On the structure of mirrored operators obtained from optimal entanglement witnesses
arXiv:2212.14820 · doi:10.1038/s41598-023-37771-0
Abstract
Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin -- a mirrored EW -- whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.
arXiv comment13 pages, 3 figures, 1 table, comments are welcome
References in corpus (35)
- Quantum entanglement
- Entanglement detection
- Bell Inequalities and the Separability Criterion
- Unextendible Product Bases and Bound Entanglement
- Optimization of entanglement witnesses
- Direct detection of quantum entanglement
- Entanglement witnesses: construction, analysis and classification
- Optimal entanglement criterion for mixed quantum states
- 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
- On the dimension of subspaces with bounded Schmidt rank
- 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
- Detecting multipartite entanglement structure with minimal resources
- Constructing new optimal entanglement witnesses
- 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
- Composite parameterization and Haar measure for all unitary and special unitary groups
- One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps
- Entanglement Witness : Compressed/Mirrored Entanglement Witnesses
- Optimal entanglement witnesses from generalized reduction and Robertson maps
- On structural physical approximations and entanglement breaking maps
- The structural physical approximations and optimal entanglement witnesses
- How many mutually unbiased bases are needed to detect bound entangled states?
- Entanglement detection under coherent noise: Greenberger-Horne-Zeilinger-like states
- Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
- Checking the optimality of entanglement witnesses: an application to structural physical approximations
- Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits
- Disproving the conjecture on structural physical approximation to optimal decomposable entanglement witnesses
- A class of Bell diagonal entanglement witnesses in : optimization and the spanning property
- Is bound entanglement Lorentz invariant?
- Information complementarity in multipartite quantum states and security in cryptography
- A class of optimal positive maps in