A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist

Abstract

Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This contribution studies the structure of EWs. Exploiting the very concept of mirrored EWs, increasing the detection power, we show, in contrast to the conjecture in a recent paper (Sci. Rep. {\bf 13}, 10733 (2023)), there exist pairs of optimal EWs, which are both non-decomposible, i.e. can detect bound/PPT-entangled states in an optimal way. Since we show that the structure also extends to higher dimensions, our results reveal a further structure of entanglement witnesses.

arXiv comment14 pages, 4 figues

References in corpus (21)

• Quantum entanglement
• Entanglement detection
• Optimization of entanglement witnesses
• Characterization of separable states and entanglement witnesses
• The state space for two qutrits has a phase space structure in its core
• A special simplex in the state space for entangled qudits
• Structural approximations to positive maps and entanglement breaking channels
• Witnessing entanglement sequentially: Maximally entangled states are not special
• The geometry of bipartite qutrits including bound entanglement
• A completely entangled subspace of maximal dimension
• Facial structures for various notions of positivity and applications to the theory of entanglement
• Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• Entanglement witnesses from mutually unbiased bases
• Entanglement Witness $2.0$: Compressed/Mirrored Entanglement Witnesses
• Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
• A class of Bell diagonal entanglement witnesses in ${\mathbb{C}}^4\otimes {\mathbb{C}}^4$: optimization and the spanning property
• Is bound entanglement Lorentz invariant?
• Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
• On the structure of mirrored operators obtained from optimal entanglement witnesses
• A class of optimal positive maps in $M_n$
• Mutually Unbiased Bases in Composite Dimensions -- A Review

Cited by in corpus (2)

• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Spectral characterizations of entanglement witnesses