Hybrid Quantum Repeater Research Articles

Study of different performance measures and their relations in satellite‐based and terrestrial quantum communication

Rapid developments in quantum communication are paving the way forward for more advanced technologies. Conventional channels like optical fibres have been a great resource in recent decades. However, they suffer largely from exponential transmissivity decays and are not suitable for very long-distance communication. Satellite links along with quantum cryptography can be the foundation of modern quantum communication systems. This work presents an overview of the hybrid quantum repeater with a detailed analysis of different parametric relations in satellite-based communication from experimental data. The link efficiency between the satellite-based scheme and terrestrial scheme is also compared, emphasising the satellite-based scheme's importance for quantum communication. Finally, we present a performance analysis of different quantities and derive relations between them.

Memory-assisted long-distance phase-matching quantum key distribution

We propose a scheme that generalizes the loss scaling properties of twin-field or phase-matching quantum key distribution (QKD) related to a channel of transmission $\eta_{total}$ from $\sqrt{\eta_{total}}$ to $\sqrt[2n]{\eta_{total}}$ by employing n-1 memory stations with spin qubits and n beam-splitter stations including optical detectors. Our scheme's resource states are similar to the coherent-state-based light-matter entangled states of a previous hybrid quantum repeater, but unlike the latter our scheme avoids the necessity of employing 2n-1 memory stations and writing the transmitted optical states into the matter memory qubits. The full scaling advantage of this memory-assisted phase-matching QKD (MA-PM QKD) is obtainable with threshold detectors in a scenario with only channel loss. We mainly focus on the obtainable secret-key rates per channel use for up to n=4 including memory dephasing and for n=2 (i.e., $\sqrt[4]{\eta_{total}}$-MA-PM QKD assisted by a single memory station) for error models including dark counts, memory dephasing and depolarization, and phase mismatch. By combining the twin-field concept of interfering phase-sensitive optical states with that of storing quantum states up to a cutoff memory time, distances well beyond 700 km with rates well above $\eta_{total}$ can be reached for realistic, high-quality quantum memories (up to 1s coherence time) and modest detector efficiencies. Similarly, the standard single-node quantum repeater, scaling as $\sqrt{\eta_{total}}$, can be beaten when approaching perfect detectors and exceeding spin coherence times of 5s; beating ideal twin-field QKD requires 1s. As for further experimental simplifications, our treatment includes the notion of weak nonlinearities for the light-matter states, a discussion on the possibility of using homodyne detectors, and a comparison between sequential and parallel entanglement distributions.

Entanglement Swapping with Semiconductor-Generated Photons Violates Bell's Inequality.

Transferring entangled states between photon pairs is essential in quantum communication. Semiconductor quantum dots are the leading candidate for generating polarization-entangled photons deterministically. Here we show for the first time swapping of entangled states between two pairs of photons emitted by a single dot. A joint Bell measurement heralds the successful generation of the Bell state Ψ^{+}, yielding a fidelity of 0.81±0.04 and violating the CHSH and Bell inequalities. Our photon source matches atomic quantum memory frequencies, facilitating implementation of hybrid quantum repeaters.

Hybrid quantum repeater for qudits

We present a "hybrid quantum repeater" protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable $d$-level systems, each of, in principle, arbitrary dimension $d$, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially (but not restricted to) efficient continuous-variable homodyne detections ("hybrid" here refers to the simultaneous exploitation of discrete and continuous variable degrees of freedom for the local processing and storage of entangled states as well as their non-local distribution, respectively). For qutrits we quantify the light-matter entanglement that can be effectively shared through an elementary lossy channel, and for a repeater spacing of up to 10 km we show that the realistic (lossy) qutrit entanglement is even larger than any ideal (loss-free) qubit entanglement. After including qudit entanglement purification and swapping procedures, we calculate the long-distance entangled-pair distribution rates and the final entangled-state fidelities for total communication distances of up to 1280 km. With three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at rates of the order of, in principle, 100 Hz.

Erratum: Hybrid quantum repeater based on resonant qubit-field interactions [Phys. Rev. A 96 , 052329 (2017)

Erratum: Hybrid quantum repeater based on resonant qubit-field interactions [Phys. Rev. A <b>96</b> , 052329 (2017)

Device-independent secret-key-rate analysis for quantum repeaters

The device-independent approach to quantum key distribution (QKD) aims to establish a secret key between two or more parties with untrusted devices, potentially under full control of a quantum adversary. The performance of a QKD protocol can be quantified by the secret key rate, which can be lower bounded via the violation of an appropriate Bell inequality in a setup with untrusted devices. We study secret key rates in the device-independent scenario for different quantum repeater setups and compare them to their device-dependent analogon. The quantum repeater setups under consideration are the original protocol by Briegel et al. and the hybrid quantum repeater protocol by van Loock et al.. For a given repeater scheme and a given QKD protocol, the secret key rate depends on a variety of parameters, such as the gate quality or the detector efficiency. We systematically analyze the impact of these parameters and suggest optimized strategies.

Hybrid quantum repeater based on resonant qubit-field interactions

We propose a hybrid quantum repeater based on ancillary coherent field states and material qubits coupled to optical cavities. For this purpose, resonant qubit-field interactions and postselective field measurements are determined which are capable of realizing all necessary two-qubit operations for the actuation of the quantum repeater. We explore both theoretical and experimental possibilities of generating near-maximally-entangled qubit pairs ($F>0.999$) over long distances. It is shown that our scheme displays moderately low repeater rates, between $5 \times 10^{-4}$ and $23$ pairs per second, over distances up to $900$ km, and it relies completely on current technology of cavity quantum electrodynamics.

Centre-of-mass motion-induced decoherence and entanglement generation in a hybrid quantum repeater

Quantum communication over long distances relies on the ability to create entanglement between two remote quantum nodes. Recent proposals aiming at experimental realization propose a hybrid quantum repeater setup where two distant material qubits are entangled by light–matter interaction. Motivated by these developments, we investigate possible decoherence effects originating from the centre-of-mass motion of the spatially well-separated trapped qubits. Within the Lamb–Dicke regime we use photon exchange involving coherent states of the radiation field to entangle the two material qubits. Optimal generalized photonic field measurements are used to achieve entangled qubit pairs with high fidelities and high success probabilities. We demonstrate that the quality of the achievable two-qubit entanglement crucially depends on the trap frequencies involved. Furthermore, dynamical decoupling schemes are proposed which are capable of suppressing centre-of-mass motion-induced decoherence effects significantly and which involve only local operations acting on the spatially well-separated material qubits.

Hybrid entanglement purification for quantum repeaters

We present an entanglement purification protocol (EPP) to reconstruct some maximally hybrid entangled states (HESs) from nonmaximally mixed HESs. We use simple linear optical elements such as a polarization beam splitter (PBS) and beam splitter (BS) to achieve this task. Meanwhile, it is shown that the parity-check gates acted by PBS and BS are enough to complete the task, and the controlled-not (cnot) gates or similar logic operations are not needed. Unlike the current EPPs, this protocol can purify not only the conventional bit-flip error and phase-flip error but also the dissipation error coming from the photon loss of the coherent state. It can also be extended to achieve the purification for multiphoton and multicoherent state HES. This protocol may be useful in current hybrid quantum repeaters.

Quantum repeaters and quantum key distribution: Analysis of secret-key rates

We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution.

Hybrid quantum repeater with encoding

We present an encoded hybrid quantum repeater scheme using qubit-repetition and Calderbank-Shor-Steane codes. For the case of repetition codes, we propose an explicit implementation of the quantum error-correction protocol. Moreover, we analyze the entangled-pair distribution rate for the hybrid quantum repeater with encoding and we clearly identify a triple trade-off between the efficiency of the codes, the memory decoherence time, and the local gate errors. Finally, we show that in the presence of reasonable imperfections our system can achieve rates of roughly 24 Hz per memory for 20 km repeater spacing, a final distance of 1280 km, and a final fidelity of about 0.95.

Hybrid quantum repeater protocol with fast local processing

We propose a hybrid quantum repeater protocol combining the advantages of continuous and discrete variables. The repeater is based on the previous work of Brask et al. [Phys. Rev. Lett. 105, 160501 (2010)] but we present two ways of improving this protocol. In the previous protocol entangled single-photon states are produced and grown into superpositions of coherent states, known as two-mode cat states. The entanglement is then distributed using homodyne detection. To improve the protocol, we replace the time-consuming nonlocal growth of cat states with local growth of single-mode cat states, eliminating the need for classical communication during growth. Entanglement is generated in subsequent connection processes. Furthermore the growth procedure is optimized. We review the main elements of the original protocol and present the two modifications. Finally the two protocols are compared and the modified protocol is shown to perform significantly better than the original protocol.

Rate analysis for a hybrid quantum repeater

We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. The hybrid quantum repeater protocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. An exact, analytical formula for the rates of entanglement generation in quantum repeaters is derived, including a study on the impacts of entanglement purification and multiplexing strategies. More specifically, we consider scenarios with as little purification as possible and we show that for sufficiently low local losses, such purifications are still more powerful than multiplexing. In a possible experimental scenario, our hybrid system can create near-maximally entangled ($F=0.98$) pairs over a distance of 1280 km at rates of the order of 100 Hz.

Hybrid Long-Distance Entanglement Distribution Protocol

We propose a hybrid (continuous-discrete variable) quantum repeater protocol for long-distance entanglement distribution. Starting from states created by single-photon detection, we show how entangled coherent state superpositions can be generated by means of homodyne detection. We show that near-deterministic entanglement swapping with such states is possible using only linear optics and homodyne detectors, and we evaluate the performance of our protocol combining these elements.

Tight bound on coherent-state-based entanglement generation over lossy channels

The first stage of the hybrid quantum repeaters is entanglement generation based on transmission of pulses in coherent states over a lossy channel. Protocols to make entanglement with only one type of error are favorable for rendering subsequent entanglement distillation efficient. Here we provide the tight upper bound on performances of these protocols that is determined only by the channel loss. In addition, we show that this bound is achievable by utilizing a proposed protocol [arXiv:0811.3100] composed of a simple combination of linear optical elements and photon-number-resolving detectors.

Optimal entanglement generation for efficient hybrid quantum repeaters

We propose a realistic protocol to generate entanglement between quantum memories at neighboring nodes in hybrid quantum repeaters. Generated entanglement includes only one type of error, which enables efficient entanglement distillation. In contrast to the known protocols with such a property, our protocol with ideal detectors achieves the theoretical limit of the success probability and the fidelity to a Bell state, promising higher efficiencies in the repeaters. We also show that the advantage of our protocol remains even with realistic threshold detectors.

Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light

We describe a system for long-distance distribution of quantum entanglement, in which coherent light with large average photon number interacts dispersively with single, far-detuned atoms or semiconductor impurities in optical cavities. Entanglement is heralded by homodyne detection using a second bright light pulse for phase reference. The use of bright pulses leads to a high success probability for the generation of entanglement, at the cost of a lower initial fidelity. This fidelity may be boosted by entanglement purification techniques, implemented with the same physical resources. The need for more purification steps is well compensated for by the increased probability of success when compared to heralded entanglement schemes using single photons or weak coherent pulses with realistic detectors. The principal cause of the lower initial fidelity is fibre loss; however, spontaneous decay and cavity losses during the dispersive atom–cavity interactions can also impair performance. We show that these effects may be minimized for emitter-cavity systems in the weak-coupling regime as long as the resonant Purcell factor is larger than one, the cavity is over-coupled, and the optical pulses are sufficiently long. We support this claim with numerical, semiclassical calculations using parameters for three realistic systems: optically bright donor-bound impurities such as 19F:ZnSe with a moderate-Q microcavity, the optically dim 31P:Si system with a high-Q microcavity, and trapped ions in large but very high-Q cavities.