On the Perfect Distinguishability of Unitary Operations

Unitary operation (or quantum logical gate) is one of the most basic
ingredients of Quantum Mechanics as well as Quantum Information Theory.
The study of various properties of unitary operations lies at the heart
of many important quantum information processing tasks. Recently the
problem of distinguishing unitary operations has received considerable
attention. Most notably, it has been demonstrated that a perfect
discrimination between two unitary operations can always be achieved by
taking a suitable entangled state as input and then applying only a
finite number of runs of the unknown unitary operation.

In this talk we first review some related results on this topic. Then
we present a new scheme to show that entanglement or any joint quantum
operations are not necessary for the perfect discrimination between
unitary operations, which makes this task actually feasible in
experiment. Furthermore, we give an analytical formula for the number
of the runs needed for the perfect discrimination between two untiary
operations and rigorously prove its optimality.

We also consider the discrimination of multipartite unitary operations
by local quantum operations and classical communication (LOCC) only.
Remarkably, our result indicates that any two different multipartite
unitary operations, no matter entangled or not, can also be perfectly
discriminated by LOCC. Intuitively, this result means that the lost
identity of a nonlocal unitary operation can be recovered locally. To
the best of my knowledge, this is the first result about the local
distinguishability of multipartite quantum operations.

Reference:

1. Runyao Duan, Yuan Feng, and Mingsheng Ying, Entanglement is Not
Necessary for Perfect Discrimination between Unitary operations,
Physical Review Letters 98, 100503, 2007. Available online:
http://www.arxiv.org/abs/quant-ph/0601150.

2. Runyao Duan, Yuan Feng, and Mingsheng Ying, Local Distinguishability
of Multipartite Unitary Operations, 2007. Available online:
http://www.arxiv.org/abs/0705.1424.