Reconstructing quantum states from local data

Abstract

We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy", and we discuss its relation to emergent geometry in the context of holographic duality.

4+2 pages

References in corpus (16)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• Chaos and Quantum Thermalization
• Towards a derivation of holographic entanglement entropy
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Efficient quantum state tomography
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• A hole-ographic spacetime
• Scalable reconstruction of density matrices
• Markov entropy decomposition: a variational dual for quantum belief propagation
• From Ground States to Local Hamiltonians
• Computing complexity measures for quantum states based on exponential families
• Modulus of convexity for operator convex functions

Cited by in corpus (22)

• Does a single eigenstate encode the full Hamiltonian?
• Determining a local Hamiltonian from a single eigenstate
• Sample-efficient learning of quantum many-body systems
• Computational inverse method for constructing spaces of quantum models from wave functions
• Quantum Information in Holographic Duality
• Renormalization group constructions of topological quantum liquids and beyond
• The Information Theoretic Interpretation of the Length of a Curve
• The Fidelity of Recovery is Multiplicative
• Entanglement guided search for parent Hamiltonians
• Quantum information measures for restricted sets of observables
• Area Law for Gapless States from Local Entanglement Thermodynamics
• Learning quantum many-body systems from a few copies
• Supervised learning in Hamiltonian reconstruction from local measurements on eigenstates
• Measuring quasiprobability distribution functions of the cavity field considering field and atomic decays
• The first law of differential entropy and holographic complexity
• Automatic design of Hamiltonians
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond
• Maximum-entropy inference and inverse continuity of the numerical range
• Relationship between the ground-state wave function of a magnet and its static structure factor
• Reconstructing Quantum States from Local Observation: A Dynamical Viewpoint
• Fitness landscape for quantum state tomography from neutron scattering
• Learning mixed quantum states in large-scale experiments