Ben Fortescue

Random bipartite entanglement from W and W-like states

We describe a protocol for distilling maximally entangled bipartite states between random pairs of parties from those sharing a tripartite W state |W=(1/sqrt[3])(|100+|010+|001)(ABC), and show that the total distillation rate E(t)(infinity) [the total number of Einstein-Podolsky-Rosen (EPR) pairs distilled per W, irrespective of who shares them] may be done at a higher rate than EPR distillation between specified pairs of parties. Specifically, the optimal rate for distillation to specified parties has been previously shown to be 0.92 EPR pairs per W, while our protocol can asymptotically distill 1 EPR pair per W between random pairs of parties, which we conjecture to be optimal. We thus demonstrate a tradeoff between overall distillation rate and final distribution of EPR pairs. We further show that there exist states with fixed lower-bounded E(t)(infinity), but arbitrarily small distillable entanglement for specified parties.

Random-party entanglement distillation in multiparty states

We describe various results related to the random distillation of multiparty entangled states that is, conversion of such states into entangled states shared between fewer parties, where those parties are not predetermined. In previous work [1] we showed that certain output states (namely EinsteinPodolsky-Rosen (EPR) pairs) could be reliably acquired from a prescribed initial multipartite state (namely the W state |W 〉 = 1 √ 3 (|100〉 + |010〉 + |001〉)) via random distillation that could not be reliably created between predetermined parties. Here we provide a more rigorous definition of what constitutes “advantageous” random distillation. We show that random distillation is always advantageous for W -class three-qubit states (but only sometimes for Greenberger-Horne-Zeilinger (GHZ)-class states). We show that the general class of multiparty states known as symmetric Dicke states can be readily converted to many other states in the class via random distillation. Finally we show that random distillation is provably not advantageous in the limit of multiple copies of pure states.

Classical Analog to Entanglement Reversibility.

In this Letter we study the problem of secrecy reversibility. This asks when two honest parties can distill secret bits from some tripartite distribution p(XYZ) and transform secret bits back into p(XYZ) at equal rates using local operation and public communication. This is the classical analog to the well-studied problem of reversibly concentrating and diluting entanglement in a quantum state. We identify the structure of distributions possessing reversible secrecy when one of the honest parties holds a binary distribution, and it is possible that all reversible distributions have this form. These distributions are more general than what is obtained by simply constructing a classical analog to the family of quantum states known to have reversible entanglement. An indispensable tool used in our analysis is a conditional form of the Gács-Körner common information.

Inefficiency and classical communication bounds for conversion between partially entangled pure bipartite quantum states

We present explicit bounds on the classical communication cost and inefficiency of entanglement dilution via the Lo-Popescu protocol, for the case of two-term (single-qubit) entangled states. By considering a two-stage dilution, we consequently use prior results to obtain meaningful bounds on the classical communication cost and inefficiency of dilution between two-term partially entangled states

Experimental implementation of a three-party quantum key distribution protocol

We present a proof-of-principle experimental implementation of provably secure three-party quantum key distribution. The protocols security relies on the quantum correlations of GHz states but it is implemented using bipartite entanglement.

Graph state secret sharing in higher-dimensional systems

We present a formalism within which, using entangled graph states of prime-dimensional systems, a variety of different secret-sharing schemes (involving both quantum and classical secrets and quantum and classical channels shared between parties) may be unified. We review the explicit protocols we have found for three varieties of secret sharing within this formalism, including some for which the analogous formalism using qubit graph states is not sufficient.