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ACTA PHOTONICA SINICA

Efficient Entanglement Distribution by Separable States

蔡虹 CAI Hong, 陈炯 CHEN Jiong

Published Jan 1, 2011• 0 citations
Publisher

Abstract

An effcient entanglement distribution protocol was proposed using a qudit(4-dimensional space) as a separable mediating ancilla.Two qubits were used to describe a qudit in order to simplify the description.Firstly,both of the two ancilla qubits and the two distant qubits(a and b) were formed into a four-qubit unlockable bound entangled state,called the Smolin state.Then,a projective measurement in the Bell basis was performed on the two ancilla qubits and the measurement results was delivered to a and b.Based on the measurement results,the qubits a and b can be converted into a standard singlet state locally.At any stage of the protocol,the two ancilla qubits was always separable from the subsystem(a and b).This scheme provides an effective way to distribute the maximally entangled states by separable states,and presents a concise formalism to describe and understand this physical process.

DOI
10.3788/gzxb20114004.0622

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An effcient entanglement distribution protocol was proposed using a qudit(4-dimensional space) as a separable mediating ancilla.Two qubits were used to describe a qudit in order to simplify the description.Firstly,both of the two ancilla qubits and the two distant qubits(a and b) were formed into a four-qubit unlockable bound entangled state,called the Smolin state.Then,a projective measurement in the Bell basis was performed on the two ancilla qubits and the measurement results was delivered to a and b.Based on the measurement results,the qubits a and b can be converted into a standard singlet state locally.At any stage of the protocol,the two ancilla qubits was always separable from the subsystem(a and b).This scheme provides an effective way to distribute the maximally entangled states by separable states,and presents a concise formalism to describe and understand this physical process.
Entangling two systems at distant locations using a separable mediating ancilla is a counterintuitive phenomenon proposed for qubits by T. Cubitt et al. [Phys. Rev. Lett. 91, 037902 (2003)]. We show that such entanglement distribution is possible with Gaussian states, using a certain three-mode fully separable mixed Gaussian state and linear optics elements readily available in experiments. Two modes of the state become entangled by sequentially mixing them on two beam splitters, while the third one remains separable in all stages of the protocol.
Abstract The ability to reliably distribute entanglement among the nodes of a network is an essential requirement for the development of effective quantum communication protocols and the realization of useful quantum networks. It has been demonstrated, in different contexts, that two remote systems can be entangled via local interactions with a carrier system that always remains in a separable state with respect to such distant particles. We develop a strategy for entanglement distribution via separable carriers that can be applied to any number of network nodes to achieve various entanglement distribution patterns. We show that our protocol results in multipartite entanglement, while the carrier mediating the process is always in a separable state with respect to the network. We provide examples showcasing the flexibility of our approach and propose a scheme of principle for the experimental demonstration of the protocol.
The main focus of this thesis is quantum entanglement and, more specifically, pro- tocols that allow its distribution between distant places. In the last decades, with the rise of attention on quantum technologies, entangle- ment is mostly seen as a resource, that could be exchanged, measured, and ideally stored and used when convenient. However, entanglement is not as stable and cheap as the classical resources. One reason for this is that entanglement between two quantum systems is easily disrupted by the interaction with the environment that surrounds them. The presence of noise is even more significant when we wish to entangle two systems that are very far away, a task that is essential for quantum communication technologies. In this case, what can disrupt the entanglement is not only the noise that the particles experience locally, but also the noise in the quantum channel during the communication process, which can be significant over long distances. For this reason, it is important to design distribution protocols that work well in such conditions. In 2003, Cubitt et al. showed the existence of a very curious class of protocols, often called entanglement distribution with separable states (EDSS). They proved that a non-entangled (separable) carrier can be used to increase, or even gener- ate entanglement between two already distant parties. From this, some questions arise. First, what limits or allows an entanglement distribution protocol, if not the entanglement that is sent. Quantum discord was shown to be a necessary, but not sufficient, resource for entanglement distribution. Another natural question is whether these protocols can beat others, for technological purposes, especially in noisy conditions. I will describe some work I have done in an attempt to partially 9 address both of these questions. After introducing various tools and concepts that are useful to understand this topic (chapter 1) and motivate the necessity of entanglement distribution in quantum communication (chapter 2), I will describe a proof-of-principle experiment demon- strating EDSS schemes (chapter 3). Later (chapter 4), I will introduce a more general classification of distribution protocols (excessive or non-excessive protocols), based on whether the entanglement gain is larger than the one that is communicated, describing specific examples and general properties of such protocols. I will then partially address the problem regarding the robustness to the noise of communica- tion protocols (chapter 5). Finally, in chapter 6, I will describe how entanglement of a bipartite state can grow with a quantum measurement with unknown results. I discuss the properties of the measurement and of the initial state that make this process effective.
Four qubit bound entangled Smolin states are generalised in a natural way to even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, though they do not admit quantum security. They are also shown to serve for remote quantum information concentration like in the case of the original four qubit states. Application of the information concentration to the process of unlocking of classical correlations and quantum entanglement by quantum bit is pointed out.
I present a four-party unlockable bound entangled state, that is, a four-party quantum state which cannot be written in a separable form and from which no pure entanglement can be distilled by local quantum operations and classical communication among the parties, and yet when any two of the parties come together in the same laboratory they can perform a measurement which enables the other two parties to create a pure maximally entangled state between them without coming together. This unlocking ability can be viewed in two ways, either as a determination of which Bell state is shared in the mixture or as a kind of quantum teleportation with cancellation of Pauli operators.
Four-qubit bound entangled Smolin states are generalized with help of the Hilbert-Schmidt formalism to any even number of qubits. They are shown to maximally violate simple correlation Bell inequalities and, as such, to reduce communication complexity, although they do not admit quantum security. They are also shown to serve for remote quantum information concentration, as in the case of the original four-qubit states. It is proven that the latter effect allows us to unlock some entanglement measures and classical correlations. Also the possibility of quantum secret sharing by the considered state is pointed out.