Quantifying High-Order Interdependencies in Entangled Quantum States
arXiv:2310.03681 · doi:10.1103/PhysRevA.109.042605
Abstract
Here, we leverage recent advances in information theory to develop a novel method to characterise the dominant character of the high-order dependencies of quantum systems. To this end, we introduce the Q-information: an information-theoretic measure capable of distinguishing quantum states dominated by synergy or redundancy. We illustrate the measure by investigating the properties of paradigmatic entangled Qubit states and find that -- in contrast to classical systems -- quantum systems need at least four variables to exhibit high-order properties. Furthermore, our results reveal that unitary evolution can radically affect the internal information organisation in a way that strongly depends on the corresponding Hamiltonian. Overall, the Q-information sheds light on novel aspects of the internal organisation of quantum systems and their time evolution, opening new avenues for studying several quantum phenomena and related technologies.
arXiv comment7 pages, 3 figures, 1 table
References in corpus (30)
- Topological entanglement entropy
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Four qubits can be entangled in nine different ways
- Monogamy of entanglement and other correlations
- Teleportation and Dense Coding with Genuine Multipartite Entanglement
- Induced measures in the space of mixed quantum states
- Circuit complexity in quantum field theory
- Explosive higher-order Kuramoto dynamics on simplicial complexes
- The Second Law of Quantum Complexity
- Quantifying High-order Interdependencies via Multivariate Extensions of the Mutual Information
- How entangled can two couples get?
- Maximally multipartite entangled states
- Partial Information Decomposition as a Unified Approach to the Specification of Neural Goal Functions
- Linear growth of quantum circuit complexity
- Quantum Correlations and Coherence in Spin-1 Heisenberg Chains
- Disentangling high-order mechanisms and high-order behaviours in complex systems
- Higher-order simplicial synchronization of coupled topological signals
- Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
- Simplicial complexes: higher-order spectral dimension and dynamics
- Efficient verification of Dicke states
- Topological Information Data Analysis
- High-order couplings in geometric complex networks of neurons
- Unveiling quantum entanglement in many-body systems from partial information
- Quantifying high-order interdependencies on individual patterns via the local O-information: theory and applications to music analysis
- Classification of four-qubit entangled states via Machine Learning
- Entangled graphs: A classification of four-qubit entanglement
- Greenberger-Horne-Zeilinger states and few-body Hamiltonians
- Multipartite entanglement in qubit systems
- Local Hamiltonians for Maximally Multipartite Entangled States
- Detection of quantum phase transition in spin-1 chain through multipartite high-order correlations