Secret key rates for an encoded quantum repeater

Bratzik, Sylvia; Kampermann, Hermann; Bruß, Dagmar

doi:10.1103/physreva.89.032335

Cited by 23 publications

(44 citation statements)

References 29 publications

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“…The temporal resource depends on the rate, which is limited by the time delay from the two-way classical signaling (first and second generations) and the local gate operation (second and third generations, see details below) 23 . The physical resource depends on the total number of qubits needed for HEP (first and second generations) and QEC (second and third generations) 9 24 . We propose to quantitatively compare the three generations of QRs using a cost function 9 related to the required number of qubit memories to achieve a given transmission rate.…”

Section: Resultsmentioning

confidence: 99%

Optimal architectures for long distance quantum communication

Muralidharan

Kim

et al. 2016

Sci Rep

388

409

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Despite the tremendous progress of quantum cryptography, efficient quantum communication over long distances (≥1000 km) remains an outstanding challenge due to fiber attenuation and operation errors accumulated over the entire communication distance. Quantum repeaters (QRs), as a promising approach, can overcome both photon loss and operation errors, and hence significantly speedup the communication rate. Depending on the methods used to correct loss and operation errors, all the proposed QR schemes can be classified into three categories (generations). Here we present the first systematic comparison of three generations of quantum repeaters by evaluating the cost of both temporal and physical resources, and identify the optimized quantum repeater architecture for a given set of experimental parameters for use in quantum key distribution. Our work provides a roadmap for the experimental realizations of highly efficient quantum networks over transcontinental distances.

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Section: Resultsmentioning

confidence: 99%

Optimal architectures for long distance quantum communication

Muralidharan

Kim

et al. 2016

Sci Rep

388

409

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show abstract

“…As an alternative to entanglement distillation, several forward-quantumerror-corrected protocols have been proposed and analyzed [11,12], which can afford a better rate performance at the expense of more frequent memory-based repeaters capable of universal quantum logic. Some of the more recently proposed forward-coded protocols do not even need any matter quantum memories, but come at the expense of requiring fast quantum logic and feedforward at all-optical center stations, as well as a potentially huge overhead in terms of the number of photons used for error correction [13,14].…”

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confidence: 99%

Rate-loss analysis of an efficient quantum repeater architecture

et al. 2015

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We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multi-mode quantum memories and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss and noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle non-idealities, that this scheme achieves a secret key rate that surpasses the TGW bound-a recently-found fundamental limit to the rate-vs.-loss scaling achievable by any QKD protocol over a direct optical link-thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement distillation rate, as a function of the number of repeater nodes, total range, and various loss and noise parameters of the system. We extend our theoretical analysis to encompass sources with non-zero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols, and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.Shared entanglement underlies many quantum information protocols such as quantum key distribution (QKD) [1], teleportation [2] and dense coding [3], and is a fundamental information resource that can boost reliable classical and quantum communication rates over noisy quantum channels [4,5]. Optical photons are arguably the only candidate for distributing entanglement across long distances. They however are susceptible to loss and noise in the channel, which is the bane of practical realizations of long-distance quantum communication. The maximum entanglement-generation rate over a lossy optical channel with no classical-communication assistance is zero when the total loss exceeds 3 dB [6]. With two-way classical-communication assistance, the rates achievable for entanglement generation, as well as those for reliable quantum communication and secretkey generation (i.e., QKD) over a lossy optical channel must decay linearly with the channel's transmittance (i.e., exponentially with optical fiber length), regardless of the specific protocol used, for loss exceeding ∼ 5 dB [7], while the rate plunges to zero at a maximum loss threshold that is determined by the excess noise in the channel and detectors. In order to generate entanglement over long distances at high rates, intermediate nodes equipped with quant...

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“…However, the attenuation in the optical fiber poses a significant challenge for the long-distance transmission of single photons [9,10]. Quantum repeaters [11,12] solve the attenuation problem by dividing the total communication distance into shorter channels connected by intermediate nodes, where the photon loss is detected [13][14][15][16][17][18] and can be corrected by using an active mechanism [19][20][21][22][23][24][25][26]. In addition to photon loss errors, operation errors accumulate over the quantum channel that degrades the quality of the transmitted entangled state.…”

Section: Introductionmentioning

confidence: 99%

Quantum repeaters based on two species trapped ions

et al. 2019

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We examine the viability of quantum repeaters based on two-species trapped ion modules for longdistance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and memory ions and to achieve entanglement swapping between two memory ions. We describe simple modular quantum repeater architectures realizable with the ion-trap modules and numerically study the dependence of the quantum key distribution rate on various experimental parameters, including coupling efficiency, gate infidelity, operation time and length of the elementary links. Our analysis suggests crucial improvements necessary in a physical implementation for cotrapped two-species ions to be a competitive platform in long-distance quantum communication. efficiently entangled to photons and a different longer lived species of ions ( 9 Be + or 171 Yb + ) that can be utilized as a quantum memory qubit and for local processing. A high-fidelity transfer of quantum information between the two species of ions can also be achieved [29]. Furthermore, due to transition-frequency difference the optical operations with the communication ions do not disturb the quantum memory ions even though they are only a few microns away. Despite such experimental advances an analysis of quantum key generation rates, among the most promising uses of a quantum network, using TSTI for quantum repeaters is lacking.We describe in this paper a quantum repeater architecture based on modules of two species of trapped ions. We study the viability of using these modules as building blocks for the construction of long-distance quantum repeaters by analyzing quantum key distribution rates. The architecture can potentially work for any pair of communication and memory ions. For the numerical results later in the paper, however, we consider the advances made with the 171 Yb + -138 Ba + pair described in [41] with the following features: excellent isolation between 171 Yb + quantum memory ions and 138 Ba + communication ions was achieved and a state transfer between them was demonstrated; Ba + coherence times of 100 μs in unstabilized magnetic fields and a coherence time of 4 ms with stabilized magnetic fields were measured; same-species two-qubit gates between 171 Yb + ions with 98% fidelity and cross-species two-qubit gates between a 171 Yb + ion and 138 Ba + ion with 75% fidelty in 200 μs were demonstrated; light collection efficiency from the 138 Ba + ion of about 10% and fiber coupling efficiency of 17% in the absence of a cavity were reported. Our analysis suggests crucial improvements in the performance parameters that can maximize key generation rates. We foc...

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Secret key rates for an encoded quantum repeater

Cited by 23 publications

References 29 publications

Optimal architectures for long distance quantum communication

Optimal architectures for long distance quantum communication

Rate-loss analysis of an efficient quantum repeater architecture

Quantum repeaters based on two species trapped ions

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