Exact Cost of Redistributing Multipartite Quantum States

How correlated are two quantum systems from the perspective of a third? We answer this by providing an optimal “quantum state redistribution” protocol for multipartite product sources. Specifically, given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, we identify the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob. The communication cost gives the first known operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived

The Jones polynomial: quantum algorithms and applications in quantum complexity theory

We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the braid group. We use these to provide new quantum algorithms for approximately evaluating a family of specializations of the HOMFLYPT two-variable polynomial of trace closures of braids. We also give algorithms for approximating the Jones polynomial of a general class of closures of braids at roots of unity. Next we provide a self-contained proof of a result of Freedman et al. that any quantum computation can be replaced by an additive approximation of the Jones polynomial, evaluated at almost any primitive root of unity. Our proof encodes two-qubit unitaries into the rectangular representation of the eight-strand braid group. We then give QCMA-complete and PSPACE-complete problems which are based on braids. We conclude with direct proofs that evaluating the Jones polynomial of the plat closure at most primitive roots of unity is a #P-hard problem, while learning its most significant bit is PP-hard, circumventing the usual route through the Tutte polynomial and graph coloring.Comment: 34 pages. Substantial revision. Increased emphasis on HOMFLYPT, greatly simplified arguments and improved organizatio

Capacity Theorems for Quantum Multiple Access Channels: Classical-Quantum and Quantum-Quantum Capacity Regions

We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the corresponding region has a single-letter description. One of our examples relies on a new result proved here, perhaps of independent interest, stating that the coherent information over any degradable channel is concave in the input density operator. We conclude with connections to other work and a discussion on generalizations where each user simultaneously sends classical and quantum information.Comment: 38 pages, 1 figure. Fixed typos, added new example. Submitted to IEEE Tranactions on Information Theor

Quantum broadcast channels

We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pairs of parties with the assistance of free classical communication.Comment: 15 pages; IEEE Trans. Inform. Theory, vol. 57, no. 10, October 201

Capacity Theorems for Quantum Multiple Access Channels

We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region characterizes the rates at which it is possible for one sender to send classical information while the other sends quantum information. The second region gives the rates at which each sender can send quantum information. We give an example of a channel for which each region has a single-letter description, concluding with a characterization of the rates at which each user can simultaneously send classical and quantum information.Comment: 5 pages. Conference version of quant-ph/0501045, to appear in the proceedings of the IEEE International Symposium on Information Theory, Adelaide, Australia, 200

The Toxicity of Weathered Oil on an Oil Resistant Diatom Species

This project investigated the toxicity of weathered oil on an oil resistant diatom species, Phaeodactylum tricornutum. Most oil toxicology studies focus on the use of fresh oil, while phytoplankton that live in the euphotic zone are exposed to photo-oxidized oil. The main research questions focused on the toxicity of weathered oil in comparison to fresh oil and how P. tricornutum responds to this form of pollution. These and related questions are of utmost importance when discussing the lasting effects of an oil spill event on primary producers. These questions were explored through batch-culture experiments, where cultures of P. tricornutum were exposed to fresh (WAF) and weathered oil (PhotoWAF) in the form of a water accommodated fraction of oil. We found that photo-oxidized oil targets the cell’s ability to harvest light and reduces relative electron transport rates after the initial exposure. In addition, the observed negative physiological effects impacted cell growth throughout the experiment. Our data shows that photo-oxidized oil negatively effects the physiology and growth of P. tricornutum, specifically targeting the cell’s light harvesting capabilities. Thus, using photo-oxidized oil is an important consideration for oil toxicity studies when simulating real life conditions versus laboratory settings