Generating and detecting bound entanglement in two-qutrits using a family of indecomposable positive maps

Abstract

The problem of bound entanglement detection is a challenging aspect of quantum information theory for higher dimensional systems. Here, we propose an indecomposable positive map for two-qutrit systems, which is shown to generate a class of positive partial transposed (PPT) states. A corresponding witness operator is constructed and shown to be weakly optimal and locally implementable. Further, we perform a structural physical approximation of the indecomposable map to make it a completely positive one, and find a new PPT entangled state which is not detectable by certain other well-known entanglement detection criteria.

arXiv comment9 pages, 3 figures, Comments are welcome!

References in corpus (51)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement detection
• Separability criterion and inseparable mixed states with positive partial transposition
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Bell Inequalities and the Separability Criterion
• One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• Witnessing multipartite entanglement
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Further results on the cross norm criterion for separability
• Randomness vs Non Locality and Entanglement
• Direct detection of quantum entanglement
• Experimental multiparticle entanglement dynamics induced by decoherence
• Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
• Optimal entanglement criterion for mixed quantum states
• Covariance matrices and the separability problem
• A Quantum solution to the Byzantine agreement problem
• Observable measure of bipartite quantum correlations
• Construction of quantum states with bound entanglement
• Unifying several separability conditions using the covariance matrix criterion
• Separability criteria and bounds for entanglement measures
• Universal observable detecting all two-qubit entanglement and determinant based separability tests
• Experimental bound entanglement in a four-photon state
• Entanglement witness operator for quantum teleportation
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• Construction of entangled states with positive partial transposes based on indecomposable positive linear maps
• Witness of mixed separable states useful for entanglement creation
• Detecting mixedness of qutrit systems using the uncertainty relation
• Positive finite rank elementary operators and characterizing entanglement of states
• Optimality for indecomposable entanglement witnesses
• A class of 2^N x 2^N bound entangled states revealed by non-decomposable maps
• Non-negativity of conditional von Neumann entropy and global unitary operations
• A class of positive atomic maps
• Bound entangled states fit for robust experimental verification
• Verifying the quantumness of bipartite correlations
• A class of exposed indecomposable positive maps
• Sufficient separability criteria and linear maps
• Rank properties of exposed positive maps
• Projection of two biphoton qutrits onto a maximally entangled state
• Universal detection of entanglement in two-qubit states using only two copies
• Witness for edge states and its characteristics
• Separability in terms of a single entanglement witness
• Construction of optimal teleportation witness operators from entanglement witnesses
• Structural Physical Approximation make possible to realize the optimal singlet fraction with two measurements
• New tools for investigating positive maps in matrix algebras
• Stable subspaces of positive maps of matrix algebras
• A class of bistochastic positive optimal maps in $M_d(\mathbb{C})$
• On positive decomposable maps
• Merging of positive maps: a construction of various classes of positive maps on matrix algebras

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