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International Journal of Theoretical Physics

A Continuous Variable Quantum Key Distribution Protocol Based on Entanglement Swapping of Quasi-Bell Entangled Coherent States

Dong Li, Junxi Wang, Xiao‐Ming Xiu, Dan Li, Yajun Gao, X. X. Yi

Published May 22, 2014• 3 citations
Publisher
DOI
10.1007/s10773-014-2115-8

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Distributing and sharing entanglement at a distance is a key ingredient in many future quantum communication protocols, however entanglement is a fragile resource and can break down upon interacting with the environment. Within this thesis we present two possible entanglement swapping protocols, and show that these protocols are resilient to small levels of photonic losses. We propose the use of these protocols in quantum communication schemes that require shared entangled qubits, in the form of a Bell state. \nThe input states to our proposed protocols are hybrid entangled states, which are discrete-variable and continuous-variable entangled states. We use the vacuum and \nsingle photon Fock state as our discrete half, which is stationary in our entanglement swapping protocol, whereas the continuous variable half is modelled as travelling through lossy optical fibre before being measured. The first protocol uses coherent states in a superposition as propagating modes in our entanglement swapping setup, \nwhereas the second, more complicated, protocol uses superposed cat states. \nWe model photonic losses by applying a beam-splitter of transmission T to our propagating continuous variable modes, along with an input vacuum state. We also model the more realistic circumstance in which the losses in these two continuous variable modes are not equal. We then detect these continuous variable modes using a vacuum projective measurement and balanced homodyne detection. We also investigate homodyne measurement imperfections and non-ideal outcomes, as well as success probabilities of these measurement schemes. We calculate the entanglement negativity and linear entropy of our final two qubit state, as well as fidelity against the |\\Phi^+> Bell state in the coherent state protocol, and a phase-rotated |\\Phi^+(\\alpha)> Bell state in the cat state regime. \nWe demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.
The study of entanglement between discrete and continuous variables is an important theoretical and experimental topic in quantum information processing, for which entanglement swapping is one of the interesting elements. Entanglement swapping allows two particles without interacting with each other in any way, to form an entangled state by the action of another pair of entangled particles. In this paper, we propose an experimentally feasible scheme to realize deterministic entanglement swapping in the hybrid system with discrete and continuous variables. The process is achieved by preparing two pairs of entangled states, each is formed by a qubit and two quasi-orthogonal coherent state elements of a cavity, performing a Bell-state analysis through nonlocal operations on the continuous variable states of the two cavities, and projecting the two qubits into a maximally entangled state. The present scheme may be applied to other physical systems sustaining such hybrid discrete and continuous forms, providing a typical paradigm for entanglement manipulation through deterministic swapping operations.
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state super- position) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5 -- 10 km , when used with a suitable entanglement purification scheme.