Understanding and exploiting quantum effects in quantum communications and entanglement manipulation

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All data is stored in and transmitted by physical systems, which are all ultimately governed by quantum mechanics. Our information technology is optimized for classical communication and processing, but it is beginning to encounter this quantum frontier. We are uncovering new possibilities such as quantum data compression, quantum cryptography, teleportation, and efficient factoring algorithms.******This proposal will develop a broad theory of quantum communication. The tremendous successes of modern communication science are founded in Shannon theory; our objective is to extend the insights and approaches of Shannon theory to quantum communication.******Significant progress has been made in understanding quantum information, but the foundations of quantum communication theory are still under construction, and significant open questions remain. We have no algorithms to determine what communication rates can be achieved in general, or even whether communication is possible given certain kinds of noise, and we have yet to discover the full potential of quantum resources such as entanglement.******The most fundamental question one can ask of a communication channel is: at what rates can it transmit various kinds of data? These rates, known as the capacities, are an important focus of our research; in particular the classical, private and quantum capacities of quantum communication channels.******Quantum communication channels are complex, and quantum data is extremely sensitive to noise, but recent results hold considerable promise. We can begin by building on our growing understanding of complementary channels which describe the loss of data to the environment to fully categorize channels with zero quantum or private capacity, and to understand the difference between these two quantities. We will also investigate how quantum transmission can be strengthened by classical side channels, and how the communication of finite block-length messages can be optimized.******A twin research theme will study entanglement and other information theoretic resources, and how they can enhance information processing tasks. Following a promising approach using cooperative games, we will bound the utility of these auxiliary resources for performing tasks, and seek to understand why they cannot be bounded in all cases.******Answers to these questions will impact fields beyond communication theory, for they are essential for our understanding of quantum physics and quantum complexity theory.**