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arXiv:0806.1153 · Physical Review A

Quantum repeaters using coherent-state communication

Peter van Loock, Norbert Lütkenhaus, William J. Munro, Kae Nemoto

Published Dec 10, 2008• 102 citations
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Abstract

We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.

DOI
10.1103/physreva.78.062319

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We investigate quantum repeater protocols based upon atomic qubit-entanglement distribution through optical coherent-state communication. Various measurement schemes for an optical mode entangled with two spatially separated atomic qubits are considered in order to nonlocally prepare conditional two-qubit entangled states. In particular, generalized measurements for unambiguous state discrimination enable one to completely eliminate spin-flip errors in the resulting qubit states, as they would occur in a homodyne-based scheme due to the finite overlap of the optical states in phase space. As a result, by using weaker coherent states, high initial fidelities can still be achieved for larger repeater spacing, at the expense of lower entanglement generation rates. In this regime, the coherent-state-based protocols start resembling single-photon-based repeater schemes.
We describe a quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between qubits at intermediate stations of the channel by using a weak dispersive light-matter interaction and distributing the outgoing bright coherent-light pulses among the stations. Noisy entangled pairs of electronic spin are then prepared with high success probability via homodyne detection and postselection. The local gates for entanglement purification and swapping are deterministic and measurement-free, based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Finally, the entanglement is stored in a nuclear-spin-based quantum memory. With our system, qubit-communication rates approaching 100 Hz over 1280 km with fidelities near 99% are possible for reasonable local gate errors.
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 ddd-level systems, each of, in principle, arbitrary dimension ddd, 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 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 nonlocal distribution, respectively) and unambiguous state discrimination. 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. For example, employing unambiguous state discrimination, with three rounds of purification, entangled qudit pairs of near-unit fidelity can be distributed over 1280 km at an ideal maximal rate (assuming perfect gate operations) on the order of 100 Hz.
We describe a practical quantum repeater protocol for long-distance quantum communication. In this scheme, entanglement is created between the intermediate nodes of the quantum channel by using a weak dispersive light-matter interaction and distributing the outgoing intense coherent light pulses among the nodes. Noisy entangled pairs of electronic spin are then prepared with high success probability via homodyne detection including postselection. The local gates for entanglement purification and swapping are deterministic and measurement-free, based upon the same coherent-light resources and weak interactions as for the initial entanglement distribution. Finally, the entanglement is stored in a nuclear-spin-based quantum memory. Simulations of the system show qubit-communication rates approaching 100 Hz and fidelities above 99 % for reasonable local gate errors.
We present an efficient quantum repeater protocol that uses coupled systems of quantum-dot spins and optical microcavities, in which the spatial entanglement of a photon system can be converted into polarization entanglement of electron spins. The bit-flip and phase-flip errors on the polarization state of each qubit caused by noisy channels can be rejected, without resorting to additional qubits. Two remote parties can obtain the maximally entangled electron-spin state and store it deterministically after the transmission of photons, independent of the noise parameters. The transmission distance of photons will not be limited by the coherence time of memory units in the present protocol, unlike the previous atomic-ensemble-based quantum repeater protocols, and it can be applied directly in long-distance quantum-communication protocols.
Entangled coherent states can be prepared remotely by subtracting nonlocally a single photon from two quantum superpositions of coherent states, the so-called “Schrödinger’s cat” state. Such entanglement can further be distributed over longer distances by successive entanglement swapping operations using linear optics and photon-number resolving detectors. The aim of this paper is to evaluate the performance of this approach to quantum repeaters for long-distance quantum communications. Despite many attractive features at first sight, we show that, when using state-of-the-art photon counters and quantum memories, they do not achieve higher entanglement generation rates than repeaters based on single-photon entanglement. We discuss potential developments, which may take better advantage of the richness of entanglement based on continuous variables, including in particular efficient parity measurements.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.