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arXiv:0908.2735 · Physical Review A

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

Koji Azuma, Naoya Sota, Masato Koashi, Nobuyuki Imoto

Published Feb 25, 2010• 7 citations
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Abstract

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 [K. Azuma, N. Sota, R. Namiki, \ifmmode \mbox{\c{S}}\else \c{S}\fi{}. K. \"Ozdemir, T. Yamamoto, M. Koashi, and N. Imoto, Phys. Rev. A 80, 060303(R) (2009)] composed of a simple combination of linear optical elements and photon-number-resolving detectors.

DOI
10.1103/physreva.81.022325

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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 [K. Azuma, N. Sota, R. Namiki, \ifmmode \mbox{\c{S}}\else \c{S}\fi{}. K. "Ozdemir, T. Yamamoto, M. Koashi, and N. Imoto, Phys. Rev. A 80, 060303(R) (2009)] composed of a simple combination of linear optical elements and photon-number-resolving detectors.
Entanglement is a fundamental resource not only for quantum communication but also for distributed quantum computation. Especially, entanglement including only one type of error is favorable, compared with one including multiple types of noise. In this talk, we consider protocol that presents single-error-type entanglement for distant qubits via coherent-state transmission over lossy channels. This protocol is considered to be a subroutine to serve entanglement for larger protocol to yield a final output, such as ebits or pbits. A protocol based on remote non-destructive parity measurement (RNPM) [K. Azuma, H. Takeda, M. Koashi, and N. Imoto, Phys. Rev. A 85, 062309 (2012)] is identified as a subroutine which achieves the global optimal for typical yield functions monotonically non-decreasing with respect to the singlet fraction, such as an arbitrary convex function of a singlet fraction and two-way distillable entanglement/key.
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.
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.
Quantum information degrades over distance due to the unavoidable imperfections of the transmission channels, with loss as the leading factor. This simple fact hinders quantum communication, as it relies on propagating quantum systems. A solution to this issue is to introduce quantum repeaters at regular intervals along a lossy channel, to revive the quantum signal. In this work we study unitary one-way quantum repeaters, which do not need to perform measurements and do not require quantum memories, and are therefore considerably simpler than other schemes. We introduce and analyze two methods to construct Hamiltonians that generate a repeater interaction that can beat the fundamental repeaterless key rate bound even in the presence of an additional coupling loss, with signals that contain only a handful of photons. The natural evolution of this work will be to approximate a repeater interaction by combining simple optical elements.
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.