Partial Hermitian Conjugate Separability Criteria for Pure Quantum States

We propose a criterion for the separability of quantum pure states using the concept of a partial Hermitian conjugate. It is equivalent to the usual positive partial transposition criteria, with a simple physical interpretation.     

Separability Criteria for Quantum Mixed States

We investigate separability of mixed states in bipartite and multipartite quantum systems. If a quantum state in a bipartite system of arbitrary dimension (or in $2\times2\times N$ quantum systems) is separable, we show that some quantity in relation to Hermitian matrix is positive.     

Dynamic Entanglement and Separability Criteria for Quantum Computing Bit States

A theoretical framework is demonstrated to evaluate the degree of entanglement of bit states in quantum computing. Separability of general superposition of Hilbert space unit vectors is discussed, and criteria in amplitude as well as in phase are derived. By these criteria the possibility of different quantum gates such as controlled not (CN), controlled controlled not (CCN), controlled rotation (CR), and controlled phase shift (CPS), to create the entanglement is examined. Furthermore, the selection of measurement mode external to the quantum system is incorporated in the formula using Kronecker delta (δ _kx ), introducing the concept of dynamic entanglement. With this the process of wavefunction collapse upon measurement is understood as the result of the activation of the dynamic entanglement. A firefly in a box model is used to show a pure state of ontological uncertainty, which is in a dynamically entangled state in Hilbert space.     

Separability Criteria for Quantum Mixed States in Terms of Trace Norm

A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite （or multipartite） system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.     

Separability of Pure States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the pure states of the quantumnetwork of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantumnetwork theory.     

Separability of Pure States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the pure states of the quantum network of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Criteria for Separability of Multipartite Quantum System

We first present the Hamel base of the density operator space for multipartite quantum system, and thus establish a representation of density matrix. Moreover, according to the structure of the density matrix for multipartite quantum system, we present two necessary criteria for separability of multipartite quantum system of arbitrary dimensions.     

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of twonodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum networktheory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor Mjk(1, 2) is equal to zerofor all possible j and k.     

Separability of Pure and Mixed States of the Quantum Network of Four Nodes

This article discusses the separability of the pure and mixed states of the quantum network of four nodesby means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Concrete Representation and Separability Criteria for Symmetric Quantum State

Using the typical generators of the special unitary groups S U(2), the concrete representation of symmetric quantum state is established, then the relations satisfied by those coefficients in the representation are presented. Based on the representation of density matrix, the PPT criterion and CCNR criterion are proved to be equivalent on judging the separability of symmetric quantum states. Moreover, it is showed that the matrix Γ _ρ of symmetric quantum state only has five efficient entries, thus the calculation of ∥Γ _ρ ∥ is simplified. Finally, the quantitative expressions of real symmetric quantum state under the ∥Γ _ρ ∥ separability criterion are obtained.     

Necessary and Sufficient Conditions of Separability for Multipartite Pure States

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.     

Comparison of Tomography Methods for Pure and Almost Pure Quantum States

JETP Letters - Quantum tomography is the most informative tool for estimating the quality of preparation and transformation of quantum states. Its development is crucially necessary for debugging...     

Stronger Criteria for Nonseparability in n-Partite Quantum States

We investigate the multipartite entanglement in arbitrary dimensional systems, and separability criteria for nonseparability in n-partite quantum states are derived. Examples such as the generalized noisy-W state and the GHZ basis states mixed with white noise are provided to show that our criteria are independent of and stronger than previously reported ones. Our criteria can also be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. The experimental implementation of our criteria is also discussed.     

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.     

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix （CM） separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.     

Non-Orthogonality Measure for a Collection of Pure Quantum States

Modern optical communication technology can realize a large-scale multilevel (or M-ary) optical signal. Investigating the quantum mechanical nature of such a large-scale M-ary optical signal is essential for a unified understanding of quantum information science and optical communication technology. This article focuses on the quantum-mechanical non-orthogonality for a collection of pure quantum states and proposes a non-orthogonality index based on the least squares error criterion in quantum detection theory. First, we define the index for linearly independent signals, and the proposed index is analyzed through numerical simulations. Next, the index is applied to a highly large-scale M-ary phase-shift keying (PSK) coherent state signal. Furthermore, the index is compared with the capacity of the pure state channel with the PSK signal. As a result, it is shown that a highly large-scale M-ary PSK coherent state signal exhibits a quantum nature even when the signal transmission power is very high. Thus, the theoretical characterization of a highly large-scale M-ary coherent state signal based on the proposed index will be the first step toward a better understanding of cutting-edge optical communication technologies such as the quantum stream cipher Y00.