General impossible operations in quantum information

Details General impossible operations in quantum information General impossible operations in quantum information

2001-11-29

arxiv.org/abs/quant-ph/0111153v3

Phys. Rev. A Vol 66, 062319 (2002)

Physics

Quantum Physics

15 pages, no figures, Discussion about personal quantum computer removed

Scientific paper

10.1103/PhysRevA.66.062319

We prove a general limitation in quantum information that unifies the impossibility principles such as no-cloning and no-anticloning. Further, we show that for an unknown qubit one cannot design a universal Hadamard gate for creating equal superposition of the original and its complement state. Surprisingly, we find that Hadamard transformations exist for an unknown qubit chosen either from the polar or equatorial great circles. Also, we show that for an unknown qubit one cannot design a universal unitary gate for creating unequal superpositions of the original and its complement state. We discuss why it is impossible to design a controlled-NOT gate for two unknown qubits and discuss the implications of these limitations.

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