aqora

Local discrimination of lattice states via adjacent matrix

Ying‐Hui Yang, Qi-Yue Zhao, Pei-Ying Chen +2 more

Quantum Information ProcessingMay 31, 20242 citations

Entropic topological invariant for a gapped one-dimensional system

Isaac H. Kim

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish a Majorana chain from a trivial chain under global fermion parity conservation. We argue that the order parameter can be, in principle, measured in an optical lattice system.We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish a Majorana chain from a trivial chain under global fermion parity conservation. We argue that the order parameter can be, in principle, measured in an optical lattice system.

arXiv:1306.4771Physical Review BJun 19, 20148 citations

Local distinguishability of generalized Bell states

Ying‐Hui Yang, Caihong Wang, Jiangtao Yuan +2 more

Quantum Information ProcessingDec 27, 201718 citations

Local discrimination of lattice states via complete graph

Qianqian Liu, Ying‐Hui Yang, Pei-Ying Chen +1 more

Abstract In this paper, we use graph theory to study the distinguishability of lattice states under local operations and classical communication (LOCC) in C p 2 ⨂ C p 2 . Firstly, we present that for the basis of lattice unitary matrices, there are (p 2 + 1)(p + 1) distinct maximal commuting sets in p 2-dimensional system. Secondly, for any set  of lattice states, we can obtain a graph G which consists of some k-complete subgraphs. Using the graph G, we show that the set  can be distinguished by one-way LOCC if n ( p + 1 ) − ∑ k = 1 p + 1 s k ( k − 1 ) < ( p 2 + 1 ) ( p + 1 ) , where n is the number of vertices of a graph G and s k is the number of k-complete subgraphs. Moreover, we also proved that this conclusion is necessary and sufficient in C 2 2 ⨂ C 2 2 . For C p 2 ⨂ C p 2 system, our result can cover the results in (2015, Phys. Rev. A 92, 042 320); (2020, Sci. China-Phys. Mech. Astron. 63, 280 312).Abstract In this paper, we use graph theory to study the distinguishability of lattice states under local operations and classical communication (LOCC) in C p 2 ⨂ C p 2 . Firstly, we present that for the basis of lattice unitary matrices, there are (p 2 + 1)(p + 1) distinct maximal commuting sets in p 2-dimensional system. Secondly, for any set  of lattice states, we can obtain a graph G which consists of some k-complete subgraphs. Using the graph G, we show that the set  can be distinguished by one-way LOCC if n ( p + 1 ) − ∑ k = 1 p + 1 s k ( k − 1 ) < ( p 2 + 1 ) ( p + 1 ) , where n is the number of vertices of a graph G and s k is the number of k-complete subgraphs. Moreover, we also proved that this conclusion is necessary and sufficient in C 2 2 ⨂ C 2 2 . For C p 2 ⨂ C p 2 system, our result can cover the results in (2015, Phys. Rev. A 92, 042 320); (2020, Sci. China-Phys. Mech. Astron. 63, 280 312).

Physica ScriptaSep 20, 20232 citations

Expanding the principle of local distinguishability

Claudio Carmeli, Teiko Heinosaari, Jussi Schultz +1 more

The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that, if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distinguish all pure states but not all states. Moreover, we show that, if the local measurements are such that the purity of the bipartite state can be verified from the statistics without any prior assumption, then in these special cases also this property is carried over to the composite measurement. These surprising facts give evidence that the principle of local distinguishability may be expanded beyond its usual applicability.The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement for the local measurements is that each one must be able to distinguish between all pairs of states of the respective subsystems. We show that, if the task is changed into the determination of an arbitrary bipartite pure state, then at least in certain cases it is possible to restrict to local measurements which can distinguish all pure states but not all states. Moreover, we show that, if the local measurements are such that the purity of the bipartite state can be verified from the statistics without any prior assumption, then in these special cases also this property is carried over to the composite measurement. These surprising facts give evidence that the principle of local distinguishability may be expanded beyond its usual applicability.

arXiv:1411.0828Physical Review AApr 17, 20152 citations

Distinguishability norms on high-dimensional quantum systems

Guillaume Aubrun

Jan 1, 20130 citations

Local distinguishability of lattice states in arbitrary dimensional system

Related papers

Local distinguishability of lattice states in arbitrary dimensional system

Related papers