Quantum state tomography via reduced density matrices

Abstract

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

10 pages, 10 figures. All comments are welcome!

References in corpus (32)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Scalable multi-particle entanglement of trapped ions
• Continuous-variable optical quantum state tomography
• Quantum state tomography via compressed sensing
• Area laws in quantum systems: mutual information and correlations
• Efficient quantum state tomography
• Quantum Correlations in Systems of Indistinguishable Particles
• Renormalization and tensor product states in spin chains and lattices
• Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
• Entanglement with Negative Wigner Function of Three Thousand Atoms Heralded by One Photon
• Operational Families of Entanglement Classes for Symmetric $N$-Qubit States
• Cooling-by-measurement and mechanical state tomography via pulsed optomechanics
• Liquid State NMR as a Test-bed for Developing Quantum Control Methods
• Quantum Tomography under Prior Information
• Benchmarking a Teleportation Protocol realized in Superconducting Circuits
• Spatial entanglement of bosons in optical lattices
• Simulation of chemical reaction dynamics on an NMR quantum computer
• Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-qubit Quantum Processor
• Uniqueness of Quantum States Compatible with Given Measurement Results
• Obtain $W$-state from three-qubit $GHZ$-state on rate 1
• Parts of Quantum States
• Quantum tomography as a tool for the characterization of optical devices
• Tomography is necessary for universal entanglement detection with single-copy observables
• Practical experimental certification of computational quantum gates via twirling
• Informational completeness in bounded-rank quantum-state tomography
• Strictly-complete measurements for bounded-rank quantum-state tomography
• The power of being positive: Robust state estimation made possible by quantum mechanics
• Three-party pure quantum states are determined by two two-party reduced states
• N-Qubit W States are Determined by their Bipartite Marginals
• Experimental entanglement-assisted quantum delayed-choice experiment
• From Ground States to Local Hamiltonians
• Comment on some results of Erdahl and the convex structure of reduced density matrices

Cited by in corpus (40)

• Quantum Overlapping Tomography
• Quantum simulation of photosynthetic energy transfer
• A Quantum Algorithm for Solving Linear Differential Equations: Theory and Experiment
• Demonstration of Entanglement Purification and Swapping Protocol to Design Quantum Repeater in IBM Quantum Computer
• Parameter estimation with almost no public communication for continuous-variable quantum key distribution
• Three-Photon Discrete-Energy-Entangled W State in Optical Fiber
• Learning Quantum Hamiltonians from Single-qubit Measurements
• Exact and efficient quantum simulation of open quantum dynamics for various of Hamiltonians and spectral densities
• Reconstructing quantum states from single-party information
• Almost all four-particle pure states are determined by their two-body marginals
• Synthetic gauge field and chiral physics on two-leg superconducting circuits
• Entanglement Measures in Embedding Quantum Simulators with Nuclear Spins
• Self-testing using only marginal information
• Controlling NMR spin systems for quantum computation
• Experimental sample-efficient quantum state tomography via parallel measurements
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms
• Uniquely determined pure quantum states need not be unique ground states of quasi-local Hamiltonians
• Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems
• A Tailor-made Quantum State Tomography Approach
• Improved Quantum State Tomography for the Systems with XX+YY Couplings and Z Readouts
• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• High-dimentional Multipartite Entanglement Structure Detection with Low Cost
• Quantum state tomography on a plaquette in the 2D Hubbard model
• Dual-Capability Machine Learning Models for Quantum Hamiltonian Parameter Estimation and Dynamics Prediction
• Generic pure quantum states as steady states of quasi-local dissipative dynamics
• Supercomputer simulations of transmon quantum computers
• Systematic errors in direct state measurements with quantum controlled measurements
• Adaptive Lattice Gas Algorithm: Classical and Quantum implementations
• The additivity of states uniquely determined by marginals
• True experimental reconstruction of quantum states and processes via convex optimization
• Investigating Pure State Uniqueness in Tomography via Optimization
• Reconstructing Quantum States from Local Observation: A Dynamical Viewpoint
• Quantum Entanglement Control in Two-Spin-1/2 NMR Systems Through Magnetic Fields and Temperature
• Determining the ensemble N-representability of Reduced Density Matrices
• Distinguishing dynamical quantum criticality through local fidelity distances
• Is the matrix completion of reduced density matrices unique?
• K-sparse Pure State Tomography with Phase Estimation
• Measuring entanglement without local addressing in quantum many-body simulators via spiral quantum state tomography
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka