Asymptotic theory of finite dimensional normed spaces
Asymptotic theory of finite dimensional normed spaces
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Communication complexity
How to Fool an Unbounded Adversary with a Short Key
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptography In the Bounded Quantum-Storage Model
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Uncertainty principles, extractors, and explicit embeddings of l2 into l1
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem
Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak
A tight high-order entropic quantum uncertainty relation with applications
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Quantum entropic security and approximate quantum encryption
IEEE Transactions on Information Theory
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Quantum and classical message protect identification via quantum channels
Quantum Information & Computation
Entropic security and the encryption of high entropy messages
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Quantum fingerprints that keep secrets
Quantum Information & Computation
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Quantum uncertainty relations are at the heart of many quantum cryptographic protocols performing classically impossible tasks. One operational manifestation of these uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message (the message is "locked"). Furthermore, knowing the key, it is possible to recover (or "unlock") the message. In this paper, we make the following contributions by exploiting a connection between uncertainty relations and low-distortion embeddings of L2 into L1. * We introduce the notion of metric uncertainty relations and connect it to low-distortion embeddings of L2 into L1. A metric uncertainty relation also implies an entropic uncertainty relation. * We prove that random bases satisfy uncertainty relations with a stronger definition and better parameters than previously known. Our proof is also considerably simpler than earlier proofs. We apply this result to show the existence of locking schemes with key size independent of the message length. * We give efficient constructions of bases satisfying metric uncertainty relations. These bases are computable by quantum circuits of almost linear size. This leads to the first explicit construction of a strong information locking scheme. Moreover, we present a locking scheme that can in principle be implemented with current technology. These constructions are obtained by adapting an explicit norm embedding due to Indyk (2007) and an extractor construction of Guruswami, Umans and Vadhan (2009). * We apply our metric uncertainty relations to give communication protocols that perform equality-testing of n-qubit states. We prove that this task can be performed by a single message protocol using O(log(1/e)) qubits and n bits of communication, where e is an error parameter. We also give a single message protocol that uses O(log^2 n) qubits, where the computation of the sender is efficient.