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arXiv:quant-ph/0507274 · Physical Review A

Entanglement creation and distribution on a graph of exchange-coupled qutrits

Christopher Hadley, Alessio Serafini, Sougato Bose

Published Nov 29, 2005• 8 citations
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Abstract

We propose a protocol that allows both the creation and the distribution of entanglement, resulting in two distant parties (Alice and Bob) conclusively sharing a bipartite Bell state. The system considered is a graph of three-level objects (``qutrits'') coupled by SU(3) exchange operators. The protocol begins with a third party (Charlie) encoding two lattice sites in unentangled states, and allowing unitary evolution under time. Alice and Bob perform a projective measurement on their respective qutrits at a given time, and obtain a maximally entangled Bell state with a certain probablility. We also consider two further protocols, one based on simple repetition and the other based on successive measurements and conditional resetting, and show that the cumulative probability of creating a Bell state between Alice and Bob tends to unity.

DOI
10.1103/physreva.72.052333

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We propose a protocol that allows both the creation and the distribution of entanglement, resulting in two distant parties (Alice and Bob) conclusively sharing a bipartite Bell state. The system considered is a graph of three-level objects (``qutrits'') coupled by SU(3) exchange operators. The protocol begins with a third party (Charlie) encoding two lattice sites in unentangled states, and allowing unitary evolution under time. Alice and Bob perform a projective measurement on their respective qutrits at a given time, and obtain a maximally entangled Bell state with a certain probablility. We also consider two further protocols, one based on simple repetition and the other based on successive measurements and conditional resetting, and show that the cumulative probability of creating a Bell state between Alice and Bob tends to unity.
We propose an entanglement sharing protocol based on separable states. Initially, two parties, Alice and Bob, share a two-mode separable Gaussian state. Alice then splits her mode into two separable modes and distributes them between two players. Bob is separable from the players but he can create entanglement with either of the players if the other player moves to his location and collaborates with him. Any two parties are separable and the creation of entanglement is thus mediated by transmission of a mode which is separable from individual modes on Alice's side and Bob's side. For the state shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to Gaussian measurements and the state thus carries a nontrivial signature of bound entanglement. The present protocol also demonstrates switching between different separability classes of tripartite systems by coherent operations on its bipartite parts and complements studies on protocols utilizing mixed partially entangled multipartite states.
Abstract We develop a protocol for entanglement generation in the quantum internet that allows a repeater node to use n-qubit Greenberger-Horne-Zeilinger (GHZ) projective measurements that can fuse n successfully-entangled links, i.e., two-qubit entangled Bell pairs shared across n network edges, incident at that node. Implementing n-fusion, for n≥3, is in principle not much harder than 2-fusions (Bell-basis measurements) in solid-state qubit memories. If we allow even 3-fusions at the nodes, we find---by developing a connection to a modified version of the site-bond percolation problem---that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end parties Alice and Bob at a rate that stays constant as the distance between them increases. We prove that this powerful network property is not possible to attain with any quantum networking protocol built with Bell measurements and multiplexing alone. We also design a two-party quantum key distribution protocol that converts the entangled states shared between two nodes into a shared secret, at a key generation rate that is independent of the distance between the two parties.
We study entanglement activation in a generalized entanglement swapping process involving two Bell pairs and generalized measurements. The conventional understanding posits entangled measurements as both necessary and sufficient for establishing entanglement between distant parties. In this study, we reassess the role of measurement operators in entanglement generation within a generalized entanglement swapping process. We focus on maximally entangled two-qubit initial states and generalized measurements, investigating the necessity and sufficiency conditions for entangled measurement operators. By utilizing two Bell pairs, (1, 2) shared between Alice and Bob, and (3, 4) shared between Bob and Charlie, we demonstrate that while entangled measurements are sufficient, they are not indispensable for establishing entanglement between spatially separated observers. Through a sequential approach, if Bob performs an initial measurement which is not able to establish entanglement then followed by another measurement after postprocessing the first measurement it is possible to establish entanglement. We identify specific criteria for different measurement operators that enable the potential for performing a second measurement to establish entanglement. Our findings highlight the feasibility of generating entanglement between distant parties through a combination of measurements, shedding light on entanglement distribution in quantum networks. Additionally, we showcase through illustrative examples how successive measurements enhance entanglement compared to single measurements, underscoring the practical benefits of our approach in enhancing entanglement. Moreover, our protocol extends beyond bipartite qubit states to higher-dimensional maximally entangled states, emphasizing its versatility and applicability.
Abstract This paper presents a theoretical framework for generating and controlling high-dimensional quantum entanglement by harnessing the scattering properties of quantum graphs (QGs). By mapping the three scattering channels of a QG onto the basis states of a quantum three-level system (qutrit), we have successfully extended the entanglement-generation protocol based on the QG from two to three dimensions. A novel triple-controlled scattering operator is introduced, which enables the conditional reconfiguration of Bob’s QG based on the scattering outcome of Alice’s. Through rigorous theoretical derivation, we establish the precise analytical conditions under which the composite system resides in either a maximally entangled or a separable state. Our findings indicate that achieving maximal entanglement requires the simultaneous satisfaction of two conditions. First, the scattering entropy of Alice’s QG must be maximal, meaning that the exit probability through each of its three channels is equal to 1 3 . Second, the three conditional output states prepared by Bob must be mutually orthogonal. Finally, we demonstrate that tunable phases can be employed to regulate the degree of entanglement actively, thereby verifying the feasibility and controllability of the proposed framework for high-dimensional quantum information processing.
A scheme is proposed by which two parties, Alice and Bob, can securely exchange real numbers. The scheme requires Alice and Bob to share entanglement and both to perform Bell-state measurements. With a qubit system two real numbers can each be sent by Alice and Bob, resulting in four real numbers shared by them. The number of real numbers that can be shared increases if higher-dimensional systems are utilized. The number of significant figures of each shared real number depends upon the number of Bell-state measurements that Alice and Bob perform. The security of the scheme against individual eavesdropping attacks is analyzed and the effects of channel losses and errors discussed.