A Group-Theoretic Perspective on the PPT and Realignment Entanglement Criteria

• URL: http://arxiv.org/abs/2508.18393v1
• Date: Mon, 25 Aug 2025 18:32:53 GMT
• Title: A Group-Theoretic Perspective on the PPT and Realignment Entanglement Criteria
• Authors: Tobias C. Sutter, Christopher Popp, Beatrix C. Hiesmayr,
• Abstract summary: Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing.<n>In this work, we analyze the PPT and realignment criteria for Bell-diagonal states from a group-theoretic point of view.<n>Our results demonstrate that the group structure of Bell-diagonal states provides a clear framework for analyzing and computing these two entanglement detection criteria.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the PPT and realignment criteria are well-established tools for entanglement detection in general, and are especially effective in Bell-diagonal states, their connection to the underlying group structure of this state family has not been fully explored. In this work, we analyze the PPT and realignment criteria for Bell-diagonal states from a group-theoretic point of view. Our results demonstrate that the group structure of Bell-diagonal states provides a clear framework for analyzing and computing these two entanglement detection criteria. This unified perspective offers new insights into the mathematical and physical properties of entanglement in structured quantum systems, like the connection of the PPT criterion to experimentally accessible entanglement witnesses, thus opening a path for extending the group formalism to more complex quantum systems.

Related papers

• Quantum Entanglement as a Cohomological Obstruction [0.0]
  We recast quantum entanglement as a cohomological obstruction to reconstruct a global quantum state from locally compatible information.<n>We introduce a Quantum Entment Index (QEI) as an index-theoretic invariant of entangled states and explain its behavior.
  arXiv  Detail & Related papers  (2025-11-06T12:55:28Z)
• Unveiling non-Hermitian band structures with non-Bloch supercells [23.45255537572689]
  Non-Hermitian systems exhibit complex band structures where both energy and momentum have imaginary parts.<n>We introduce a non-Bloch supercell framework designed to overcome this challenge by decoupling Bloch phase control from the imaginary part of momentum.
  arXiv  Detail & Related papers  (2025-10-23T03:18:23Z)
• Structure-Fair Quantum Circuit Complexity: An Auditable Information-Theoretic Lower Bound [0.2606834301724095]
  This paper introduces the Reference-Contingent Complexity (RCC), an information-theoretic measure calibrated by the available quantum operations.<n>Our central result is a key theorem that rigorously proves the RCC serves as a lower bound for the complexity of any universal quantum circuit.<n>This work provides a "ruler" for quantum technology that is structure-fair and enables cross-platform comparison.
  arXiv  Detail & Related papers  (2025-09-20T14:58:34Z)
• Implementing a Universal Set of Geometric Quantum Gates through Dressed-State assisted STA [39.27725073249277]
  We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field.<n>We show how the dynamical phase can be canceled to obtain purely geometric operations.<n>We extend the protocol to construct non two-qubit gates, highlighting its feasibility for scalable quantum information processing.
  arXiv  Detail & Related papers  (2025-09-10T16:14:34Z)
• Entanglement distribution in quantum networks via swapping of partially entangled states [0.44998333629984877]
  The entanglement swapping protocol (ESP) is a primitive for distributing quantum correlations across distant nodes in a quantum network.<n>Recent studies have demonstrated that even when the involved qubit pairs are only partially entangled, it is still possible to concentrate and transmit entanglement via Bell-basis measurements.<n>We extend these ideas to quantum networks with various topologies by analyzing the application of the ESP to initially partially entangled states.
  arXiv  Detail & Related papers  (2025-08-06T15:22:51Z)
• Formal Verification of Variational Quantum Circuits [44.06507276521908]
  Variational quantum circuits (VQCs) are a central component of many quantum machine learning algorithms.<n>We present the first in-depth theoretical and practical study of the formal verification problem for VQCs.
  arXiv  Detail & Related papers  (2025-07-14T12:28:32Z)
• Quantum Entanglement with Geometric Measures [0.0]
  This thesis extends the geometric measure of entanglement (GME) to introduce and investigate a suite of monotone entanglements tailored for diverse quantum contexts.<n>These monotones are applicable to both bipartite and multipartite systems, offering a unified framework for characterizing entanglement across various scenarios.
  arXiv  Detail & Related papers  (2025-06-13T04:05:03Z)
• Exploring nontrivial topology at quantum criticality in a superconducting processor [23.278631632470628]
  We present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits.<n>We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study.<n>Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.
  arXiv  Detail & Related papers  (2025-01-08T18:39:44Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework.<n>This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.<n>Our findings demonstrate universal properties at quantum criticality, such as nonanalytic behaviors of steady-state observables, divergence of correlation lengths, and closing of the imaginary-Liouville gap.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Zero Curvature Condition for Quantum Criticality [0.4506616924250028]
  We propose a geometric approach to quantum phase transitions (QPTs) that shifts focus from microscopic order to the competition between non-commuting operators.<n>We show that QPTs occur at zero-curvature points on the quantum observable space boundary, signaling maximal commutativity and suggesting an underlying integrable structure at criticality.
  arXiv  Detail & Related papers  (2023-03-16T18:35:19Z)
• Detecting entanglement in quantum many-body systems via permutation moments [4.376631240407246]
  We propose a framework for designing multipartite entanglement criteria based on permutation moments. These criteria show strong detection capability in the multi-qubit Ising model with a long-range $XY$ Hamiltonian. Our framework can also be generalized to detect the much more complicated entanglement structure in quantum many-body systems.
  arXiv  Detail & Related papers  (2022-03-16T04:39:54Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Quantum communication complexity beyond Bell nonlocality [87.70068711362255]
  Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks. Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. We prove that a new class of communication complexity tasks can be associated to Bell-like inequalities.
  arXiv  Detail & Related papers  (2021-06-11T18:00:09Z)
• Probing Topological Spin Liquids on a Programmable Quantum Simulator [40.96261204117952]
  We use a 219-atom programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states. The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators.
  arXiv  Detail & Related papers  (2021-04-09T00:18:12Z)
• Concurrence Percolation in Quantum Networks [3.52359746858894]
  We introduce a new statistical theory, concurrence percolation theory (ConPT) We find that the entanglement transmission threshold predicted by ConPT is lower than the known classical-percolation-based results. ConPT also shows a percolation-like universal critical behavior derived by finite-size analysis on the Bethe lattice.
  arXiv  Detail & Related papers  (2021-03-25T17:14:48Z)

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.