Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Manufacturing Engineer

Zero-error information and applications in cryptography

Stefan Wolf, J. Wultschleger

Published Apr 6, 2005• 46 citations
Publisher

Abstract

In analogy to the zero-error variant of the channel capacity, the zero-error information between two random variables is defined. We show that our definition is natural in the sense that the representation of the channel capacity with respect to mutual information carries over to the zero-error variants of the quantities. It is shown that the new notion, together with two operators introduced in the same context, namely the common random variable of two random variables and the dependent part of a random variable with respect to another, is useful for giving characterizations of the possibility of realizing cryptographic tasks - such as bit commitment, coin tossing, or oblivious transfer - from correlated pieces of information.

DOI
10.1109/itw.2004.1405264

Related papers

Quantum cryptography -- an information theoretic security

Nadeem, Muhammad

Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure computations and ideal coin tossing in quantum regime leaves an obvious question on the completeness of quantum cryptography. Instead of using wide range of rules and techniques for a variety of cryptographic applications, we demonstrate here a unified structure for quantum cryptography based on quantum non-local correlations. The unified framework achieves same goals in information-theoretic way as classical cryptography does with computational hardness. To cover the broad range of cryptographic applications, we show that the framework (i) assures secrecy by providing encryption completely unintelligible to eavesdroppers, (ii) guarantees that input from distant parties is concealed unless they are willing to reveal, (iii) assures binding, (iv) allows splitting information between several parties securely and more generally, (v) evades both quantum and classical attacks from internal as well as external eavesdropping.

arXiv:1507.07918•Jul 28, 2015•3 citations

Unique Informations and Deficiencies

Pradeep Kr. Banerjee, Eckehard Olbrich, Jurgen Jost +1 more

Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le Cam deficiencies and differ on whether one channel can approximate the other by a randomization at either its input or output. We relate the proposed quantities to an existing measure of unique information which we call the minimum-synergy unique information. We give an operational interpretation of the latter in terms of an upper bound on the one-way secret key rate and discuss the role of the unique informations in the context of nonnegative mutual information decompositions into unique, redundant and synergistic components.

arXiv:1807.05103•Allerton Conference on Communication, Control, and Computing•Oct 1, 2018•20 citations

Nonlocality-assisted enhancement of error-free communication in noisy classical channels

Kunika Agarwal, Sahil Gopalkrishna Naik, Ananya Chakraborty +5 more

The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.

arXiv:2412.04779•Physical Review A•Mar 10, 2026•0 citations

Rates for bit commitment and coin tossing from noisy correlation

H. Imai, Joern Mueller-Quade, Anderson C. A. Nascimento +1 more

This paper studies the optimisation of the channel with cryptographic primitives such as coin tossing and oblivious transfer by committing to a set of strings. The main contribution of this paper is that the commitment is possible from any nontrivial correlation at rates when the sender is Alice and Bob, those rates are optimal. Also the coin tossing capacity is infinite for every channel having a positive bit commitment rate.

IEEE International Symposium on Information Theory (ISIT)•Dec 23, 2004•17 citations

Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations

Toby S. Cubitt, Debbie Leung, William Matthews +1 more

The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i.e., shared randomness, shared entanglement and arbitrary nonsignalling correlations. When the channel being simulated is noiseless, this is zero-error coding assisted by correlations. When the resource channel is noiseless, it is the reverse problem of simulating a noisy channel exactly by a noiseless one, assisted by correlations. In both cases, separations between the power of the different classes of assisting correlations are exhibited for finite block lengths. The most striking result here is that entanglement can assist in zero-error communication. In the large block length limit, shared randomness is shown to be just as powerful as arbitrary nonsignalling correlations for exact simulation, but not for asymptotic zero-error coding. For assistance by arbitrary nonsignalling correlations, linear programming formulas for the asymptotic capacity and simulation rates are derived, the former being equal (for channels with nonzero unassisted capacity) to the feedback-assisted zero-error capacity derived by Shannon. Finally, a kind of reversibility between nonsignalling-assisted zero-error capacity and exact simulation is observed, mirroring the usual reverse Shannon theorem.

arXiv:1003.3195•IEEE Transactions on Information Theory•Aug 1, 2011•70 citations

Information Capacity of Quantum Transfer Channels and Thermodynamic Analogies

Bohdan Hejna

We will begin with a simple type of stationary stochastic1 systems of quantum physics using them within a frame of the Shannon Information Theory and Thermodynamics but starting with their algebraic representation. Based on this algebraic description a model of information transmission in those systems by defining the Shannon information will be stated in terms of variable about the system state. Measuring on these system is then defined as a spectral decomposition of measured quantities operators. The information capacity formulas, now of the narrow-band nature, are derived consequently, for the simple system governed by the Bose–Einstein (B–E) Law [bosonic (photonic) channel] and that one governed by the Fermi-Dirac (F–D) Law [fermionic (electron) channel]. The not-zero value for the average input energy needed for information transmission existence in F–D systems is stated [11, 12].

InTech eBooks•Oct 3, 2012•0 citations
In analogy to the zero-error variant of the channel capacity, the zero-error information between two random variables is defined. We show that our definition is natural in the sense that the representation of the channel capacity with respect to mutual information carries over to the zero-error variants of the quantities. It is shown that the new notion, together with two operators introduced in the same context, namely the common random variable of two random variables and the dependent part of a random variable with respect to another, is useful for giving characterizations of the possibility of realizing cryptographic tasks - such as bit commitment, coin tossing, or oblivious transfer - from correlated pieces of information.
Methods of quantum mechanics promise information-theoretic security for various protocols in cryptography. However, impossibility of some cryptographic applications such as standard bit commitment, oblivious transfer, multiparty secure computations and ideal coin tossing in quantum regime leaves an obvious question on the completeness of quantum cryptography. Instead of using wide range of rules and techniques for a variety of cryptographic applications, we demonstrate here a unified structure for quantum cryptography based on quantum non-local correlations. The unified framework achieves same goals in information-theoretic way as classical cryptography does with computational hardness. To cover the broad range of cryptographic applications, we show that the framework (i) assures secrecy by providing encryption completely unintelligible to eavesdroppers, (ii) guarantees that input from distant parties is concealed unless they are willing to reveal, (iii) assures binding, (iv) allows splitting information between several parties securely and more generally, (v) evades both quantum and classical attacks from internal as well as external eavesdropping.
Given two channels that convey information about the same random variable, we introduce two measures of the unique information of one channel with respect to the other. The two quantities are based on the notion of generalized weighted Le Cam deficiencies and differ on whether one channel can approximate the other by a randomization at either its input or output. We relate the proposed quantities to an existing measure of unique information which we call the minimum-synergy unique information. We give an operational interpretation of the latter in terms of an upper bound on the one-way secret key rate and discuss the role of the unique informations in the context of nonnegative mutual information decompositions into unique, redundant and synergistic components.
The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.
The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver i.e., shared randomness, shared entanglement and arbitrary nonsignalling correlations. When the channel being simulated is noiseless, this is zero-error coding assisted by correlations. When the resource channel is noiseless, it is the reverse problem of simulating a noisy channel exactly by a noiseless one, assisted by correlations. In both cases, separations between the power of the different classes of assisting correlations are exhibited for finite block lengths. The most striking result here is that entanglement can assist in zero-error communication. In the large block length limit, shared randomness is shown to be just as powerful as arbitrary nonsignalling correlations for exact simulation, but not for asymptotic zero-error coding. For assistance by arbitrary nonsignalling correlations, linear programming formulas for the asymptotic capacity and simulation rates are derived, the former being equal (for channels with nonzero unassisted capacity) to the feedback-assisted zero-error capacity derived by Shannon. Finally, a kind of reversibility between nonsignalling-assisted zero-error capacity and exact simulation is observed, mirroring the usual reverse Shannon theorem.
We will begin with a simple type of stationary stochastic1 systems of quantum physics using them within a frame of the Shannon Information Theory and Thermodynamics but starting with their algebraic representation. Based on this algebraic description a model of information transmission in those systems by defining the Shannon information will be stated in terms of variable about the system state. Measuring on these system is then defined as a spectral decomposition of measured quantities operators. The information capacity formulas, now of the narrow-band nature, are derived consequently, for the simple system governed by the Bose–Einstein (B–E) Law [bosonic (photonic) channel] and that one governed by the Fermi-Dirac (F–D) Law [fermionic (electron) channel]. The not-zero value for the average input energy needed for information transmission existence in F–D systems is stated [11, 12].