A simple protocol for certifying graph states and applications in quantum networks

Markham, Damian; Krause, Alexandra

doi:10.48550/arxiv.1801.05057

Cited by 15 publications

(46 citation statements)

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“…This limitation can be overcome using quantum de Finetti arguments to obtain non-i.i.d. tomographic regions [23,99] and distance certificates [91], the use of which has been optimized in various works for the case of graph states [66,90] as well as for continuous variable states [22].…”

Section: Box 1: Measures Of Qualitymentioning

confidence: 99%

Quantum certification and benchmarking

Eisert,

Hangleiter,

Walk

et al. 2019

Preprint

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Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can be reached and their functioning guaranteed. This Expert Recommendation provides a brief overview of the known characterization methods of certification, benchmarking, and tomographic recovery of quantum states and processes, as well as their applications in quantum computing, simulation, and communication.

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Section: Box 1: Measures Of Qualitymentioning

confidence: 99%

Quantum certification and benchmarking

Eisert,

Hangleiter,

Walk

et al. 2019

Preprint

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“…As demonstrated by Markham and Krause in [10], the technique of stabiliser-based verification can be naturally extended to graph states. In Protocol 3, we give a modified version of their protocol that incorporates a failure threshold.…”

Section: Extension To Graph State Verificationmentioning

confidence: 99%

“…We use and extend a simple verification protocol from [9], based on measuring stabilisers of the state, which can be applied to more complicated situations such as verifying graph states [10]. Rather than requiring a large entangled state over multiple copies as in the quantum authentication scheme of [6], our protocol simply requires many separate copies of the state.…”

Section: Introductionmentioning

confidence: 99%

“…Graph states are a family of states which act as useful resources for quantum networks and computation, with applications including error correction [11], fault tolerant quantum computation [12,13], cryptography [14,15] and sensing [16,17]. As such, their verification is important and has been studied in various works [10,[18][19][20]. This work analyses more deeply the effect of noise in protocols such as that presented in [10].…”

Section: Introductionmentioning

confidence: 99%

“…As such, their verification is important and has been studied in various works [10,[18][19][20]. This work analyses more deeply the effect of noise in protocols such as that presented in [10].…”

Section: Introductionmentioning

confidence: 99%

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Authenticated teleportation and verification in a noisy network

Unnikrishnan,

Markham

2019

Preprint

Self Cite

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Authenticated teleportation aims to certify the transmission of a quantum state through teleportation, even in the presence of an adversary. This scenario can be pictured in terms of an untrusted source distributing a Bell state between two parties who wish to verify it using some simple tests. We propose a protocol that achieves this goal in a practical way, and analyse its performance and security when the parties have noisy measurement devices. Further, we model a realistic experimental scenario where the state is subject to noise and dephasing. We finally apply our analysis to the verification of graph states with noisy measurement devices.

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Resource-efficient verification of quantum computing using Serfling’s bound

et al. 2019

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Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks. In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing. Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one. The best protocol currently known requires O(n 15 ) copies of the state, where n is the size of the graph state. In this paper, we construct a significantly more resource-efficient verification protocol for graph states that only requires O(n 5 log n) copies. The key idea is to employ Serfling's bound, which is a probability inequality in classical statistics. Utilizing Serfling's bound also enables us to generalize our protocol for qudit and continuous-variable graph states. Constructing a resource-efficient verification protocol for them is non-trivial. For example, the previous verification protocols for qubit graph states that use the quantum de Finetti theorem cannot be generalized to qudit and continuous-variable graph states without tremendously increasing the resource overhead. This is because the overhead caused by the quantum de Finetti theorem depends on the local dimension. On the other hand, in our protocol, the resource overhead is independent of the local dimension, and therefore generalizing to qudit or continuous-variable graph states does not increase the overhead. The flexibility of Serfling's bound also makes our protocol robust: our protocol accepts slightly noisy but still

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A simple protocol for certifying graph states and applications in quantum networks

Cited by 15 publications

References 0 publications

Quantum certification and benchmarking

Quantum certification and benchmarking

Authenticated teleportation and verification in a noisy network

Resource-efficient verification of quantum computing using Serfling’s bound

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