Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Fu, Honghao

doi:10.22331/q-2022-01-03-614

Cited by 7 publications

(4 citation statements)

References 25 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our test requires constant size (1 trit) input questions for Alice, and for Bob requires O(log n) bit inputs. With a few exceptions [27][28][29][30] (in each of which robustness is either not explicitly constructed or doubly exponential in n), other works have achieved at best logarithmic input complexities (see for example [22,24]). In our protocol, one of the players need only receive questions of a constant size.…”

Section: Discussionmentioning

confidence: 99%

“…Work in another direction is offered by Šupić et al [27], who exhibit (without consideration of robustness) a constant-input-size parallel self-test for many copies of an arbitrary state given a self-test for a single copy. On self-testing maximally-entangled states of arbitrary local dimension d, the results of Fu [28] and Mančinska et al [29] provide robust self-tests using constant-sized questions and answers. However, the robustness of the former is exponential in d and in the latter is not constructed.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Practical parallel self-testing of Bell states via magic rectangles

Adamson¹,

Wallden²

2022

Phys. Rev. A

View full text Add to dashboard Cite

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Practical parallel self-testing of Bell states via magic rectangles

Adamson¹,

Wallden²

2022

Phys. Rev. A

View full text Add to dashboard Cite

“…All the previous discussion eventually might give the wrong impression that to identify and classify quantum correlations is a rather straightforward task. In fact, from a technical point of view this is not usually the case [9,[32][33][34]. But perhaps more surprisingly, in certain instances even a conceptual intuition about correlations can fail in the quantum context.…”

Section: Of 17mentioning

confidence: 99%

Correlations in the EPR States Observables

Orsini,

Oliveira,

Luz

2023

Preprint

View full text Add to dashboard Cite

The identification and physical interpretation of quantum correlations, more recently explored beyond entanglement, is not always a simple task. Two assumptions that, at least in principle, should lead to a relatively large dispersion for the observables of a quantum bipartite formed by systems I and II are to assume that; (a) all the possible observables describing the composite are potentially equally probable as outcomes of measurements; and (b) there cannot be concurrence (positive reinforcement) between any of the observables within a given system, meaning all their corresponding operators do not commute. The so-called EPR states are known to observe (a). Here we demonstrate in general terms that they also verify (b). As examples, we discuss three-level systems. Given the character of (a) and (b), one may expect the CHSH correlation for qubits to naturally violate its associated Bell’s inequality (i.e., it would yield values greater than 2) when applied to EPR states. Surprisingly, we show the CHSH contradicts such prediction. This finding emphasizes the subtleties of correlations in quantum mechanics, where the conceivable dispersive interdependence of EPR states observables results counterintuitively in a more limited range of values for the CHSH correlation, not surpassing the nonlocality threshold of 2.

show abstract

“…The literature on this nonlocal type of self-test is vast [ ŠB20]. They address topics such as which correlations can self-test which states, e.g., [CGS17, GKW + 18, BKM19]; how efficient and robust a self-test can be, e.g., [MYS12,McK17,NV17,NV18,CRSV18,Fu22]; and how to use self-testing to, e.g., certify a quantum computer's components [SBWS18], delegate quantum computations [RUV13,CGJV19], and characterize the complexity of quantum correlations [JNV + 20].…”

Section: Introductionmentioning

confidence: 99%

Computational self-testing of multi-qubit states and measurements

Fu¹,

Wang²,

Zhao³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Self-testing is a fundamental technique within quantum information theory that allows a classical verifier to force (untrusted) quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [MV21] showed that a single EPR pair of a single quantum device can be self-tested under standard computational assumptions. In this work, we generalize their techniques to give the first protocol that self-tests N EPR pairs and measurements in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N ) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ǫ must be poly(N, ǫ)-close to being honest in the appropriate sense. In particular, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which we cannot enforce spatial separation, using only classical communication.

show abstract

Constant-sized correlations are sufficient to self-test maximally entangled states with unbounded dimension

Cited by 7 publications

References 25 publications

Practical parallel self-testing of Bell states via magic rectangles

Practical parallel self-testing of Bell states via magic rectangles

Correlations in the EPR States Observables

Computational self-testing of multi-qubit states and measurements

Contact Info

Product

Resources

About