Approximate Randomization of Quantum States With Fewer Bits of Key

Details Approximate Randomization of Quantum States With Fewer Bits of Key Approximate Randomization of Quantum States With Fewer Bits of Key

2006-11-02

arxiv.org/abs/quant-ph/0611033v1

Physics

Quantum Physics

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

Scientific paper

10.1063/1.2400876

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.

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