Typicality in random matrix product states

Abstract

Recent results suggest that the use of ensembles in Statistical Mechanics may not be necessary for isolated systems, since typically the states of the Hilbert space would have properties similar to the ones of the ensemble. Nevertheless, it is often argued that most of the states of the Hilbert space are non-physical and not good descriptions of realistic systems. Therefore, to better understand the actual power of typicality it is important to ask if it is also a property of a set of physically relevant states. Here we address this issue, studying if and how typicality emerges in the set of matrix product states. We show analytically that typicality occurs for the expectation value of subsystems' observables when the rank of the matrix product state scales polynomially with the size of the system with a power greater than two. We illustrate this result numerically and present some indications that typicality may appear already for a linear scaling of the rank of the matrix product state.

9 pages, 6 figures; accepted for publication in PRA

References in corpus (12)

• Thermalization and its mechanism for generic isolated quantum systems
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Randomizing quantum states: Constructions and applications
• Most quantum states are too entangled to be useful as computational resources
• Typicality for Generalized Microcanonical Ensembles
• Minimally entangled typical quantum states at finite temperature
• Sequential Generation of Matrix-Product States in Cavity QED
• Are random pure states useful for quantum computation?
• Random Unitaries Give Quantum Expanders
• Large Deviation Bounds for k-designs

Cited by in corpus (46)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• The role of quantum information in thermodynamics --- a topical review
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Random matrix techniques in quantum information theory
• Preparation of matrix product states with log-depth quantum circuits
• Quantum entanglement in random physical states
• Necessity of Eigenstate Thermalization
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Statistical properties of random matrix product states
• Concentration of measure for quantum states with a fixed expectation value
• Emergent statistical mechanics from properties of disordered random matrix product states
• Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy
• Bell sampling from quantum circuits
• Ensembles of physical states and random quantum circuits on graphs
• Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement
• Markovianization with approximate unitary designs
• Symmetry Breaking and the Geometry of Reduced Density Matrices
• Symmetry Breaking and Convex Set Phase Diagrams for the q-state Potts Model
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• Typical entanglement for Gaussian states
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Anticoncentration and state design of random tensor networks
• Is macroscopic entanglement a typical trait of many-particle quantum states?
• Generalized quantum microcanonical ensemble from random matrix product states
• Page curves and typical entanglement in linear optics
• Probability density of quantum expectation values
• Purity of thermal mixed quantum states
• Pure state thermodynamics with matrix product states
• Microscopic electronic configurations after ultrafast magnetization dynamics
• Entanglement phase diagrams from partial transpose moments
• Fermionic Magic Resources of Quantum Many-Body Systems
• Local random quantum circuits: ensemble CP maps and swap algebras
• Typicality at quantum-critical points
• Ground-state properties via machine learning quantum constraints
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• A protocol to characterize errors in quantum simulation of many-body physics
• On the separability of unitarily invariant random quantum states - the unbalanced regime
• Robust quantum metrology with random Majorana constellations
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Necessity of entanglement for the typicality argument in statistical mechanics
• Learning Agents in Black-Scholes Financial Markets: Consensus Dynamics and Volatility Smiles
• Estimating the entanglement of random multipartite quantum states
• Entanglement criteria for the bosonic and fermionic induced ensembles