Construction of three-qubit positive-partial-transpose entangled states of rank four

• URL: http://arxiv.org/abs/2605.19530v1
• Date: Tue, 19 May 2026 08:32:15 GMT
• Title: Construction of three-qubit positive-partial-transpose entangled states of rank four
• Abstract summary: Multiqubit positive-partial-transpose (PPT) entangled states play an important role in quantum information theory.<n>We classify such states into two types: type I and type II.<n>We also investigate the Lorentz invariants of multiqubit states with rank less than three.
• Score: 4.115763274264731
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multiqubit positive-partial-transpose (PPT) entangled states play an important role in quantum information theory. We characterize such states of minimum rank in three-qubit system, namely rank four. Depending on whether the Lorentz invariant is zero, we classify such states into two types. The PPT entangled states constructed by unextendible product bases (UPB) have nonzero invariants, which belong to type I. We provide a method to effectively determine whether a state can be constructed from UPB. For states with zero invariant, which belong to type II, we provide an explicit expression up to equivalence of stochastic local operations and classical communications (SLOCC). It turns out that we can represent them with only one complex parameter. We further study SLOCC-equivalence relation within the expression. We also investigate the Lorentz invariants of multiqubit states with rank less than three and analyze their range.

Related papers

• Frame-Dependent Traces and the Third-Particle Paradox [45.88028371034407]
  We show that the Paradox of the Third Particle arises when comparing subsystem descriptions across Quantum Reference Tracing perspectives.<n>We argue that our condition captures the Paradox content: rather than imposing consistency on the whole state space, we reproduce exactly the states on which it holds.
  arXiv  Detail & Related papers  (2026-07-23T18:00:01Z)
• Classification of four-qubit pure codes and five-qubit absolutely maximally entangled states [0.6526824510982802]
  We prove that every 5-qubit absolutely maximally entangled (AME) states is equivalent by a local unitary transformation to a point in the unique ((5,2,3)) quantum error code C.<n>We also show that every 4-qubit pure code is equivalent to a subspace of the unique ((4,2)) and construct an infinite family of 3-uniform n-qubit states for even $ngeq 6$.
  arXiv  Detail & Related papers  (2025-07-02T22:45:10Z)
• Explicit C*-algebraic Protocol for Exact Universal Embezzlement of Entanglement [7.410574751379865]
  We present an explicit construction of a universal embezzlement protocol in the C*-algebraic model of quantum information.<n>Our approach is both exact and state-independent.<n>This offers a conceptually intuitive model for universal entanglement embezzlement in infinite-dimensional settings.
  arXiv  Detail & Related papers  (2025-06-12T14:26:11Z)
• Pure state entanglement and von Neumann algebras [41.94295877935867]
  We develop the theory of local operations and classical communication (LOCC) for bipartite quantum systems represented by commuting von Neumann algebras.<n>Our central result is the extension of Nielsen's Theorem, stating that the LOCC ordering of bipartite pure states is equivalent to the majorization of their restrictions.<n>In the appendix, we provide a self-contained treatment of majorization on semifinite von Neumann algebras and $sigma$-finite measure spaces.
  arXiv  Detail & Related papers  (2024-09-26T11:13:47Z)
• Multipartite Embezzlement of Entanglement [44.99833362998488]
  Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via local operations and without communication.<n>We show that finite-dimensional approximations of multipartite embezzling states form multipartite embezzling families.<n>We discuss our results in the context of quantum field theory and quantum many-body physics.
  arXiv  Detail & Related papers  (2024-09-11T22:14:22Z)
• Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras [41.94295877935867]
  We study the quantum information theoretic task of embezzlement of entanglement in the setting of von Neumann algebras.<n>We quantify the performance of a given resource state by the worst-case error.<n>Our findings have implications for relativistic quantum field theory, where type III algebras naturally appear.
  arXiv  Detail & Related papers  (2024-01-14T14:22:54Z)
• Unextendibility, uncompletability, and many-copy indistinguishable ensembles [49.1574468325115]
  We show that the complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality.<n>We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.
  arXiv  Detail & Related papers  (2023-03-30T16:16:41Z)
• Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor [4.291616110077346]
  We introduce a protocol to classify three-qubit pure states into different entanglement classes and implement it on an NMR quantum processor. The protocol is designed in such a way that the experiments performed to classify the states can also measure the amount of entanglement present in the state.
  arXiv  Detail & Related papers  (2022-06-12T14:54:21Z)
• Robust preparation of Wigner-negative states with optimized SNAP-displacement sequences [41.42601188771239]
  We create non-classical states of light in three-dimensional microwave cavities. These states are useful for quantum computation. We show that this way of creating non-classical states is robust to fluctuations of the system parameters.
  arXiv  Detail & Related papers  (2021-11-15T18:20:38Z)
• Discrimination of quantum states under locality constraints in the many-copy setting [18.79968161594709]
  We prove that the optimal average error probability always decays exponentially in the number of copies. We show an infinite separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB) On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.
  arXiv  Detail & Related papers  (2020-11-25T23:26:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.