Four locally indistinguishable ququad-ququad orthogonal maximally entangled states.

We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of d locally indistinguishable d⊗d orthogonal maximally entangled states for some positive integer d. We further show that a 2⊗2 maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of entanglement discrimination catalysis. Based on this set of states, we construct a new set K consisting of four locally indistinguishable states such that K(⊗m) (with 4(m) members) is locally distinguishable for some m greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.

Perfect distinguishability of quantum operations.

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretly selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, we find that an optimal perfect discrimination between two isometries is always achievable without auxiliary systems or entanglement.

State-based control of fuzzy discrete-event systems.

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete-event systems (DESs) as a generalization of conventional DESs have been introduced recently. Supervisory-control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy DESs in this paper. An approach to finding all fuzzy states that are reachable by controlling the system is presented first. After introducing the notion of controllability for fuzzy states, a necessary and sufficient condition for a set of fuzzy states to be controllable is then provided. It was also found that event- and state-based controls are not equivalent, and the relationship between them was further discussed. Finally, we examine the possibility of driving a fuzzy DES under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely.

Local distinguishability of multipartite unitary operations.

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguished by local operations and classical communication when a finite number of runs is allowed. Intuitively, this result indicates that the lost identity of a nonlocal unitary operation can be recovered locally. No entanglement between distant parties is required.

Entanglement is not necessary for perfect discrimination between unitary operations.

We show that a unitary operation (quantum circuit) secretly chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum operations are required in our scheme. We further show that our scheme is optimal in the sense that the number of the runs is minimal when discriminating only two unitary operations.

Distinguishing arbitrary multipartite basis unambiguously using local operations and classical communication.

We show that an arbitrary basis of a multipartite quantum state space consisting of K distant parties such that the kth party has local dimension dk always contains at least N= Sigma(k=1)(K) (dk-1)+1 members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show that this lower bound is optimal by analytically constructing a special product basis having only N members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon "nonlocality without entanglement," but also implies the existence of a locally distinguishable entangled basis.

Identification and distance measures of measurement apparatus.

We propose simple schemes that can perfectly identify projective measurement apparatuses secretly chosen from a finite set. Entanglement is used in these schemes both to make possible the perfect identification and to improve the efficiency significantly. Based on these results, a brief discussion on the problem of how to appropriately define distance measures of measurements is also provided.