Starting with Shannon's perfect secrecy theorem, information theory has provided a tool for quantifying the amount of secrecy available for a fixed transmission setup. In this paper, we derive tight upper bounds on the secrecy offered for a broad class of problems consisting of distributed encryption and joint decryption. In particular, we consider the scenario where correlated messages must be encrypted independently, transmitted through perfect channels to a common receiver, and jointly decrypted. The main result we present is a theorem stating that the secrecy of a distributed system does not depend on whether dependent messages are encrypted jointly or separately, as long as joint decryption is allowed. This result is analogous to the Slepian-Wolf theorem for data compression, which states that asymptotically, distributed data compression performs as well as joint compression. We show that the equivalence of distributed and joint encryption is true whether the system uses a key or not, and consequently we demonstrate that if the system does not rely on a key, no secrecy can be offered. We briefly discuss how the results obtained may be applied to the problem of drone or sensor networks, as well as parallel encryption
Starting with Shannon's perfect secrecy theorem, information theory has provided a tool for quantifying the amount of secrecy available for a fixed transmission setup. In this paper, we derive tight upper bounds on the secrecy offered for a broad class of problems consisting of distributed encryption and joint decryption. In particular, we consider the scenario where correlated messages must be encrypted independently, transmitted through perfect channels to a common receiver, and jointly decrypted. The main result we present is a theorem stating that the secrecy of a distributed system does not depend on whether dependent messages are encrypted jointly or separately, as long as joint decryption is allowed. This result is analogous to the Slepian-Wolf theorem for data compression, which states that asymptotically, distributed data compression performs as well as joint compression. We show that the equivalence of distributed and joint encryption is true whether the system uses a key or not, and consequently we demonstrate that if the system does not rely on a key, no secrecy can be offered. We briefly discuss how the results obtained may be applied to the problem of drone or sensor networks, as well as parallel encryption
Suppose there are two correlated sources, one producing classical data and the other producing mixed states with commuting density operators. We combine the two sources into one and call it a classical-quantum source. In this paper, we consider the problem of distributed compression of the classical-quantum source. This is a special case of the classical-quantum Slepian-Wolf problem addressed by Devetak and Winter [1]. Suppose Alice (resp. Bob) receives classical (resp. quantum) data from the classical-quantum source. Alice and Bob, who cannot communicate with each other, want to send their received data to Charlie at the minimum communication cost. We consider two scenarios, the blind and visible scenarios, for Bob's quantum data compression. We formulate our problem in terms of classical information theory and then using some results in classical information theory, we show partial results on the achievable rate region for asymptotically lossless distributed compression of the classical-quantum source in the blind and visible scenarios.
In this paper we study interactive "one-shot" analogues of the classical Slepian-Wolf theorem. Alice receives a value of a random variable X, Bob receives a value of another random variable Y that is jointly distributed with X. Alice's goal is to transmit X to Bob (with some error probability ε). Instead of one-way transmission, which is studied in the classical coding theory, we allow them to interact. They may also use shared randomness. We show, that Alice can transmit X to Bob in expected H(X∣Y)+2H(X∣Y)+O(log2(ε1)) number of bits. Moreover, we show that every one-round protocol π with information complexity I can be compressed to the (many-round) protocol with expected communication about I+2I bits. This improves a result by Braverman and Rao \cite{braverman2011information}, where they had 5I. Further, we show how to solve this problem (transmitting X) using 3H(X∣Y)+O(log2(ε1)) bits and 4 rounds on average. This improves a result of~\cite{brody2013towards}, where they had 4H(X∣Y)+O(log1/ε) bits and 10 rounds on average. In the end of the paper we discuss how many bits Alice and Bob may need to communicate on average besides H(X∣Y). The main question is whether the upper bounds mentioned above are tight. We provide an example of (X,Y), such that transmission of X from Alice to Bob with error probability ε requires H(X∣Y)+Ω(log2(ε1)) bits on average.
The problem of distributed compression for correlated quantum sources is considered. The classical version of this problem was solved by Slepian and Wolf, who showed that distributed compression could take full advantage of redundancy in the local sources created by the presence of correlations. Here it is shown that, in general, this is not the case for quantum sources, by proving a lower bound on the rate sum for irreducible sources of product states which is stronger than the one given by a naive application of Slepian–Wolf. Nonetheless, strategies taking advantage of correlation do exist for some special classes of quantum sources. For example, Devetak and Winter demonstrated the existence of such a strategy when one of the sources is classical. Optimal nontrivial strategies for a different extreme, sources of Bell states, are presented here. In addition, it is explained how distributed compression is connected to other problems in quantum information theory, including information-disturbance questions, entanglement distillation and quantum error correction.
We pose and investigate the distributed secure source coding based on the common key cryptosystem. This cryptosystem includes the secrecy amplification problem for distributed encrypted sources with correlated keys using post-encryption-compression, which was previously studied by Santoso and Oohama. In this paper we propose another new security criterion which is generally more strict compared with the commonly used security criterion based on the upper-bound of mutual information between the plaintext and the ciphertext. Under this criterion, we establish the necessary and sufficient condition for the secure transmission of correlated sources.
A single quantum state can be shared by many distant parties. In this thesis, we try to characterize the information contents of such distributed states by defining the multiparty information and the multiparty squashed entanglement, two steps toward a general theory of multiparty quantum information. As a further step in that direction, we partially solve the multiparty distributed compression problem where multiple parties use quantum communication to faithfully transfer their shares of a state to a common receiver. We build a protocol for multiparty distributed compression based on the fully quantum Slepian-Wolf protocol and prove both inner and outer bounds on the achievable rate region. We relate our findings to previous results in information theory and discuss some possible applications.
In this paper, we consider a quantum generalization of the task considered by Slepian and Wolf regarding distributed source compression. In our task, Alice, Bob, Charlie, and Reference share a joint pure state. Alice and Bob wish to send a part of their respective systems to Charlie without collaborating with each other. We give achievability bounds for this task in the one-shot setting and provide the asymptotic and independent identically distributed analysis in the case when there is no side information with Charlie. Our result implies the result of Abeyesinghe et al., who studied a special case of this problem. As another special case wherein Bob holds trivial registers, we recover the result of Devetak and Yard regarding quantum state redistribution.