Notes on Canadian Units and Formations Engaged: Battles of the Somme, March-April 1918

Although the Canadian Corps did not participate directly in the German Spring Offensives that began on 21 March 1918, detached Canadian cavalry, artillery, and motor machine gun units serving with British divisions played important roles at various points in the battles. In one of the better known instances, Canadian cavalry were instrumental in delaying a German drive on 30 March south of Amiens at Moreuil Wood where, in one of the most dramatic cavalry actions of the war, Lieutenant Gordon Flowerdew led a mounted charge with sabres drawn. For that action, he was awarded a posthumous Victoria Cross. Le Corps canadien n’a pas participé directement aux batailles durant l’offensive du printemps des Allemands qui a commencé le 21 mars 1918, mais des unités de cavalerie, d’artillerie et de mitrailleuses du pays ayant servi au sein de divisions britanniques ont joué un rôle important à différents moments. Dans l’un de ces épisodes les mieux connus, la cavalerie canadienne a joué un rôle déterminant en retardant l’avance des Allemands, le 30 mars, au sud d’Amiens, au bois de Moreuil. Dans une des charges de cavalerie les plus mémorables de la Première Guerre mondiale, le lieutenant Gordon Flowerdew a dirigé ses hommes, armés d’épées déployées. Pour cet exploit, la Croix de Victoria lui a été attribuée à titre posthume

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

We derive lower limits on the inefficiency and classical communication costs of dilution between two-term bipartite pure states that are partially entangled. We first calculate explicit relations between the allowable error and classical communication costs of entanglement dilution using the protocol of Lo-Popescu and then consider a two-stage dilution from singlets with this protocol followed by some unknown protocol for conversion between partially entangled states. Applying the lower bounds on classical communication and inefficiency of Harrow-Lo and Hayden-Winter to this two-stage protocol, we derive bounds for the unknown protocol. In addition we derive analogous (but looser) bounds for general pure states.Comment: Revised version: 8 pages, 3 figures, two-column. Have added bounds for general pure states, corrected typos and updated format to PRA versio

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, and show that, rather surprisingly, the total distillation rate (the total number of EPR pairs distilled per W, irrespective of who shares them) may be done at a higher rate than distillation of bipartite entanglement between specified pairs of parties. Specifically, the optimal distillation rate for specified entanglement for the W has been previously shown to be the asymptotic entanglement of assistance of 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 the overall asymptotic rate of EPR distillation and the distribution of final EPR pairs between parties. We further show that by increasing the number of parties in the protocol that there exist states with fixed lower-bounded distillable entanglement for random parties but arbitrarily small distillable entanglement for specified parties.Comment: 5 pages, 1 figure, RevTeX. v2 - upper bound on random distillation is expressed more generally and corollaries to the bound added. Minor notation changes. v3 - further notation changes (Ernd now designated Et), discussion of finite distillation rounds and single-copy bound on Et added. Theorem added - relative entropy is shown to be an upper bound to Et for all pure states. Discussion of W formation from EPRs (previously shown in others' work) removed. Some addition, removal and reordering of reference

Reducing the quantum communication cost of quantum secret sharing

We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such scheme (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabiliser codes.Comment: 8 pages, 1 figure; v2: Corrected typos and acknowledgements. v3: New, rewritten final section (on optimal schemes), incorporates more intuitive stabiliser-based construction for the (3,4) scheme and a new (5,6) schem