Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
arXiv:2411.16461 · doi:10.1103/PhysRevA.111.042418
Abstract
The equivalence between absolutely separable states and absolutely positive partial transposed (PPT) states in general remains an open problem in quantum entanglement theory. In this work, we study an analogous question for symmetric multiqubit states. We show that symmetric absolutely PPT (SAPPT) states (symmetric states that remain PPT after any symmetry-preserving unitary evolution) are not always symmetric absolutely separable by providing explicit counterexamples. More precisely, we construct a family of entangled five-qubit SAPPT states. Similar counterexamples for larger odd numbers of qubits are identified.
arXiv comment9 pages, 2 figure
References in corpus (30)
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- A complete family of separability criteria
- Classification of multi-qubit mixed states: separability and distillability properties
- Largest separable balls around the maximally mixed bipartite quantum state
- Geometry of entangled states
- Spin squeezing inequalities and entanglement of qubit states
- The entangling power of passive optical elements
- Entanglement between identical particles is a useful and consistent resource
- Separability from Spectrum for Qubit-Qudit States
- Gaussian entanglement revisited
- PPT from spectra
- Four-qubit entangled symmetric states with positive partial transpositions
- Entangled symmetric states of N qubits with all positive partial transpositions
- Witness of mixed separable states useful for entanglement creation
- Partial transpose criteria for symmetric states
- Entangled states close to the maximally mixed state
- Entanglement and the truncated moment problem
- Cones of ball-ball separable elements
- Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
- The Inverse Eigenvalue Problem for Entanglement Witnesses
- Absolutely separating quantum maps and channels
- Absolutely classical spin states
- Spectral Properties of Symmetric Quantum States and Symmetric Entanglement Witnesses
- Generating a 4-photon Tetrahedron State: Towards Simultaneous Super-sensitivity to Non-commuting Rotations
- Absolute separability witnesses for symmetric multiqubit states
- Maximum entanglement of mixed symmetric states under unitary transformations
- Spin Rotations in a Bose-Einstein Condensate Driven by Counterflow and Spin-independent Interactions