A classical leash for a quantum system

Reichardt, Ben W.; Unger, Falk; Vazirani, Umesh

doi:10.1145/2422436.2422473

Cited by 45 publications

(65 citation statements)

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“…In particular, the existence of non-local correlations, apart from revealing a counter intuitive feature of nature, has led to the development of device-independent protocols for quantum key distribution (QKD), quantum random number generation (QRNG) and verified delegated quantum computation (VDQC) [3,[9][10][11][12][13][14][15][16]. In these applications two parties, Alice and Bob, do not trust their devices throughout the run of the protocol.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, approaches to QKD and QRNG rely on using a bound on the correlations of the parties' devices in order to derive a bound for a quantity of interest, such as key rate, mutual information, entropy etc [15,[27][28][29][30][31]. In contrast to this, existing protocols for device-independent VDQC use the bound on correlations to recover the underlying quantum state used in the protocol, as well as the operations being performed on this quantum state [9][10][11][12]. This allows for the correctness certification (referred to here as verification) of an arbitrary universal quantum computation strictly from the non-local correlations.…”

Section: Introductionmentioning

confidence: 99%

“…To achieve this one needs, at the same time, to obtain close to maximal non-local correlations and not only recover a characterisation of one Bell pair but of a tensor product of Bell pairs. Such a result is possible due to the rigidity of repeated CHSH games, manifesting non-local correlations, as shown in [9]. In this context, rigidity means that if two non-communicating devices playing CHSH games are achieving the optimal win rate, then they share a state which is close to a tensor product of maximally entangled states and, moreover, their strategy is fixed and uniquely determined.…”

Section: Introductionmentioning

confidence: 99%

“…However, in general, it is necessary to play a large number of games in order to certify few Bell states. For this reason the existing device-independent VDQC protocols have impractically large communication complexity [9,10,12].…”

Section: Introductionmentioning

confidence: 99%

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Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

Gheorghiu¹,

Wallden²,

Kashefi³

2017

Quantum Information and Measurement (QIM) 2017

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The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein et al (1935 Phys. Rev. 47 777-80). Tsirelson proved that Bell states, shared among two parties, when measured suitably, achieve the maximum non-local correlations allowed by quantum mechanics (Cirel'son 1980 Lett. Math. Phys. 4 93-100). Conversely, Reichardt et al showed that observing the maximal correlation value over a sequence of repeated measurements, implies that the underlying quantum state is close to a tensor product of maximally entangled states and, moreover, that it is measured according to an ideal strategy (Reichardt et al 2013 Nature 496 456-60). However, this strong rigidity result comes at a high price, requiring a large number of entangled pairs to be tested. In this paper, we present a significant improvement in terms of the overhead by instead considering quantum steering where the device of the one side is trusted. We first demonstrate a robust one-sided device-independent version of self-testing, which characterises the shared state and measurement operators of two parties up to a certain bound. We show that this bound is optimal up to constant factors and we generalise the results for the most general attacks. This leads us to a rigidity theorem for maximal steering correlations. As a key application we give a onesided device-independent protocol for verifiable delegated quantum computation, and compare it to other existing protocols, to highlight the cost of trust assumptions. Finally, we show that under reasonable assumptions, the states shared in order to run a certain type of verification protocol must be unitarily equivalent to perfect Bell states.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

Gheorghiu¹,

Wallden²,

Kashefi³

2017

Quantum Information and Measurement (QIM) 2017

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“…The resulting complexity class was proved to contain NEXP. Theorem 6.5 on simulating a quantum verifier by a classical one was proved in [142]. (See also [143] for a high-level exposition of the results.)…”

mentioning

confidence: 99%

Quantum Proofs

Vidick

Watrous

2016

FNT in Theoretical Computer Science

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Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum state plays the role of a proof (also called a certificate or witness), and is checked by a polynomial-time quantum computation. For some problems, the fact that a quantum proof state could be a superposition over exponentially many classical states appears to offer computational advantages over classical proof strings. In the interactive proof system setting, one may consider a verifier and one or more provers that exchange and process quantum information rather than classical information during an interaction for a given input string, giving rise to quantum complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit some properties from their classical counterparts, they also possess distinct and uniquely quantum features that lead to an interesting landscape of complexity classes based on variants of this model. In this survey we provide an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, we discuss non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class \class{QSZK}, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*.Comment: Survey published by NOW publisher

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Verifier-on-a-Leash: New Schemes for Verifiable Delegated Quantum Computation, with Quasilinear Resources

Coladangelo

Grilo

Jeffery

et al. 2019

Advances in Cryptology – EUROCRYPT 2019

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The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as O(g log g) for delegating a circuit of size g. This is in contrast to previous protocols, whose overhead in terms of resources employed, while polynomial, is far beyond what is feasible in practice. Our first protocol requires a number of rounds that is linear in the depth of the circuit being delegated, and is blind, meaning neither prover can learn the circuit or its input. The second protocol is not blind, but requires only a constant number of rounds of interaction.Our main technical innovation is an efficient rigidity theorem that allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of singlequbit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m. Our two-prover classical-verifier delegation protocols are obtained by combining this rigidity theorem with a single-prover quantum-verifier protocol for the verifiable delegation of a quantum computation, introduced by Broadbent (Theory of Computing, 2018).

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A classical leash for a quantum system

Cited by 45 publications

References 0 publications

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

Quantum Proofs

Verifier-on-a-Leash: New Schemes for Verifiable Delegated Quantum Computation, with Quasilinear Resources

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