Related papers: Leftover Hashing Against Quantum Side Information
We present a version of quantum hash function based on non-binary discrete functions. The proposed quantum procedure is "classical-quantum", that is, it takes a classical bit string as an input and produces a quantum state. The resulting…
It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
We consider state redistribution of a "hybrid" information source that has both classical and quantum components. The sender transmits classical and quantum information at the same time to the receiver, in the presence of classical and…
In the classical setting, public-key encryption requires randomness in order to be secure against a forward search attack, whereby an adversary compares the encryption of a guess of the secret message with that of the actual secret message.…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of…
The multivariate covering lemma states that given a collection of $k$ codebooks, each of sufficiently large cardinality and independently generated according to one of the marginals of a joint distribution, one can always choose one…
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
The guesswork is an information-theoretic quantity which can be seen as an alternate security criterion to entropy. Recent work has established the theoretical framework for guesswork in the presence of quantum side information, which we…
We address the question whether quantum memory is more powerful than classical memory. In particular, we consider a setting where information about a random n-bit string X is stored in r classical or quantum bits, for r<n, i.e., the stored…
Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This…
Randomness extractors, widely used in classical and quantum cryptography and other fields of computer science, e.g., derandomization, are functions which generate almost uniform randomness from weak sources of randomness. In the quantum…
In conventional cryptography, information-theoretically secure message authentication can be achieved by means of universal hash functions, and requires that the two legitimate users share a random secret key, which is twice as long as the…
Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…
Random hashing can provide guarantees regarding the performance of data structures such as hash tables---even in an adversarial setting. Many existing families of hash functions are universal: given two data objects, the probability that…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed (C. Miller, Y. Shi, Quant.…