Bounds on Instantaneous Nonlocal Quantum Computation

Gonzales, Alvin; Chitambar, Eric

doi:10.1109/tit.2019.2950190

Cited by 14 publications

(4 citation statements)

References 40 publications

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“…As another open question, note that our bounds are given in terms of the number of qubits. It is interesting to see whether it is possible to give a comparable proof which bounds an entanglement measure instead, as is done for instance by Gonzales and Chitambar [GC19] for controlled unitaries in this setting.…”

Section: Discussionmentioning

confidence: 99%

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A single-qubit position verification protocol that is secure against multi-qubit attacks

Bluhm,

Christandl,

Speelman

2021

Preprint

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While it is known that unconditionally secure position-based cryptography is impossible both in the classical and the quantum setting, it has been shown that some quantum protocols for position verification are secure against attackers which share a quantum state of bounded dimension. In this work, we consider the security of the qubit routing protocol. The protocol has the advantage that an honest prover only has to manipulate a single qubit and a classical string of length 2n. We show that the protocol is secure if each of the attackers holds at most n/2 − 3 qubits. With this, we show for the first time that there exists a quantum position verification protocol where the ratio between the quantum resources an honest prover needs and the quantum resources the attackers need to break the protocol is unbounded. The verifiers need only increase the amount of classical resources to force the attackers to use more quantum resources. Finally, we show that the qubit routing protocol is robust with respect to noise, making it appealing for applications.

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Section: Discussionmentioning

confidence: 99%

“…Different lines of work include the security of PV protocols against special forms of attacks [LL11, BFSS13, CL15, RG15, Spe16, OCCG20], the consideration of different measures of entanglement [GC19] or the investigation of different security models [Ken10,Unr14].…”

Section: Introductionmentioning

confidence: 99%

A single-qubit position verification protocol that is secure against multi-qubit attacks

Bluhm,

Christandl,

Speelman

2021

Preprint

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“…An extreme example is INQC, which, instead of classical communication, only allows the broadcast of local results. Such class of operations has been termed as LOBC [104], as a subset of LOCC. A primary setting is a two-party nonlocal task: A and B each gets an input x, y, and then use LOBC operations to output a, b, which are then used to compute the result f (x, y).…”

Section: Post-magical Quantum Computingmentioning

confidence: 99%

Universal resources for quantum computing

Wang

2023

Commun. Theor. Phys.

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Unravelling the source of quantum computing power has been a major goal in the field of quan tum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require in vestigation. The so-called universal quantum computing model (UQCM), e.g., the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum com puters etc. In this work, we combine the study of UQCM together with QRT. We find, on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among resources and classify them.We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum ofUQCMs and the corresponding universal resources. Depending on a hierarchical structure of resourcetheories, we find models can be classified into families. In this work, we study three natural familiesof UQCMs in details: the amplitude family, the quasi-probability family, and the Hamiltonian family.They include some well known models, like the measurement-based model and adiabatic model, andalso inspire new models such as the contextual model we introduce. Each family contains at leasta triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture toinvestigate resources and design models. It also provides a rigorous framework to resolve puzzles,such as the role of entanglement vs. interference, and unravel resource-theoretic features of quantumalgorithms.

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“…This has been referred to as broadcast LOCC (BLOCC) in Ref. [41], and this model has also been consider in Ref. [42].…”

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confidence: 99%

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

Liu¹,

George²,

Chitambar³

2022

Preprint

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A powerful operational paradigm for distributed quantum information processing involves manipulating pre-shared entanglement by local operations and classical communication (LOCC). The LOCC round complexity of a given task describes how many rounds of classical communication are needed to complete the task. Despite some results separating one-round versus two-round protocols, very little is known about higher round complexities. In this paper, we revisit the task of one-shot random-party entanglement distillation as a way to highlight some interesting features of LOCC round complexity. We first show that for random-party distillation in three qubits, the number of communication rounds needed in an optimal protocol depends on the entanglement measure used; for the same fixed state some entanglement measures need only two rounds to maximize whereas others need an unbounded number of rounds. In doing so, we construct a family of LOCC instruments that require an unbounded number of rounds to implement. We then prove explicit tight lower bounds on the LOCC round number as a function of distillation success probability. Our calculations show that the original W-state random distillation protocol by Fortescue and Lo is essentially optimal in terms of round complexity.

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Bounds on Instantaneous Nonlocal Quantum Computation

Cited by 14 publications

References 40 publications

A single-qubit position verification protocol that is secure against multi-qubit attacks

A single-qubit position verification protocol that is secure against multi-qubit attacks

Universal resources for quantum computing

The Round Complexity of Local Operations and Classical Communication (LOCC) in Random-Party Entanglement Distillation

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