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Quantum Information Theory
- M. Wilde
- 10 June 2013
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.
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy
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.
From Classical to Quantum Shannon Theory
- M. Wilde
- 7 June 2011
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.
Optimal entanglement formulas for entanglement-assisted quantum coding
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…
Polar Codes for Classical-Quantum Channels
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.
Fundamental rate-loss tradeoff for optical quantum key distribution.
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.
Converse Bounds for Private Communication Over Quantum Channels
- M. Wilde, M. Tomamichel, M. Berta
- Computer ScienceIEEE Transactions on Information Theory
- 29 February 2016
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.
Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy
- M. Junge, R. Renner, David Sutter, M. Wilde, A. Winter
- MathematicsAnnales Henri Poincaré
- 23 September 2015
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.
Entanglement-Assisted Communication of Classical and Quantum Information
The main result is a capacity theorem that gives a 3-D achievable rate region that justifies the need for simultaneous coding of classical and quantum information over an EAQ channel.