Quantum state comparison and the universal-NOT operation

Abstract

We show that the form of the optimal universal-NOT operation for a single qubit can be determined by considering quantum-limited state comparison. Similarly, optimal state comparison can be derived from the properties of the universal-NOT. This points to the possibility of a fundamental link between these processes.

Keywords:

• quantum information
• quantum operations
• entanglement

Acknowledgements

I thank, for their encouragement and helpful suggestions, Sarah Croke, Mark Hillery, Daniel Oi and especially Vladimir Bužek, who asked me about the universal-NOT operation for the real states. I gratefully acknowledge the support of the Royal Society and the Wolfson Foundation.

Notes

Notes

1. Note that these probabilities are precisely the same if we use the pure states |ψ⟩ ⊗ |ψ⟩ and |ψ⟩ ⊗ |ψ^⊥⟩ in place of the averaged states and .

2. This situation is reminiscent, of course, of the process of teleportation of the state of a qubit 25.