Fisher discord as a quantifier of quantum complexity

• URL: http://arxiv.org/abs/2510.15375v1
• Date: Fri, 17 Oct 2025 07:20:28 GMT
• Title: Fisher discord as a quantifier of quantum complexity
• Authors: Huihui Li, Shunlong Luo, Yue Zhang,
• Abstract summary: Two classically equivalent expressions of mutual information of probability distributions diverge when extended to quantum systems.<n>This difference may be exploited to characterize the complex nature of quantum states.<n>We introduce an information-theoretic quantifier of complexity for quantum states.
• Score: 9.658211625390937
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Two classically equivalent expressions of mutual information of probability distributions (classical bipartite states) diverge when extended to quantum systems, and this difference has been employed to define quantum discord, a quantifier of quantum correlations beyond entanglement. Similarly, equivalent expressions of classical Fisher information of parameterized probability distributions diverge when extended to quantum states, and this difference may be exploited to characterize the complex nature of quantum states. By complexity of quantum states, we mean some hybrid nature which intermingles the classical and quantum features. It is desirable to quantify complexity of quantum states from various perspectives. In this work, we pursue the idea of discord and introduce an information-theoretic quantifier of complexity for quantum states (relative to the Hamiltonian that drives the evolution of quantum systems) via the notion of Fisher discord, which is defined by the difference between two important versions of quantum Fisher information: the quantum Fisher information defined via the symmetric logarithmic derivatives and the Wigner-Yanase skew information defined via the square roots of quantum states. We reveal basic properties of the quantifier of complexity, and compare it with some other quantifiers of complexity. In particular, we show that equilibrium states (or stable states, which commute with the Hamiltonian of the quantum system) and all pure states exhibit zero complexity in this setting. As illustrations, we evaluate the complexity for various prototypical states in both discrete and continuous-variable quantum systems.

Related papers

• Quantum Mechanics Relative to a Quantum Reference System: Relative State Approach [0.0]
  This paper proposes an intrinsic or background-independent quantum framework based on entangled state rather than absolute quantum state.<n>It describes a quantum relative state between the under-study quantum system and the quantum measuring apparatus as a quantum reference system.
  arXiv  Detail & Related papers  (2025-10-20T13:11:39Z)
• Topological control of quantum speed limits [55.2480439325792]
  We show that even if the quantum state is completely dispersionless, QFI in this state remains momentum-resolved.<n>We find bounds on quantum speed limit which scales as $sqrt|C|$ in a (dispersionless) topological phase.
  arXiv  Detail & Related papers  (2025-07-21T18:00:07Z)
• Quantifying complexity of continuous-variable quantum states via Wehrl entropy and Fisher information [8.52497147463548]
  We introduce a quantifier of complexity of continuous-variable states, e.g. quantum optical states, based on the Husimi quasiprobability distribution.<n>We analyze the basic properties of the quantifier and illustrate its features by evaluating complexity of Gaussian states and some relevant non-Gaussian states.
  arXiv  Detail & Related papers  (2025-05-14T17:59:31Z)
• Estimating quantum relative entropies on quantum computers [4.4539446220650065]
  We use the Kullback-Leibler divergence to estimate quantum relative between two quantum states.<n>We also investigate the superadditivity of quantum computer channels.
  arXiv  Detail & Related papers  (2025-01-13T13:00:24Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Quantitative bounds to propagation of quantum correlations in many-body systems [0.0]
  We establish limits to bipartite quantum correlations in many-body systems. Results confirm that proliferation of classical information in the Universe suppresses quantum correlations.
  arXiv  Detail & Related papers  (2023-10-04T00:24:06Z)
• No-signalling constrains quantum computation with indefinite causal structure [45.279573215172285]
  We develop a formalism for quantum computation with indefinite causal structures. We characterize the computational structure of higher order quantum maps. We prove that these rules, which have a computational and information-theoretic nature, are determined by the more physical notion of the signalling relations between the quantum systems.
  arXiv  Detail & Related papers  (2022-02-21T13:43:50Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality [0.0]
  Quantum coherence quantifies the amount of superposition in a quantum system. We develop the corresponding resource theory, identifying the free states and operations. We obtain a complementarity relation between the so-defined quantum coherence and the which-path information in an interferometric set-up.
  arXiv  Detail & Related papers  (2021-08-12T16:55:40Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)
• Distribution of quantum coherence and quantum phase transition in the Ising system [2.318473106845779]
  Quantifying quantum coherence of a given system plays an important role in quantum information science. We propose an analysis on the critical behavior of two types Ising systems when distribution of quantum coherence.
  arXiv  Detail & Related papers  (2020-01-29T07:28:04Z)

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.