Estimation, operation and discrimination of quantum state

Unitary Transformations Can Be Distinguished Locally
    It is well-known that two pure states cannot be perfectly discriminated unless they are orthogonal. Quantum states discrimination is an interesting problem in quantum information science, and has been extensively studied. However, things become very different when we refer to quantum operations. It was proved that two nonorthogonal unitary operations U and V can be perfectly discriminated if we can run the selected unitary gate a finite number (k) of times in parallel and prepare a suitable input state. This result is surprising and nontrivial.
We show that, in principle, N-partite unitary transformations can be perfectly discriminated under local operations and classical communication despite their nonlocal properties. Based on this result, some related topics, including the construction of the appropriate quantum circuit together with the extension to general completely positive trace preserving operations, are discussed.

Physical accessible transformations on a finite number of quantum states
    We consider treating the usual probabilistic cloning, state separation, unambiguous state discrimination, etc., in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive trace-nonincreasing maps on a finite number of input states. From the system-ancilla model we construct the corresponding unitary implementation of pure→pure, pure→mixed, mixed→pure, and mixed→mixed state transformations in the whole system and obtain the necessary and sufficient conditions for the existence of the desired maps.

State estimation from a pair of conjugate qudits
    We show that, for N parallel input states, an antilinear map with respect to a specific basis is essentially a classical operation. We also consider the information contained in a phase-conjugate pair, and prove that there is more information about a quantum state encoded in a phase-conjugate pair than in a parallel pair.

Local distinguishability of orthogonal quantum states and generators of SU(N)
    Orthogonal multipartite quantum states can always be distinguished when global measurements can be implemented, but it is a different case if only local operations and classical communication (LOCC) are allowed. Bennett et al. presented a set of nine orthogonal product states that cannot be distinguished by LOCC, which demonstrates that there is nonlocality different from quantum entanglement. Since then the possibility of distinguishing a set of orthogonal states by LOCC has attracted much interest. The problem has now been connected to many other research fields in quantum information science such as the bound entanglement and the global robustness of entanglement.
    We connect this problem with generators of SU(N) and present a condition that is necessary for a set of orthogonal states to be locally distinguishable. We show that even in multipartite cases there exists a systematic way to check whether the presented condition is satisfied for a given set of orthogonal states. Based on the proposed checking method, we find that LOCC cannot distinguish three mutually orthogonal states in which two of them are Greenberger-Horne-Zeilinger-like states.