Overcoming erasure errors with multilevel systems

Muralidharan, Sreraman; Zou, Chang‐Ling; Li, Linshu; Wen, Jianming; Jiang, Liang

doi:10.1088/1367-2630/aa573a

Cited by 58 publications

(56 citation statements)

References 54 publications

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“…(24) ← uniform random sample from [0, 1] // Success probability: eq. (6)24 if u ≤ p dist (w A , w B ) then retry , w retry ← sample_dist(n, d)28 return t + t retry , w retry 29 end 30 end bility distribution of T +1 is calculated from the distribution of the conditional random variable T +1 |K as…”

mentioning

confidence: 99%

Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

Brand

Coopmans

Elkouss

2020

IEEE J. Select. Areas Commun.

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Quantum communication enables a host of applications that cannot be achieved by classical communication means, with provably secure communication as one of the prime examples. The distance that quantum communication schemes can cover via direct communication is fundamentally limited by losses on the communication channel. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. In this work, we provide two efficient algorithms for determining the generation time and fidelity of the first generated entangled pair between the end nodes of a quantum repeater chain. The runtime of the algorithms increases polynomially with the number of segments of the chain, which improves upon the exponential runtime of existing algorithms. Our first algorithm is probabilistic and can analyze refined versions of repeater chain protocols which include intermediate entanglement distillation. Our second algorithm computes the waiting time distribution up to a pre-specified truncation time, has faster runtime than the first one and is moreover exact up to machine precision. Using our proof-of-principle implementation, we are able to analyze repeater chains of thousands of segments for some parameter regimes. The algorithms thus serve as useful tools for the analysis of large quantum repeater chain protocols and topologies of the future quantum internet.

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mentioning

confidence: 99%

Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

Brand

Coopmans

Elkouss

2020

IEEE J. Select. Areas Commun.

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“…Note that QECCs do not exist for all code parameters, e.g., all QECCs fulfill the quantum singleton bound 2d − 1 ≤ n. However, if D is a prime number and d ≤ (D − 1)/2, an explicit construction of 2d − 1, 1, d D QECCs saturating the quantum singleton bound is known in the form of quantum polynomial codes [56][57][58][59]. We focus on this encoding because quantum polynomial codes can give an advantage over other QECCs for quantum repeaters [31,32].…”

Section: Error-corrected Qudit Repeaters and The Quantum-repeater Gainmentioning

confidence: 99%

“…(See Refs. [31][32][33][34] for previous investigations in quantum repeaters based on qudits.) To conclude that a quantum repeater can overcome the PLOB-repeaterless bound, it is instrumental to find a lower bound on the achievable quantum capacity of quantum repeaters.…”

Section: Introductionmentioning

confidence: 99%

Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

Miller

Holz

Kampermann

et al. 2019

Quantum

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A potential quantum internet would open up the possibility of realizing numerous new applications, including provably secure communication. Since losses of photons limit long-distance, direct quantum communication and widespread quantum networks, quantum repeaters are needed. The so-called PLOBrepeaterless bound [Pirandola et al., Nat. Commun. 8, 15043 (2017)] is a fundamental limit on the quantum capacity of direct quantum communication.Here, we analytically derive the quantum-repeater gain for error-corrected, one-way quantum repeaters based on higher-dimensional qudits for two different physical encodings: Fock and multimode qudits. We identify parameter regimes in which such quantum repeaters can surpass the PLOB-repeaterless bound and systematically analyze how typical parameters manifest themselves in the quantum-repeater gain. This benchmarking provides a guideline for the implementation of error-corrected qudit repeaters.Daniel Miller: daniel.miller@hhu.de arXiv:1906.05172v1 [quant-ph]

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“…This feature appears to be crucial in the case where one can select a part of the whole quantum state, which is affected by the decoherence. It is important to note that the suggested scheme is able in principle to supplement existing error correction and error suppression techniques [13,[15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Protecting quantum systems from decoherence with unitary operations

2020

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Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information processing devices. In this work, we suggest an approach for suppressing errors by employing pre-processing and post-processing unitary operations, which precede and follow the action of a decoherence channel. In contrast to quantum error correction and measurement-based methods, the suggested approach relies on specifically designed unitary operators for a particular state without the need in ancillary qubits or post-selection procedures. We consider the case of decoherence channels acting on a single qubit belonging to a many-qubit state. Pre-processing and post-processing operators can be either individual, that is acting on the qubit effected by the decoherence channel only, or collective, that is acting on the whole multi-qubit state. We give a classification of possible strategies for the protection scheme, analyze them, and derive expressions for the optimal unitary operators providing the maximal value of the fidelity regarding initial and final states. Specifically, we demonstrate the equivalence of the schemes where one of the unitary operations is individual while the other is collective. We then consider the realization of our approach for the basic decoherence models, which include single-qubit depolarizing, dephasing, and amplitude damping channels. We also demonstrate that the decoherence robustness of multi-qubit states for these decoherence models is determined by the entropy of the reduced state of the qubit undergoing the decoherence channel.

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Overcoming erasure errors with multilevel systems

Cited by 58 publications

References 54 publications

Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters

Protecting quantum systems from decoherence with unitary operations

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