arXiv:1505.03837•Physical Review A•Apr 18, 2016•139 citations

Self-Testing of any Pure Entangled State with the Minimal Number of Measurements and Optimal Randomness Certification in a One-Sided Device-Independent Scenario

Shubhayan Sarkar, Jakub J. Borkała, Chellasamy Jebarathinam +3 more

Certification of quantum systems and their properties has become a field of intensive study. Here, taking advantage of the one-sided device-independent (1SDI) scenario (also known as the quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including nonprojective ${d}^{2}$-outcome measurements, which in turn can be used for certification of the maximal amount of randomness, that is, $2{\mathrm{log}}_{2}d$ bits. Finally, in the particular case of $d=3$, we propose an extended Bell scenario that transforms a 1SDI scheme to ``almost device independent.''

arXiv:2110.15176•Physical Review Applied•Mar 13, 2023•21 citations

Maximal randomness from partially entangled states

Erik Woodhead, Jędrzej Kaniewski, Boris Bourdoncle +4 more

We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus.For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally.We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits.The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained.We point out this is a consequence of the fact that nonprojective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment.

arXiv:1901.06912•Physical Review Research•Nov 13, 2020•37 citations

Certification of the maximally entangled state using nonprojective measurements

Shubhayan Sarkar

In recent times, device-independent certification of quantum states has been one of the intensively studied areas in quantum information. However, all such schemes utilize projective measurements which are practically difficult to generate. In this paper, we consider the one-sided device-independent scenario and propose a self-testing scheme for the two-qubit maximally entangled state using nonprojective measurements, in particular, three three-outcome extremal positive operator-valued measures. We also analyze the robustness of our scheme against white noise.

arXiv:2210.14099•Physical Review A•Mar 8, 2023•8 citations

Certified Randomness From Steering Using Sequential Measurements

Brian Coyle, Elham Kashefi, Matty J. Hoban

The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, ie, we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.

•Dec 6, 2019•3 citations

Quantum randomness beyond projective measurements

Fionnuala Curran

The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness is then quantified by the probability that she correctly guesses the measurement outcomes, optimised over all possible strategies. Extremal measurements are appealing here, since they do not allow information to leak to such an eavesdropper. Beyond projective measurements, however, a simple question remains open: how much intrinsic randomness can be generated by a given extremal measurement? In a step towards solving it, we characterise the randomness generated by any unbiased extremal rank-one measurement acting on any state, solving the problem explicitly in dimension two. Four-outcome qubit measurements of this type are tomographic, so these results hold for fully source-device-dependent randomness too. The tetrahedral symmetric informationally complete (SIC) measurement, we find, has the least intrinsic randomness within this class. We also present the skewed SIC family of measurements, and use them to partially solve an open problem: we prove that $2 \log d$ bits of randomness, the maximal amount, can be generated device-dependently (or source-device-independently) in any dimension in which there exists a SIC measurement.

quant-pharXiv:2605.18291•Quantum Science and Technology•May 19, 2026•0 citations
While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way, the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of 2log23 random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit a device-independent method for certification of the full Weyl-Heisenberg basis in three-dimensional Hilbert spaces together with a one-sided device-independent method for certification of two-qutrit partially entangled states.
Certification of quantum systems and their properties has become a field of intensive study. Here, taking advantage of the one-sided device-independent (1SDI) scenario (also known as the quantum steering scenario), we propose a self-testing scheme for all bipartite entangled states using a single family of steering inequalities with the minimal number of two measurements per party. Building on this scheme we then show how to certify all rank-one extremal measurements, including nonprojective d2{d}^{2}d2-outcome measurements, which in turn can be used for certification of the maximal amount of randomness, that is, 2log2d2{\mathrm{log}}_{2}d2log2​d bits. Finally, in the particular case of d=3d=3d=3, we propose an extended Bell scenario that transforms a 1SDI scheme to ``almost device independent.''
We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus.For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally.We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits.The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained.We point out this is a consequence of the fact that nonprojective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment.
In recent times, device-independent certification of quantum states has been one of the intensively studied areas in quantum information. However, all such schemes utilize projective measurements which are practically difficult to generate. In this paper, we consider the one-sided device-independent scenario and propose a self-testing scheme for the two-qubit maximally entangled state using nonprojective measurements, in particular, three three-outcome extremal positive operator-valued measures. We also analyze the robustness of our scheme against white noise.
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, ie, we do not need to make assumptions about the devices used. Due to the work of Curchod et al. a single entangled two-qubit pure state can be used to produce arbitrary amounts of certified randomness. However, the obtaining of this randomness is experimentally challenging as it requires a large number of measurements, both projective and general. Motivated by these difficulties in the device-independent setting, we instead consider the scenario of one-sided device independence where certain devices are trusted, and others are not; a scenario motivated by asymmetric experimental set-ups such as ion-photon networks. We show how certain aspects of previous works can be adapted to this scenario and provide theoretical bounds on the amount of randomness that can be certified. Furthermore, we give a protocol for unbounded randomness certification in this scenario, and provide numerical results demonstrating the protocol in the ideal case. Finally, we numerically test the possibility of implementing this scheme on near-term quantum technologies, by considering the performance of the protocol on several physical platforms.
The unpredictability of quantum physics gives rise to intrinsic randomness. In an adversarial scenario, any additional degrees of freedom must be attributed to an eavesdropper with correlations to the measurement set-up. The true randomness is then quantified by the probability that she correctly guesses the measurement outcomes, optimised over all possible strategies. Extremal measurements are appealing here, since they do not allow information to leak to such an eavesdropper. Beyond projective measurements, however, a simple question remains open: how much intrinsic randomness can be generated by a given extremal measurement? In a step towards solving it, we characterise the randomness generated by any unbiased extremal rank-one measurement acting on any state, solving the problem explicitly in dimension two. Four-outcome qubit measurements of this type are tomographic, so these results hold for fully source-device-dependent randomness too. The tetrahedral symmetric informationally complete (SIC) measurement, we find, has the least intrinsic randomness within this class. We also present the skewed SIC family of measurements, and use them to partially solve an open problem: we prove that 2log⁡d2 \log d2logd bits of randomness, the maximal amount, can be generated device-dependently (or source-device-independently) in any dimension in which there exists a SIC measurement.