Quantum network communication -- the butterfly and beyond

We study the k-pair communication problem for quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (i) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (ii) For two particular networks (including the butterfly network) routing is proved optimal, and the free assisting classical communication can at best be used to modify the directions of quantum channels in the network. Consequently, the achievable rate regions are given by counting edge avoiding paths, and precise achievable rate regions in all four assisting scenarios can be obtained. (iii) Optimality of routing can also be proved in classes of networks. The first class consists of directed unassisted networks in which (1) the receivers are information sinks, (2) the maximum distance from senders to receivers is small, and (3) a certain type of 4-cycles are absent, but without further constraints (such as on the number of communicating and intermediate parties). The second class consists of arbitrary backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair communication problem, observations are made on quantum multicasting and a static version of network communication related to the entanglement of assistance.Comment: 15 pages, 17 figures. Final versio

Zero-error channel capacity and simulation assisted by non-local correlations

Shannon's theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly, and in the presence of various resources that are all classes of non-signalling correlations: Shared randomness, shared entanglement and arbitrary non-signalling correlations. Specifically, when the channel being simulated is noiseless, this reduces to the zero-error capacity of the channel, assisted by the various classes of non-signalling correlations. When the resource channel is noiseless, it results in the "reverse" problem of simulating a noisy channel exactly by a noiseless one, assisted by correlations. In both cases, 'one-shot' separations between the power of the different assisting correlations are exhibited. The most striking result of this kind is that entanglement can assist in zero-error communication, in stark contrast to the standard setting of communicaton with asymptotically vanishing error in which entanglement does not help at all. In the asymptotic case, shared randomness is shown to be just as powerful as arbitrary non-signalling correlations for noisy channel simulation, which is not true for the asymptotic zero-error capacities. For assistance by arbitrary non-signalling correlations, linear programming formulas for capacity and simulation are derived, the former being equal (for channels with non-zero unassisted capacity) to the feedback-assisted zero-error capacity originally derived by Shannon to upper bound the unassisted zero-error capacity. Finally, a kind of reversibility between non-signalling-assisted capacity and simulation is observed, mirroring the famous "reverse Shannon theorem".Comment: 18 pages, 1 figure. Small changes to text in v2. Removed an unnecessarily strong requirement in the premise of Theorem 1

Remote preparation of quantum states

Remote state preparation is the variant of quantum state teleportation in which the sender knows the quantum state to be communicated. The original paper introducing teleportation established minimal requirements for classical communication and entanglement but the corresponding limits for remote state preparation have remained unknown until now: previous work has shown, however, that it not only requires less classical communication but also gives rise to a trade-off between these two resources in the appropriate setting. We discuss this problem from first principles, including the various choices one may follow in the definitions of the actual resources. Our main result is a general method of remote state preparation for arbitrary states of many qubits, at a cost of 1 bit of classical communication and 1 bit of entanglement per qubit sent. In this "universal" formulation, these ebit and cbit requirements are shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then yields the exact trade-off curve for arbitrary ensembles of pure states and pure entangled states (including the case of incomplete knowledge of the ensemble probabilities), based on the recently established quantum-classical trade-off for quantum data compression. The paper includes an extensive discussion of our results, including the impact of the choice of model on the resources, the topic of obliviousness, and an application to private quantum channels and quantum data hiding.Comment: 21 pages plus 2 figures (eps), revtex4. v2 corrects some errors and adds obliviousness discussion. v3 has section VI C deleted and various minor oversights correcte

Improving zero-error classical communication with entanglement

Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behaviour constitutes the field of classical zero-error information theory, the quantum generalisation of which has started to develop recently. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent with no chance of error. In particular, we show how to construct such a channel based on any proof of the Bell-Kochen-Specker theorem. This is a new example of the use of quantum effects to improve the performance of a classical task. We investigate the connection between this phenomenon and that of ``pseudo-telepathy'' games. The use of generalised non-signalling correlations to assist in this task is also considered. In this case, a particularly elegant theory results and, remarkably, it is sometimes possible to transmit information with zero-error using a channel with no unassisted zero-error capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus figure 1 and the non-signalling box exampl

Aspects of generic entanglement

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.Comment: 22 pages, 1 figure, 1 tabl

Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection argument that also at p=0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Renyi entropy is non-additive for all p < 0.11. We conjecture however that violations of additivity exist for all p<1.Comment: 7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs) - note that the explicit example was changed and the more conservative estimate of the bound up to which violations occur, additionally some other small issues are straightened ou

An “Electronic Fluorescent Pictograph” Browser for Exploring and Analyzing Large-Scale Biological Data Sets

Background. The exploration of microarray data and data from other high-throughput projects for hypothesis generation has become a vital aspect of post-genomic research. For the non-bioinformatics specialist, however, many of the currently available tools provide overwhelming amounts of data that are presented in a non-intuitive way. Methodology/Principal Findings. In order to facilitate the interpretation and analysis of microarray data and data from other large-scale data sets, we have developed a tool, which we have dubbed the electronic Fluorescent Pictograph – or eFP – Browser, available a

Phosphatidylethanol confirmed alcohol use among ART-naïve HIV-infected persons who denied consumption in rural Uganda

Under-reporting of alcohol use by HIV-infected patients could adversely impact clinical care. This study examined factors associated with under-reporting of alcohol consumption by patients who denied alcohol use in clinical and research settings using an alcohol biomarker. We enrolled ART-naïve, HIV-infected adults at Mbarara Hospital HIV clinic in Uganda. We conducted baseline interviews on alcohol use, demographics, Spirituality and Religiosity Index (SRI), health and functional status; and tested for breath alcohol content and collected blood for phosphatidylethanol (PEth), a sensitive and specific biomarker of alcohol use. We determined PEth status among participants who denied alcohol consumption to clinic counselors (Group 1, n = 104), and those who denied alcohol use on their research interview (Group 2, n = 198). A positive PEth was defined as ≥8 ng/ml. Multiple logistic regression models were used to examine whether testing PEth-positive varied by demographics, literacy, spirituality, socially desirable reporting and physical health status. Results showed that, among the 104 participants in Group 1, 28.8% were PEth-positive. The odds of being PEth-positive were higher for those reporting prior unhealthy drinking (adjusted odds ratio (AOR): 4.7, 95% confidence interval (CI): 1.8, 12.5). No other factors were statistically significant. Among the 198 participants in Group 2, 13.1% were PEth-positive. The odds of being PEth-positive were higher for those reporting past unhealthy drinking (AOR: 4.6, 95% CI: 1.8, 12.2), the Catholics (AOR: 3.8, 95% CI: 1.3, 11.0) compared to Protestants and lower for the literate participants (AOR: 0.3, 95% CI: 0.1, 0.8). We concluded that under-reporting of alcohol use to HIV clinic staff was substantial, but it was lower in a research setting that conducted testing for breath alcohol and PEth. A report of past unhealthy drinking may highlight current alcohol use among deniers. Strategies to improve alcohol self-report are needed within HIV care settings in Uganda