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Quantum Communications and Quantum Imaging

Optimal single-error-type entanglement generation via coherent-state transmission (Conference Presentation)

Koji Azuma

Published Oct 3, 2022• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.2633279

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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.
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.
Maximally entangled states---a resource for quantum information processing---can only be shared through noiseless quantum channels, whereas in practice channels are noisy. Here we ask: Given a noisy quantum channel, what is the maximum attainable purity (measured by singlet fraction) of shared entanglement for single channel use and local trace preserving operations? We find an exact formula of the maximum singlet fraction attainable for a qubit channel and give an explicit protocol to achieve the optimal value. The protocol distinguishes between unital and nonunital channels and requires no local postprocessing. In particular, the optimal singlet fraction is achieved by transmitting part of an appropriate pure entangled state, which is maximally entangled if and only if the channel is unital. A linear function of the optimal singlet fraction is also shown to be an upper bound on the distillable entanglement of the mixed state dual to the channel.
Quantum entanglement plays a central role in many quantum communication protocols. It allows distant particles to share correlations beyond the limits of classical interactions. Entanglement is essential for superdense coding, quantum teleportation, and secure cryptographic key distribution in quantum communication. It is also a pillar for developing quantum networks, where the management and distribution of entanglement are crucial for connecting distant nodes. Although perfect entanglement is a sought-after ideal, experimental imperatives, including entanglement distribution over long distances, often limit the quality of entangled states. An important question is whether weaker entanglement still offers advantages. First, we study more general tasks than dense coding to show that simpler measurements, combined with entanglement, allow advantageous and sometimes even optimal qubit communication protocols to be obtained. We also demonstrate that simple measurements can generate quantum correlations that cannot be modelled by two classical communication bits and can constitute an optimal protocol with quantum resources. We implement a novel Bell-type inequality tailored for certifying full network non-locality (FNN) to develop certification methods guaranteeing security on an entanglement-based network. Our experiment uses two pairs of polarised entangled photons in a network configuration with three nodes, briefly referred to as a bilocal network scenario. Finally, we show that weakly entangled states can improve communication over a qubit channel using only separate (local) measurements on isotropic non-steerable two-qubit states, without interference, of individual photons, across two communication tasks: secret sharing and its stochastic variant.
We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a theorem to reduce LOCC via a local unital qubit channel to local filtering. We also present an optimal protocol based on beam splitters and a quantum nondemolition (QND) measurement on photons. Even if we replace the QND measurement with photon detectors, the protocol can achieve near-optimal performance, outperforming known entanglement generation schemes.
Compared with entanglement with multiple types of noise, entanglement including only one type of error is a favorable fundamental resource not only for quantum communication but also for distributed quantum computation. We consider protocols that present single-error-type entanglement for distant qubits via coherent-state transmission over a lossy channel. Such a protocol is regarded as a subroutine to serve entanglement for larger protocol to yield a final output, such as ebits or pbits. In this paper, we provide a subroutine protocol which achieves the global optimal for typical jointly convex yield functions monotonically nondecreasing with respect to the singlet fraction, such as an arbitrary convex function of a singlet fraction, two-way distillable entanglement, and two-way distillable key. Entanglement generation based on remote nondestructive parity measurement protocol [K. Azuma et al., Phys. Rev. A 85, 062309 (2012)] is identified as such an optimal subroutine.
The generation of entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote-entanglement generation have been proposed, many of which have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online. Published by the American Physical Society 2024