Counterfactual Computation

Suppose that we are given a quantum computer programmed ready to perform a computation if it is switched on. Counterfactual computation is a process by which the result of the computation may be learnt without actually running the computer. Such processes are possible within quantum physics and to achieve this effect, a computer embodying the possibility of running the computation must be available, even though the computation is, in fact, not run. We study the possibilities and limitations of general protocols for the counterfactual computation of decision problems (where the result r is either 0 or 1). If p(r) denotes the probability of learning the result r ``for free'' in a protocol then one might hope to design a protocol which simultaneously has large p(0) and p(1). However we prove that p(0)+p(1) never exceeds 1 in any protocol and we derive further constraints on p(0) and p(1) in terms of N, the number of times that the computer is not run. In particular we show that any protocol with p(0)+p(1)=1-epsilon must have N tending to infinity as epsilon tends to 0. These general results are illustrated with some explicit protocols for counterfactual computation. We show that "interaction-free" measurements can be regarded as counterfactual computations, and our results then imply that N must be large if the probability of interaction is to be close to zero. Finally, we consider some ways in which our formulation of counterfactual computation can be generalised.Comment: 19 pages. LaTex, 2 figures. Revised version has some new sections and expanded explanation

Transport enhancement from incoherent coupling between one-dimensional quantum conductors

We study the non-equilibrium transport properties of a highly anisotropic two-dimensional lattice of spin-1/2 particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite temperature as an array of incoherently coupled one-dimensional chains. We show that in the regime of strong intrachain interactions, the weak interchain coupling considerably boosts spin transport in the driven system. Interestingly, we show that this enhancement increases with the length of the chains, which is related to superdiffusive spin transport. We describe the mechanism behind this effect, compare it to a similar phenomenon in single chains induced by dephasing, and explain why the former is much stronger

Protein-DNA computation by stochastic assembly cascade

The assembly of RecA on single-stranded DNA is measured and interpreted as a stochastic finite-state machine that is able to discriminate fine differences between sequences, a basic computational operation. RecA filaments efficiently scan DNA sequence through a cascade of random nucleation and disassembly events that is mechanistically similar to the dynamic instability of microtubules. This iterative cascade is a multistage kinetic proofreading process that amplifies minute differences, even a single base change. Our measurements suggest that this stochastic Turing-like machine can compute certain integral transforms.Comment: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC129313/ http://www.pnas.org/content/99/18/11589.abstrac

On Nonzero Kronecker Coefficients and their Consequences for Spectra

A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A, r^B, r^{AB}). How can we characterise such triples? It turns out that the admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means that the irreducible representation V_lambda is contained in the tensor product of V_mu and V_nu. Here, we show that such triples form a finitely generated semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a complete information-theoretic proof of the correspondence between triples of spectra and representations. Finally, we show that spectral triples form a convex polytope.Comment: 13 page

The detection of airborne transmission of tuberculosis from HIV-infected patients, using an in vivo air sampling model

Background. Nosocomial transmission of tuberculosis remains an important public health problem. We created an in vivo air sampling model to study airborne transmission of tuberculosis from patients coinfected with human immunodeficiency virus (HIV) and to evaluate environmental control measures. Methods. An animal facility was built above a mechanically ventilated HIV‐tuberculosis ward in Lima, Peru. A mean of 92 guinea pigs were continuously exposed to all ward exhaust air for 16 months. Animals had tuberculin skin tests performed at monthly intervals, and those with positive reactions were removed for autopsy and culture for tuberculosis. Results. Over 505 consecutive days, there were 118 ward admissions by 97 patients with pulmonary tuberculosis, with a median duration of hospitalization of 11 days. All patients were infected with HIV and constituted a heterogeneous group with both new and existing diagnoses of tuberculosis. There was a wide variation in monthly rates of guinea pigs developing positive tuberculin test results (0%–53%). Of 292 animals exposed to ward air, 159 developed positive tuberculin skin test results, of which 129 had laboratory confirmation of tuberculosis. The HIV‐positive patients with pulmonary tuberculosis produced a mean of 8.2 infectious quanta per hour, compared with 1.25 for HIV‐negative patients with tuberculosis in similar studies from the 1950s. The mean monthly patient infectiousness varied greatly, from production of 0–44 infectious quanta per hour, as did the theoretical risk for a health care worker to acquire tuberculosis by breathing ward air. Conclusions. HIV‐positive patients with tuberculosis varied greatly in their infectiousness, and some were highly infectious. Use of environmental control strategies for nosocomial tuberculosis is therefore a priority, especially in areas with a high prevalence of both tuberculosis and HIV infection