The Optimal Single Copy Measurement for the Hidden Subgroup Problem

The optimization of measurements for the state distinction problem has recently been applied to the theory of quantum algorithms with considerable successes, including efficient new quantum algorithms for the non-abelian hidden subgroup problem. Previous work has identified the optimal single copy measurement for the hidden subgroup problem over abelian groups as well as for the non-abelian problem in the setting where the subgroups are restricted to be all conjugate to each other. Here we describe the optimal single copy measurement for the hidden subgroup problem when all of the subgroups of the group are given with equal a priori probability. The optimal measurement is seen to be a hybrid of the two previously discovered single copy optimal measurements for the hidden subgroup problem.Comment: 8 pages. Error in main proof fixe

Sectoral Changes in the Labour Force over the Period 1961-1980 with Particular Reference to Public Sector and Services Employment. Special Article in Quarterly Economic Commentary, Winter 2015

A knowledge of the significant changes which have been taking place in the sectoral composition of employment is fundamental to a proper understanding of the recent evolution of the labour force. This paper traces the changes in the numbers at work in broad sectors of the Irish economy over the period 1961-80. The basic information is given in Appendix I, Table A which contains an annual sectoral subdivision under four broad headings (Agriculture, Manufacturing, Building and Services); Tables 1 and lA following show these data for selected years* in this period with a somewhat more detailed sectoral subdivision, the second table giving absolute and relative employment changes by sector for the 1961/1971 and 1971/1979 periods

Competitiveness Indices for Irish Manufactured Exports. Quarterly Economic Commentary Special Article, July 1981

This paper is devoted primarily to the construction of competitiveness indices for Irish manufactured exports. Our principal motivation in conducting such an exercise is the fact that no satisf a,ctory measures of competitiveness have as yet been developed for Ireland despite which the concept of competitiveness, and the problems assoicated with declining competitiveness in particular, frequently figure in public discussions of Ireland's economic performance. This concern is exemplified, for instance, by the fact that it is a recurring theme in the Quarterly Bulletins and Annual Reports of the Central Bank

Universal Leakage Elimination

``Leakage'' errors are particularly serious errors which couple states within a code subspace to states outside of that subspace thus destroying the error protection benefit afforded by an encoded state. We generalize an earlier method for producing leakage elimination decoupling operations and examine the effects of the leakage eliminating operations on decoherence-free or noiseless subsystems which encode one logical, or protected qubit into three or four qubits. We find that by eliminating the large class of leakage errors, under some circumstances, we can create the conditions for a decoherence free evolution. In other cases we identify a combination decoherence-free and quantum error correcting code which could eliminate errors in solid-state qubits with anisotropic exchange interaction Hamiltonians and enable universal quantum computing with only these interactions.Comment: 14 pages, no figures, new version has references updated/fixe

Sectoral Changes in the Labour Force over the Period 1961-1980 with Particular Reference to Public Sector and Services Employment. Quarterly Economic Commentary Special Article, August 1982

A knowledge of the significant changes which have been taking place in the sectoral composition of employment is fundamental to a proper understanding of the recent evolution of the labour force. This paper traces the changes in the numbers at work in broad sectors of the Irish economy over the period 1961-80. The basic information is given in Appendix I, Table A which contains an annual sectoral subdivision under four broad headings (Agriculture, Manufacturing, Building and Services); Tables 1 and 1A following show these data for selected years* in this period with a somewhat more detailed sectoral subdivision, the second table giving absolute and relative employment changes by sector for the 1961/1971 and 1971/1979 periods

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Jezek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.Comment: It was not realized at the time of publication that the lower bound of Theorem 10 has a simple generalization using matrix monotonicity (See [J. Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans. Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the autho

Direct experimental evidence of free fermion antibunching

Fermion antibunching was observed on a beam of free noninteracting neutrons. A monochromatic beam of thermal neutrons was first split by a graphite single crystal, then fed to two detectors, displaying a reduced coincidence rate. The result is a fermionic complement to the Hanbury Brown and Twiss effect for photons.Comment: 4 pages, 2 figure