Small Pseudo-Random Families of Matrices: Derandomizing Approximate Quantum Encryption
Andris Ambainis,Adam Smith +1 more
- pp 249-260
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TLDR
A quantum encryption scheme is a one-time pad for quantum messages as discussed by the authors, where two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted.Abstract:
A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted. Perfect encryption schemes leak no information at all about the message. Approximate encryption schemes leak a non-zero (though small) amount of information but require a shorter shared random key. Approximate schemes with short keys have been shown to have a number of applications in quantum cryptography and information theory [8].read more
Citations
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Exact and approximate unitary 2-designs and their application to fidelity estimation
TL;DR: In this paper, the concept of unitary 2-designs was introduced as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U({2}^{n})$ on qubits.
Journal ArticleDOI
Random Quantum Circuits are Approximate 2-designs
Aram W. Harrow,Richard A. Low +1 more
TL;DR: It is shown that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1- and 2-designs.
Journal ArticleDOI
Counterexamples to the Maximal p-Norm Multiplicativity Conjecture for all p > 1
TL;DR: For all p > 1, the existence of quantum channels with non-multiplicative maximal output p-norms has been shown in this paper, where the violations are large; in all cases, the minimum output Renyi entropy of order p for a product channel need not be significantly greater than the minimum entropy of its individual factors.
Journal ArticleDOI
Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
TL;DR: For all p > 1, it is demonstrated the existence of quantum channels with non-multiplicative maximal output p-norms, and a class of channels previously studied in the context of approximate encryption lead to counterexamples for all p > 2.
Journal Article
Applications of coherent classical communication and the schur transform to quantum information theory
Isaac L. Chuang,Aram W. Harrow +1 more
TL;DR: It is found that coherent classical communication can be used to derive several new quantum protocols and unify them both conceptually and operationally with old ones, and these new protocols are used to prove optimal trade-off curves for a wide variety of coding problems.
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
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Small-bias probability spaces: efficient constructions and applications
Joseph (Seffi) Naor,Moni Naor +1 more
TL;DR: It is shown how to efficiently construct a small probability space on n binary random variables such that for every subset, its parity is either zero or one with “almost” equal probability.
Journal ArticleDOI
Simple Constructions of Almost k-wise Independent Random Variables
TL;DR: This work presents three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent and their simplicity is their simplicity.
Journal ArticleDOI
Randomizing Quantum States: Constructions and Applications
TL;DR: It is shown that there exists a set of roughly d’log d unitary operators whose average effect on every input pure state is almost perfectly randomizing, as compared to the d2 operators required to randomize perfectly.
Journal ArticleDOI
Construction of asymptotically good low-rate error-correcting codes through pseudo-random graphs
TL;DR: A novel technique, based on the pseudo-random properties of certain graphs known as expanders, is used to obtain novel simple explicit constructions of asymptotically good codes, superior to previously known explicit construction in the zero-rate neighborhood.