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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Adjunct Spectral Entanglement in Entanglement Swapping and Type-I Fusion

Travis S. Humble, Warren P. Grice

Published Jan 1, 2007• 0 citations
Publisher

Abstract

We show how adjunct spectral entanglement affects polarization-based entanglement swapping and type-I fusion gates and we explain why the concurrences of the subsequently entangled states are distinctively dependent on the initial joint spectral amplitudes.
DOI
10.1364/cqo.2007.csua32

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We examine how spectral entanglement in polarization-entangled photon states generated from bulk-crystal, spontaneous parametric down-conversion affects the success of entanglement swapping and type-I fusion gates. We quantify the success of the entanglement swapping and fusion gates by calculating the bipartite concurrence and residual tangle, respectively, in terms of the joint spectral probability amplitudes of the initial broad-bandwidth polarization-entangled states. We find that both polarization-entanglement measures depend strongly on the initial spectral entanglement, as well as on the configuration of the independent sources. Specifically, when spectral differences correlate with polarization, the optimal source configuration is different for the two protocols. We conclude that this distinction is founded in how the underlying Bell-state measurement and quantum-erasure techniques respond differently to distinguishing spectral information.
The nonlocal correlations between quantum states in an entangled system are essential to many quantum communications applications. A basic quantum operation, which permits the distribution of entanglement between two initially uncorrelated systems, is entanglement swapping. Here we present a rigorous formulation of entanglement swapping of any two partially mixed two-qubit states without limiting ourselves to any specific type of state or noise. Further, for two important classes of the input states, Bell diagonal and pure states, we describe how the concurrence of the final state is related to the concurrence of the initial states. First, we consider Bell diagonal states, and find bounds on the concurrence of the final state in terms of the concurrences of the initial states. These bounds are important for communications applications because polarization mode dispersion in fibers produces Bell diagonal states up to a local unitary rotation. Second, we show that swapping pure states occasionally results in a state of higher concurrence than either of the initial states. In addition, we find that two pure states are most likely to be capable of swapping to a state of increased concurrence when the two initial states have similar concurrences. Our analysis offers a completely general framework for investigating the behavior of any pair of two-qubit states when used for entanglement swapping.