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:1909.12759 · Quantum

Device-independent certification of tensor products of quantum states using single-copy self-testing protocols

Ivan Šupić, Daniel Cavalcanti, Joseph Bowles

Published Mar 23, 2021• 14 citations
arXivHTMLPDF

Abstract

Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.

DOI
10.22331/q-2021-03-23-418

Related papers

Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

Shubhayan Sarkar, Debashis Saha, Jędrzej Kaniewski +1 more

Abstract Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d -outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, $${{{\mathrm{log}}}\,}_{2}d$$ log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.

arXiv:1909.12722•npj Quantum Information•Oct 14, 2021•56 citations

Self-testing of Pauli observables for device-independent entanglement certification

Joseph Bowles, Ivan Šupić, Daniel Cavalcanti +1 more

We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension ${2}^{n}$ for $n\ensuremath{\in}\mathbb{N}$. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement-device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.

arXiv:1801.10446•Physical Review A•Oct 29, 2018•77 citations

Experimental Robust Self-Testing of the State Generated by a Quantum Network

Iris Agresti, Beatrice Polacchi, Davide Poderini +7 more

Self-testing is a method of quantum state and measurement estimation that does not rely on assumptions about the inner working of the devices used.Its experimental realization has been limited to sources producing single quantum states so far.In this work, we experimentally implement two significant building blocks of a quantum network involving two independent sources: namely, a parallel configuration, in which two parties share two copies of a state, and a tripartite configuration, where a central node shares two independent states with peripheral nodes.Then, by extending previous self-testing techniques, we provide device-independent lower bounds on the fidelity between the generated states and an ideal target made by the tensor product of two maximally entangled two-qubit states.Given its scalability and versatility, this technique can find application in the certification of larger networks of different topologies for quantum communication and cryptography tasks and randomness generation protocols.

arXiv:2010.07737•PRX Quantum•Jun 24, 2021•28 citations

Sample-Efficient Device-Independent Quantum State Verification and Certification

Aleksandra Gočanin, Ivan Šupić, Borivoje Dakić

Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years.When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce.Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource.Such strong assumptions deprive the verification procedure of its truly device-independent character.In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.Remarkably, we show that device-independent verification can be performed with optimal sample efficiency.Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.

arXiv:2105.05832•PRX Quantum•Feb 1, 2022•32 citations

More Than One-bit Quantum Randomness Certification and Expansion

Amélie Piveteau, Alban Seguinard, Marcus Grünfeld +4 more

One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 23, 2025•0 citations

Almost device-independent certification of multipartite quantum states with minimal measurements

Shubhayan Sarkar, Alexandre C. Orthey, Gautam Sharma +2 more

Device-independent certification of quantum states enables the characterization of states within a device under minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. Aiming to address this problem, we consider a multipartite quantum steering scenario involving an arbitrary number of parties, of which only one is trusted, meaning that the measurements performed by this party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each, which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states: graph states of arbitrary local dimension, Schmidt states of arbitrary local dimension, and $N$-qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states. Restricting to qubits, we also lift our almost device-independent scheme to device-independent self-testing.

arXiv:2402.18522•Physical Review Applied•Feb 2, 2026•2 citations
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
Abstract Bell nonlocality as a resource for device-independent certification schemes has been studied extensively in recent years. The strongest form of device-independent certification is referred to as self-testing, which given a device, certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit–qudit entangled states based on violation of a single d -outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, log 2d{{{\mathrm{log}}}\,}_{2}dlog2​d log 2 d perfect random bits, while it requires only one random bit to encode the measurement choice.
We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension 2n{2}^{n}2n for $n\ensuremath{\in}\mathbb{N}$. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement-device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject [Bowles et al., Phys. Rev. Lett. 121, 180503 (2018)] and provides all the required technical proofs.
Self-testing is a method of quantum state and measurement estimation that does not rely on assumptions about the inner working of the devices used.Its experimental realization has been limited to sources producing single quantum states so far.In this work, we experimentally implement two significant building blocks of a quantum network involving two independent sources: namely, a parallel configuration, in which two parties share two copies of a state, and a tripartite configuration, where a central node shares two independent states with peripheral nodes.Then, by extending previous self-testing techniques, we provide device-independent lower bounds on the fidelity between the generated states and an ideal target made by the tensor product of two maximally entangled two-qubit states.Given its scalability and versatility, this technique can find application in the certification of larger networks of different topologies for quantum communication and cryptography tasks and randomness generation protocols.
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing.Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years.When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce.Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the asymptotic behavior of large, identically and independently distributed (IID) samples of a quantum resource.Such strong assumptions deprive the verification procedure of its truly device-independent character.In this paper, we develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime.Remarkably, we show that device-independent verification can be performed with optimal sample efficiency.Finally, for the case of independent copies, we develop a device-independent protocol for quantum state certification: a protocol in which a fragment of the resource copies is measured to warrant the rest of the copies to be close to some target state.
One of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing private unpredictable numbers even when obtained using devices delivered by an untrusted vendor. Thus, determining the quantity of certifiable randomness that can be produced using a specific set of non-local correlations is of significant interest. First, we present an experimental realization of recent Bell-type operators designed to provide private random numbers that are secure against adversaries with quantum resources. We use semi-definite programming to give lower bounds on the generated randomness in terms of both min-entropy and von Neumann entropy in a device-independent scenario. Our results demonstrate the first experiment that certifies nearly two bits of randomness from binary measurements of two parties [1], [2]. Apart from single-round certification, we provide an analysis of finite-key protocol for quantum randomness expansion using the Entropy Accumulation Theorem. Second, we present an efficient and practical method for certifying quantum randomness using generalized measurements. Indeed, we have derived a method for self-testing the presence of POVMs. We present the certification of more than one bit of min-entropy from a single POVM on one of the qubits of an entangled state using a variant of the elegant Bell inequality. We also obtain more than one bit of randomness in a prepare and measure scenario of a similar structure with a POVM on a single qubit [3]. We provide numerical simulations to demonstrate the effectiveness of our randomness certification and expansion.
Device-independent certification of quantum states enables the characterization of states within a device under minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. Aiming to address this problem, we consider a multipartite quantum steering scenario involving an arbitrary number of parties, of which only one is trusted, meaning that the measurements performed by this party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each, which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states: graph states of arbitrary local dimension, Schmidt states of arbitrary local dimension, and NNN-qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states. Restricting to qubits, we also lift our almost device-independent scheme to device-independent self-testing.