Researches On Local Discrimination Of Maximally Entangled States

The relationship between quantum entanglement and quantum nonlocality has always been considered as the most significant and fundamental issue in quantum information theory. And one of the effective and efficient method to study the relationship is the local discrimination of mutually orthogonal quantum states, especially the local discrimination of maximally entangled states (MESs). More importantly,the local discrimination of quantum states play a significant role in the design of quantum cryptography. The local discrimination of quantum states means that, for a quantum state secretly chosen from a finitely known orthogonal states set, the spacelike-separated parties are only allowed to use local operations and classical communication (LOCC) to distinguish its identity. As is known, the orthogonal states can be discriminated by global operations. Therefore, if some orthogonal quantum states cannot be discriminated, then they will reveal quantum nonlocality, and also can be used to design quantum cryptography protocol; while if some quantum states can be discriminated locally, then they can be employed in some quantum information processing tasks,such as distributed quantum computation.In this dissertation, we study the local discrimination of two kinds of specific MESs with wide application in detail. That is, what we considered is which MESs can be locally distinguished, while others cannot. Furthermore, through constructing one-way locally indistinguishing but two-way locally distinguishing MESs, we explicitly show the generally existed difference between one-way and two-way classical communication. The details are as follows.1. For the local discrimination of generalized Bell states (GBSs), we obtain two results: (1) arbitrary four GBSs in 4(?)4 system can be partitioned into ten local-unitary (LU) equivalent classes, therein seven classes are locally one-way distinguishable while seven classes are two-way indistinguishable; (2) any three GBSs are locally distinguishable in all systems. In order for this conclusion, we firstly use the Clifford operators to realize the LU equivalence of generalized Pauli matrices as many as possible. Then by the unequal LU invariants, we can prove the LU inequivalence of the final sets. After finding out the LU equivalent sets, we only need to explore the local discrimination of one representative set, because the local discrimination keeps the same under LU operations. In other words, the classification of LU equivalent sets can be acted as an efficient method for the study of local discrimination of MESs.2. For the local discrimination of lattice states, we prove that any l lattice states including k commuting elements and satisfying l(l-1) - (k+1)(k - 2)?2pr can be locally discriminated in the pr (?) pr quantum system. In order for this, we partition all the nontrivial lattice unitary operators in this quantum system into pr+1 sets, and each one contains pr -1 mutually commuting lattice unitary operators. Thus there exist pr + 1 mutually unbiased bases, which can be taken as the measurement basis to distinguish the lattice states. This result generalized the previous result that any l MESs which satisfies l(l-1)?2p are locally distinguishable.3. For the difference between one-way and two-way classical communication in local discrimination, we prove the general existence of this difference. To obtain this conclusion, we firstly build more MESs to show the difference taking use of the existed two-way locally discriminating protocol. Moreover, we are able to find out one-way locally indistinguishable but two-way distinguishable MESs in all the quantum systems, which implies the two-way classical communication generally has advantage over one-way classical communication in local discrimination of MESs.