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Some necessary and sufficient conditions for k-separability of multipartite pure states

Yinzhu Wang, Jinchuan Hou

Quantum Information ProcessingJul 22, 20158 citations

Sufficient and necessary conditions of separability for bipartite pure states in infinite-dimensional systems

Guo Guo, Yu, Qi Qi +3 more

中国科学通报：英文版Jan 1, 20110 citations

Necessary and Sufficient Conditions of Separability for Multipartite Pure States

Dafa Li, Xiangrong Li, Huang Hongtao +1 more

In this paper we present a necessary and sufficient condition of separability for multipartite pure states and variants of it. These conditions are very simple and calculable, and they do not require Schmidt decomposition (for two subsystems) or tracing out operations. We also give a necessary condition for a local unitary equivalence class for a bipartite system in terms of the determinant of the matrix of amplitudes.

arXiv:quant-ph/0604147Communications in Theoretical PhysicsMay 1, 20087 citations

Schmidt Decomposition in Multipartite Hilbert Space

Spandan Das, Supervisors Dr. Goutam Paul, Swarnendu Datta

In this report, we discuss a necessary and sufficient condition for the existence of Schmidt decomposition of a pure state in a multipartite Hilbert space. Schmidt decomposition exists for any pure state in a bipartite Hilbert space. It is extremely useful since it reduces the number of terms needed to represent a pure state using orthonormal bases of the respective parts. However, for 3 or more partite Hilbert spaces, Schmidt decomposition does not exist in general for an arbitrary pure state. In this thesis, we derive a condition that states whether a state in an n-partite Hilbert space is Schmidt-decomposable or not, i.e., whether we can represent it through the orthonormal bases of the respective parts using less number of terms that is required in general.In this report, we discuss a necessary and sufficient condition for the existence of Schmidt decomposition of a pure state in a multipartite Hilbert space. Schmidt decomposition exists for any pure state in a bipartite Hilbert space. It is extremely useful since it reduces the number of terms needed to represent a pure state using orthonormal bases of the respective parts. However, for 3 or more partite Hilbert spaces, Schmidt decomposition does not exist in general for an arbitrary pure state. In this thesis, we derive a condition that states whether a state in an n-partite Hilbert space is Schmidt-decomposable or not, i.e., whether we can represent it through the orthonormal bases of the respective parts using less number of terms that is required in general.

May 1, 20180 citations

Separability Criterion for Bipartite States and Its Generalization to Multipartite Systems

。 Huang, Jie-Hui, H. Hu +5 more

Chinese Physics LettersJan 1, 20140 citations

Locally undetermined states, generalized Schmidt decomposition, and application in distributed computing

Yuan Feng, Runyao Duan, Mingsheng Ying

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computing. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.

Quantum Information and ComputationNov 1, 20091 citation

Necessary and Sufficient Conditions of Separability for Multipartite Pure States

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Necessary and Sufficient Conditions of Separability for Multipartite Pure States

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