Randomizing quantum states: Constructions and applications

Abstract

The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only near-perfect security is required, the size of the key can be reduced by a factor of two. More specifically, we show 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 d^2 operators required to randomize perfectly. Aside from the private quantum channel, variations of this construction can be applied to many other tasks in quantum information processing. We show, for instance, that it can be used to construct LOCC data hiding schemes for bits and qubits that are much more efficient than any others known, allowing roughly log d qubits to be hidden in 2 log d qubits. The method can also be used to exhibit the existence of quantum states with locked classical correlations, an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key. Our construction also provides the basic building block for a method of remotely preparing arbitrary d-dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement.

20 pages

References in corpus (10)

• Quantum Nonlocality without Entanglement
• Classical Communication Cost in Distributed Quantum Information Processing - A generalization of Quantum Communication Complexity
• Quantum Data Hiding
• Optimal Encryption of Quantum Bits
• Oblivious remote state preparation
• Locking classical correlation in quantum states
• Hiding classical data in multi-partite quantum states
• Truncations of random unitary matrices
• Quantum nonlocality in the presence of superselection rules and data hiding protocols
• Hiding Quantum Data

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