Approximate Randomization of Quantum States With Fewer Bits of Key

Abstract

Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional state to a state that is within trace distance epsilon of the completely mixed state. Our bound is a log d factor smaller than that of Hayden, Leung, Shor, and Winter (2004), and Ambainis and Smith (2004). Then, we show that a random sequence of essentially the same number of unitary operators, chosen from an appropriate set, with high probability form an approximately randomizing map for d-dimensional states. Finally, we discuss the optimality of these schemes via connections to different notions of pseudorandomness, and give a new lower bound for small epsilon.

18 pages, Quantum Computing Back Action, IIT Kanpur, March 2006, volume 864 of AIP Conference Proceedings, pages 18--36. Springer, New York

References in corpus (2)

• Randomizing quantum states: Constructions and applications
• Invertible Quantum Operations and Perfect Encryption of Quantum States

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