General Classes of Impossible Operations through the Existence of Incomparable States

Details General Classes of Impossible Operations through the Existence of Incomparable States General Classes of Impossible Operations through the Existence of Incomparable States

2006-09-29

arxiv.org/abs/quant-ph/0609226v1

Quantum Information and Computation, 7 (2007) 392-400

Physics

Quantum Physics

13 pages, Latex, to appear in Quantum Information and Computation

Scientific paper

In this work we show that the most general class of anti-unitary operators are nonphysical in nature through the existence of incomparable pure bipartite entangled states. It is also shown that a large class of inner-product-preserving operations defined only on the three qubits having spin-directions along x, y and z are impossible. If we perform such an operation locally on a particular pure bipartite state then it will exactly transform to another pure bipartite state that is incomparable with the original one. As subcases of the above results we find the nonphysical nature of universal exact flipping operation and existence of universal Hadamard gate. Beyond the information conservation in terms of entanglement, this work shows how an impossible local operation evolve with the joint system in a nonphysical way.

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