Capacity estimation and verification of quantum channels with arbitrarily correlated errors

Pfister, Corsin; Rol, Michiel Adriaan; Mantri, Atul; Tomamichel, Marco; Wehner, Stephanie

doi:10.1038/s41467-017-00961-2

Cited by 26 publications

(20 citation statements)

References 40 publications

(85 reference statements)

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“…Serfling's bound is a probability inequality for the sum in sampling without replacement, and is often used in classical statistics (for details, see Lemma 1). Serfling's bound has also been used in the security proofs of quantum key distribution [24][25][26][27], but to the best of our knowledge, so far, Serfling's bound has never been applied to the verification of quantum computation.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…1. We remark that there are other quantities of interest which do not assume an i.i.d structure, such as for example estimating the capacity as in [25].…”

Section: Setup and Workflowmentioning

confidence: 99%

Practical and reliable error bars for quantum process tomography

et al. 2019

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Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure-of-merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package-QPtomographer-implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Our tools can be used to reliably certify the performance of e.g. error correction codes, implementations of unitary gates or more generally any noise process affecting a quantum system.Usage: Secondary publications and information retrieval purposes.PACS numbers: May be entered using the \pacs{#1} command.Structure: You may use the description environment to structure your abstract; use the optional argument of the \item command to give the category of each item.

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“…[14][15][16]). More generally, a procedure is known to estimate the capacity of a quantum channel [17]). Finally, [18] gives a method certify whether a quantum network of nodes connected by quantum links has attained a specific stage of development.…”

Section: Introductionmentioning

confidence: 99%

A benchmarking procedure for quantum networks

Helsen¹,

Wehner²

2021

Preprint

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We propose network benchmarking: a procedure to efficiently benchmark the quality of a quantum network link connecting quantum processors in a quantum network. This procedure is based on the standard randomized benchmarking protocol and provides an estimate for the fidelity of a quantum network link. We provide statistical analysis of the protocol as well as a simulated implementation inspired by NV-center systems using Netsquid, a special purpose simulator for noisy quantum networks.

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Capacity estimation and verification of quantum channels with arbitrarily correlated errors

Cited by 26 publications

References 40 publications

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

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

Practical and reliable error bars for quantum process tomography

A benchmarking procedure for quantum networks

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