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The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi(More)
We describe how any two-party quantum computation, specified by a unitary which simultaneously acts on the registers of both parties , can be privately implemented against a quantum version of classical semi-honest adversaries that we call specious. Our construction requires two ideal functionalities to garantee privacy: a private SWAP between registers(More)
A natural measure for the amount of quantum information that a physical system E holds about another system A = A<sub>1</sub>, .. . , A<sub>n</sub> is given by the min-entropy H<sub>min</sub>(A|E). In particular, the min-entropy measures the amount of entanglement between E and A, and is the relevant measure when analyzing a wide variety of problems ranging(More)
— This paper presents numerical algorithms for the computation of the capacity for channels with non-causal transmitter side information (the Gel'fand-Pinsker problem) and the rate-distortion function for source coding with decoder side information (the Wyner-Ziv problem). The algorithms are based on the reformulation of the mutual information expressions(More)
Polar coding, introduced 2008 by Arıkan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the asymptotic limit of large block sizes. Here, we study the use of polar codes for the transmission of quantum information.(More)
A new protocol for quantum broadcast channels based on the fully quantum Slepian-Wolf protocol is presented. The protocol yields an achievable rate region for entanglement-assisted transmission of quantum information through a quantum broadcast channel that can be considered the quantum analogue of Marton's region for classical broadcast channels. The(More)
We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map F ∈ L(Ain ⊗ Bin) → L(Aout ⊗ Bout), given as a quantum circuit, upon their joint quantum input state ρin ∈ D(Ain ⊗ Bin). Our protocol leaks no more to any active adversary than an ideal(More)
An encryption scheme is said to be entropically secure if an adversary whose min-entropy on the message is upper bounded cannot guess any function of the message. Similarly, an encryption scheme is entropically indistinguishable if the encrypted version of a message whose min-entropy is high enough is statistically indistinguishable from a fixed(More)
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have their own strengths and caveats and may be relevant in different contexts. We then propose a new algorithm for(More)
We construct a channel coding scheme to achieve the capacity of any discrete memoryless channel based solely on the techniques of polar coding. In particular, we show how source polarization and randomness extraction via polarization can be employed to &#x201C;shape&#x201D; uniformly-distributed i.i.d. random variables into approximate i.i.d. random(More)