Coherent Communication of Classical Messages

We define "coherent communication" in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent communication, we are able to generalize super-dense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulae for the classical and quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed amount of entanglement per use.Comment: 5 pages, revtex, v2: updated references, v3: changed title, fixed error in eq (10

Approximate unitary tt-designs by short random quantum circuits using nearest-neighbor and long-range gates

We prove that $poly(t) \cdot n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on a $D$-dimensional lattice with n qudits are approximate $t$-designs in various measures. These include the "monomial" measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was $poly(t)\cdot n$ due to Brandao-Harrow-Horodecki (BHH) for $D=1$. We also improve the "scrambling" and "decoupling" bounds for spatially local random circuits due to Brown and Fawzi. One consequence of our result is that assuming the polynomial hierarchy (PH) is infinite and that certain counting problems are $\#P$-hard on average, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under the assumption that PH is infinite. However, to show the hardness of approximate sampling using this strategy requires that the quantum circuits have a property called "anti-concentration", meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Thus our result improves the required depth for this level of anti-concentration from linear depth to a sub-linear value, depending on the geometry of the interactions. This is relevant to a recent proposal by the Google Quantum AI group to perform such a sampling task with 49 qubits on a two-dimensional lattice and confirms their conjecture that $O(\sqrt n)$ depth suffices for anti-concentration. We also prove that anti-concentration is possible in depth O(log(n) loglog(n)) using a different model

The Art of Refusal: Promising Practice for Grant Makers and Grant Seekers

The full report of this research project provides the findings of a study of communication experiences and practices, at the point of grant refusal, among selected grant making and grant seeking organisations. Its context was the frustration and disappointment being experienced by many grant seekers in a period of enhanced competition for funding, alongside the multiple pressures facing grant makers, in responding to grant seekers' needs and in meeting their own range of obligations. The overall purpose of the research was to support learning and improvement in policy and practice among grant makers and grant seekers. A summary of the findings from the qualitative research undertaken for the project is provided at the end of this paper. In this practice paper, we focus on the direct learning question posed by the research - 'what promising practices in grant refusal communications may be identified from grant makers' and grant seekers' perspectives on their experiences?' Many respondents during the research process highlighted what were, for them, preferred and promising practices in communicating and managing grant refusal among grant seekers and grant makers. These were sometimes their own approaches and sometimes those which they had observed and welcomed. These insights, examples and possibilities are now distilled and presented below as promising practice learning and action points, illustrated by anonymous quotations taken from our research respondents

How many copies are needed for state discrimination?

Given a collection of states (rho_1, ..., rho_N) with pairwise fidelities F(rho_i, rho_j) <= F < 1, we show the existence of a POVM that, given rho_i^{otimes n}, will identify i with probability >= 1-epsilon, as long as n>=2(log N/eps)/log (1/F). This improves on previous results which were either dimension-dependent or required that i be drawn from a known distribution.Comment: 1 page, submitted to QCMC'06, answer is O(log # of states