Minimal qubit tomography

Abstract

We present, and analyze thoroughly, a highly symmetric and efficient scheme for the determination of a single-qubit state, such as the polarization properties of photons emitted by a single-photon source. In our scheme there are only four measured probabilities, just enough for the determination of the three parameters that specify the qubit state, whereas the standard procedure would measure six probabilities.

14 pages, 10 figures; final version

References in corpus (2)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View

Cited by in corpus (126)

• The classical-quantum boundary for correlations: discord and related measures
• On mutually unbiased bases
• Non-Markovian quantum processes: complete framework and efficient characterisation
• The SIC Question: History and State of Play
• Adaptive quantum state tomography improves accuracy quadratically
• Choice of Measurement Sets in Qubit Tomography
• Superfast maximum likelihood reconstruction for quantum tomography
• Constructing exact symmetric informationally complete measurements from numerical solutions
• Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
• Non-Markovian Quantum Process Tomography
• Experimental Adaptive Bayesian Tomography
• Experimental Polarization State Tomography using Optimal Polarimeters
• Optimal Measurement on Noisy Quantum Systems
• Quantum State Tomography with Joint SIC POMs and Product SIC POMs
• Statistical Estimation of Quantum Tomography Protocols Quality
• Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
• Wigner tomography of two qubit states and quantum cryptography
• Reconstructing quantum states with quantum reservoir networks
• Tomographic measurements on superconducting qubit states
• Quantum state estimation with informationally overcomplete measurements
• Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
• Statistical estimation of the quality of quantum-tomography protocols
• Protecting an optical qubit against photon loss
• Most incompatible measurements for robust steering tests
• Minimum tomography of two entangled qutrits using local measurements of one-qutrit SIC-POVM
• Practical adaptive quantum tomography
• Quantum State Tomography of a Single Qubit: Comparison of Methods
• Optimal quantum state reconstruction for cold trapped ions
• Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam
• The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
• SICs and Algebraic Number Theory
• Optimal experiment design revisited: fair, precise and minimal tomography
• Experimental certification of an informationally complete quantum measurement in a device-independent protocol
• Monte Carlo sampling from the quantum state space. II
• Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion
• Optimal estimation of entanglement in optical qubit systems
• Monte Carlo sampling from the quantum state space. I
• On the experimental feasibility of quantum state reconstruction via machine learning
• Mode expansion and Bragg filtering enable a high-fidelity fiber-based photon-pair source
• Proposal for direct measurement of concurrence via visibility in a cavity QED system
• Adaptive schemes for incomplete quantum process tomography
• Quantification of entanglement via uncertainties
• Quantum-polarization state tomography
• Adaptive quantum tomography
• Probability representation of quantum dynamics using pseudostochastic maps
• Efficiency of photonic state tomography affected by fiber attenuation
• Experimental self-characterization of quantum measurements
• Nonlocality, steering and quantum state tomography in a single experiment
• Optimal error intervals for properties of the quantum state
• Extremal eigenvalues of local Hamiltonians
• Adaptive quantum tomography of high-dimensional bipartite systems
• What are the minimal conditions required to define a SIC POVM?
• Estimating the expectation values of spin 1/2 observables with finite resources
• Tight Bounds on the Accessible Information and the Informational Power
• An Optimal Photon Counting Polarimeter
• Optimal correlations in many-body quantum systems
• Point Estimation of States of Finite Quantum Systems
• Quantum polarization transformations in anisotropic dispersive medium
• Quantum tomography of entangled qubits by time-resolved single-photon counting with time-continuous measurements
• Fundamental quantum limits in ellipsometry
• Symmetric minimal quantum tomography by successive measurements
• Measuring complete quantum states with a single observable
• Optimal reconstruction of states in qutrits system
• Accurate polarization preparation and measurement using twisted nematic liquid crystals
• Error probability analysis in quantum tomography: a tool for evaluating experiments
• Experimental proposal for symmetric minimal two-qubit state tomography
• Tensor network noise characterization for near-term quantum computers
• State tomography for two qubits using reduced densities
• Fourier Transform Quantum State Tomography
• Quantum states tomography with noisy measurement channels
• Quantum chi-squared tomography and mutual information testing
• Single observable concurrence measurement without simultaneous copies
• Systems of Imprimitivity for the Clifford Group
• Hamiltonian tomography by the quantum quench protocol with random noise
• Orthogonalization of partly unknown quantum states
• Direct estimation of minimum gate fidelity
• Quantification of Concurrence via Weak Measurement
• Accuracy matrix in generalized simultaneous measurement of a qubit system
• Precise tomography of optical polarization qubits under conditions of chromatic aberration of quantum transformations
• Single-shot characterization of vector beams by generalized measurements
• Quantum Tomography of Pure States with Projective Measurements Distorted by Experimental Noise
• Quantifying entanglement of two-qubit Werner states
• On the geometry and invariants of qubits, quartits and octits
• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• Efficient factored gradient descent algorithm for quantum state tomography
• Optimal choice of state tomography quorum formed by projection operators
• Optimization of quantum state tomography in the presence of experimental constraints
• Optically probing Schwinger angular momenta in a micromechanical resonator
• Quantum State Tomography Using Successive Measurements
• On Quantum Channel Estimation with Minimal Resources
• High-fidelity quantum tomography with imperfect measurements
• Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer
• Quantum tomography of three-qubit generalized Werner states
• Entanglement characterization by single-photon counting with random noise
• Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study
• Accuracy features for quantum process tomography using superconductor phase qubits
• Quantum State Tomography of Four-Level Systems with Noisy Measurements
• Spatial Quantum State Tomography with A Deformable Mirror
• The optimal reordering of measurements for photonic quantum tomography
• Numeric estimation of resource requirements for a practical polarization-frame alignment scheme for QKD
• Minimax mean estimator for the trine
• Completeness Stability of Quantum Measurements
• Experiment design and parameter estimation of Pauli channels using convex optimization
• Optimal observables to determine entanglement of a two qubit state
• Single plane minimal tomography of double slit qubits
• Minimax estimation of qubit states with Bures risk
• Adaptive tomography of qubits: Purity versus statistical fluctuations
• Efficient Experimental Qudit State Estimation via Point Tomography
• On the possibility to detect quantum correlation regions with the variable optimal measurement angle
• Single-loop interferometer for minimal ellipsometry
• Minimally-disturbing Heisenberg-Weyl symmetric measurements using hard-core collisions of Schrödinger particles
• Optimal nonlinear filtering of quantum state
• Machine learning methods in quantum computing theory
• Quantum Tomography and Schwinger's Picture of Quantum Mechanics
• Resource-efficient entanglement detection in high-dimensional states via two-qubit witnesses
• Entanglement quantification from collective measurements processed by machine learning
• Quantum Tomographic Cryptography with a Semiconductor Single Photon Source
• Quantum state tomography as a numerical optimization problem
• Linear-optical protocols for mitigating and suppressing noise in bosonic systems
• Ability of entanglement and purity to help to detect systematic experimental errors
• Spectrally Resolved Quantum Tomography of Polarization Entangled States
• Rigorous Maximum Likelihood Estimation for Quantum States
• Optical downlink modeling for low-earth-orbit and medium-earth-orbit satellites under atmospheric turbulence with a quantum-state-tomography use case
• Machine Learning of Quantum Entanglement from Noisy Measurements
• Optimal protocol for quantum state tomography
• State learning from pairs of states