Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices

Abstract

The coefficient matrix is an efficient tool in entanglement classification under stochastic local operation and classical communication. In this work, we take all the ranks of the coefficient matrices into account in the method of entanglement classification, and give the entanglement classification procedure for arbitrary-dimensional multipartite pure states under stochastic local operation and classical communication. As a main application, we study the entanglement classification for quantum systems in the Hilbert space $\mathcal{H}={\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^2\otimes {\mathbb{C}}^d$ in terms of the ranks of the coefficient matrices.

arXiv comment7 pages and 2 figures

References in corpus (41)

• Quantum Cryptography
• Quantum Mechanics helps in searching for a needle in a haystack
• Three qubits can be entangled in two inequivalent ways
• Persistent entanglement in arrays of interacting particles
• Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
• A Two-Step Quantum Direct Communication Protocol Using Einstein-Podolsky-Rosen Pair Block
• Theoretical efficient high capacity Quantum Key Distribution Scheme
• Security of quantum key distribution using d-level systems
• Deterministic Secure Direct Communication Using Entanglement
• Secure direct communication using entanglement
• Conditions for a class of entanglement transformations
• Bell inequalities for arbitrarily high dimensional systems
• Four qubits can be entangled in nine different ways
• Room temperature coherent control of coupled single spins in solid
• Quantum cryptography with 3-state systems
• Violations of local realism by two entangled quNits are stronger than for two qubits
• General Scheme for Super Dense Coding between Multi-Parties
• Efficient Toffoli Gates Using Qudits
• Classification of multipartite entangled states by multidimensional determinants
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• The structure of multidimensional entanglement in multipartite systems
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Security of Quantum Key Distribution with Entangled Qutrits
• Four-qubit entanglement from string theory
• Exceeding classical capacity limit in quantum optical channel
• Generic Bell inequalities for multipartite arbitrary dimensional systems
• Inductive classification of multipartite entanglement under SLOCC
• Postulates for measures of genuine multipartite correlations
• Entanglement, EPR steering, and Bell-nonlocality criteria for multipartite higher-spin systems
• Polynomial invariants for discrimination and classification of four-qubit entanglement
• Entangled qutrits violate local realism stronger than qubits - an analytical proof
• Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
• Range criterion and classification of true entanglement in $2\times M\times N$ system
• Classification and Quantification of Entangled Bipartite Qutrit Pure States
• Classification of Tripartite Entanglement with one Qubit
• Classification of arbitrary-dimensional multipartite pure states under stochastic local operations and classical communication using the rank of coefficient matrix
• Tight Correlation-Function Bell Inequality for Multipartite $d$-Dimensional System
• Detecting genuine multipartite correlations in terms of the rank of coefficient matrix
• Classification of the Entangled states L\times N\times N

Cited by in corpus (9)

• Multipartite entanglement in heterogeneous systems
• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Existence of locally maximally entangled quantum states via geometric invariant theory
• Quantum correlations in qutrit-qutrit systems under local quantum noise channels
• Criterion for SLOCC Equivalence of Multipartite Quantum States
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor
• Criteria for SLOCC and LU Equivalence of Generic Multi-qudit States
• Relations among $k$-ME concurrence, negativity, polynomial invariants, and tangle
• Freudenthal ranks: GHZ vs. W