The author develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication.Expand

It is shown that a strong converse theorem holds for the classical capacity of all entanglement-breaking channels and all Hadamard channels (the complementary channels of the former) that the probability of correctly decoding a classical message converges exponentially fast to zero in the limit of many channel uses if the rate of communication exceeds the classical Capacity.Expand

Part V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.Expand

Several known results from the quantum information literature are leveraged to demonstrate that the channel polarization effect occurs for channels with classical inputs and quantum outputs, and linear polar codes are constructed based on this effect, and the encoding complexity is O(NlogN), where N is the blocklength of the code.Expand

We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to… Expand

It is shown that the secret key agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use.Expand

If the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other.Expand

The existence of an explicit recovery map that depends only onσ and the quantum channel N to be reversed is shown, which gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.Expand

This paper establishes several converse bounds on the private transmission capabilities of a quantum channel by using the notion of a private state along with a “privacy test” to establish a general meta-converse bound for private communication, which has a number of applications.Expand