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Exponential separations for oneway quantum communication complexity, with applications to cryptography
 IN PROCEEDINGS OF 39TH ACM STOC
, 2007
"... We give an exponential separation between oneway quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of BarYossef et al.) Earlier such an exponential separation was known only for a relational problem. The communication pr ..."
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Cited by 55 (15 self)
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We give an exponential separation between oneway quantum and classical communication protocols for a partial Boolean function (a variant of the Boolean Hidden Matching Problem of BarYossef et al.) Earlier such an exponential separation was known only for a relational problem. The communication problem corresponds to a strong extractor that fails against a small amount of quantum information about its random source. Our proof uses the Fourier coefficients inequality of Kahn, Kalai, and Linial. We also give a number of applications of this separation. In particular, we show that there are privacy amplification schemes that are secure against classical adversaries but not against quantum adversaries; and we give the first example of a keyexpansion scheme in the model of boundedstorage cryptography that is secure against classical memorybounded adversaries but not against quantum ones.
The operational meaning of min and maxentropy
 IEEE Transactions on Information Theory
"... Abstract—In this paper, we show that the conditional minentropy of a bipartite state is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the part of are allowed. In the special case where is classical, this overlap corresponds to t ..."
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Cited by 46 (10 self)
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Abstract—In this paper, we show that the conditional minentropy of a bipartite state is directly related to the maximum achievable overlap with a maximally entangled state if only local actions on the part of are allowed. In the special case where is classical, this overlap corresponds to the probability of guessing given. In a similar vein, we connect the conditional maxentropy to the maximum fidelity of with a product state that is completely mixed on . In the case where is classical, this corresponds to the security of when used as a secret key in the presence of an adversary holding . Because min and maxentropies are known to characterize informationprocessing tasks such as randomness extraction and state merging, our results establish a direct connection between these tasks and basic operational problems. For example, they imply that the (logarithm of the) probability of guessing given is a lower bound on the number of uniform secret bits that can be extracted from relative to an adversary holding . Index Terms—Entropy measures, maxentropy, minentropy, operational interpretations, quantum information theory, quantum hypothesis testing, singlet fraction, singleshot information theory. I.
A tight highorder entropic quantum uncertainty relation with applications
, 2007
"... We derive a new entropic quantum uncertainty relation involving minentropy. The relation is tight and can be applied in various quantumcryptographic settings. Protocols for quantum 1outof2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove ..."
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Cited by 27 (9 self)
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We derive a new entropic quantum uncertainty relation involving minentropy. The relation is tight and can be applied in various quantumcryptographic settings. Protocols for quantum 1outof2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the boundedquantumstorage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantummemorybounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the sixstate protocol with oneway communication, a bitflip error rate of up to 17 % can be tolerated (compared to 13 % in the standard model). Our uncertainty relation also yields a lower bound on the minentropy key uncertainty against knownplaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.
A Hierarchy of Information Quantities for Finite Block Length Analysis of Quantum Tasks
, 2013
"... We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using socalled oneshot entropies. These characterizations — in contrast ..."
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Cited by 26 (15 self)
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We consider two fundamental tasks in quantum information theory, data compression with quantum side information as well as randomness extraction against quantum side information. We characterize these tasks for general sources using socalled oneshot entropies. These characterizations — in contrast to earlier results — enable us to derive tight second order asymptotics for these tasks in the i.i.d. limit. More generally, our derivation establishes a hierarchy of information quantities that can be used to investigate information theoretic tasks in the quantum domain: The oneshot entropies most accurately describe an operational quantity, yet they tend to be difficult to calculate for large systems. We show that they asymptotically agree (up to logarithmic terms) with entropies related to the quantum and classical information spectrum, which are easier to calculate in the i.i.d. limit. Our technique also naturally yields bounds on operational quantities for finite block lengths.
Unconditional security from noisy quantum storage
, 2009
"... We consider the implementation of twoparty cryptographic primitives based on the sole assumption that no largescale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide sec ..."
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Cited by 18 (1 self)
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We consider the implementation of twoparty cryptographic primitives based on the sole assumption that no largescale reliable quantum storage is available to the cheating party. We construct novel protocols for oblivious transfer and bit commitment, and prove that realistic noise levels provide security even against the most general attack. Such unconditional results were previously only known in the socalled boundedstorage model which is a special case of our setting. Our protocols can be implemented with presentday hardware used for quantum key distribution. In particular, no quantum storage is required for the honest parties.
Entropic uncertainty relations – A survey
, 2009
"... Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, rather little is known about entropic un ..."
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Cited by 17 (0 self)
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Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum cryptographic protocols. Yet, rather little is known about entropic uncertainty relations with more than two measurement settings. In this note we review known results and open questions. The uncertainty principle is one of the fundamental ideas of quantum mechanics. Since Heisenberg’s uncertainty relations for canonically conjugate variables, they have been one of the most prominent examples of how quantum mechanics differs from the classical world (Heisenberg, 1927). Uncertainty relations today are probably best known in the form given by (Robertson, 1929), who extended Heisenberg’s result to two arbitrary observables A and B. Robertson’s relation states that if we prepare many copies of the state ψ〉, and measure each copy individually using either A or B, we have