Informationally complete measurements and groups representation
arXiv:quant-ph/0310013 · doi:10.1088/1464-4266/6/6/005
Abstract
Informationally complete measurements on a quantum system allow to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kind of measurements can be achieved through positive-operator valued measures (POVM's) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.
9 pages, no figures, IOP style. Some new references added
References in corpus (3)
Cited by in corpus (79)
- Symmetric Informationally Complete Quantum Measurements
- SIC-POVMs and the Extended Clifford Group
- Tight informationally complete quantum measurements
- An Invitation to Quantum Incompatibility
- Classical randomness in quantum measurements
- A de Finetti representation for finite symmetric quantum states
- Quantum Tomography Protocols with Positivity are Compressed Sensing Protocols
- Clean Positive Operator Valued Measures
- Quantum State Tomography with Joint SIC POMs and Product SIC POMs
- Symmetric Informationally Complete Measurements of Arbitrary Rank
- On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States
- Quantum state estimation with informationally overcomplete measurements
- Distance Bounds on Quantum Dynamics
- Measurement-induced disturbances and nonclassical correlations of Gaussian states
- Informationally complete joint measurements on finite quantum systems
- On SIC-POVMs in Prime Dimensions
- Optimal quantum tomography for states, measurements, and transformations
- Optimal data processing for quantum measurements
- Simulating all quantum measurements using only projective measurements and postselection
- Relations for certain symmetric norms and anti-norms before and after partial trace
- Optimal quantum tomography
- Optimal measurements in quantum mechanics
- Characterization of informational completeness for covariant phase space observables
- Informational completeness of continuous-variable measurements
- Determining eigenvalues of a density matrix with minimal information in a single experimental setting
- Shadow tomography on general measurement frames
- Towards a unified approach to information-disturbance tradeoffs in quantum measurements
- Detecting lower bounds to quantum channel capacities
- Gaussian Discriminating Strength
- Quantum state tomography with informationally complete POVMs generated in the time domain
- Channel correction via quantum erasure
- Implementation of group-covariant POVMs by orthogonal measurements
- Implementation of quantum measurements using classical resources and only a single ancillary qubit
- Minimal disturbance measurement for coherent states is non-Gaussian
- Minimal tomography with entanglement witnesses
- Sequential measurements of conjugate observables
- Geometrical picture of photocounting measurements
- Dual frame optimization for informationally complete quantum measurements
- On the Brukner-Zeilinger approach to information in quantum measurements
- Quantum State Tomography with Conditional Generative Adversarial Networks
- Quasistates and quasiprobabilities
- Symmetric minimal quantum tomography by successive measurements
- Entanglement measures and approximate quantum error correction
- Efficient algorithm for optimizing data pattern tomography
- Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
- Sizing up entanglement in mutually unbiased bases with Fisher information
- Experimental proposal for symmetric minimal two-qubit state tomography
- Entanglement Breaking Rank and the existence of SIC POVMs
- Pairwise Completely Positive Matrices and Conjugate Local Diagonal Unitary Invariant Quantum States
- Classification and reconstruction of optical quantum states with deep neural networks
- No-activation theorem for Gaussian nonclassical correlations by Gaussian operations
- Dual form of the phase-space classical simulation problem in quantum optics
- Informationally complete measurements on bipartite quantum systems: comparing local with global measurements
- Efficient accessible bounds to the classical capacity of quantum channels
- Fluctuation Theorems for multitime processes
- Quantifying entanglement of two-qubit Werner states
- Quantum tomography with random diagonal unitary maps and statistical bounds on information generation using random matrix theory
- Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
- Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation
- Mixed-state certification of quantum capacities for noisy communication channels
- Nonclassical correlations of radiation in relation to Bell nonlocality
- Completeness Stability of Quantum Measurements
- General framework of quantum complementarity from a measurement-based perspective
- Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
- Detection of properties and capacities of quantum channels
- Bosonic randomized benchmarking with passive transformations
- Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
- Least-bias state estimation with incomplete unbiased measurements
- Do qubits dream of entangled sheep? Quantum measurement without classical output
- On constructing informationally complete covariant positive operator-valued measures
- Perspectives on Utilization of Measurements in Quantum Algorithms
- Low variance estimations of many observables with tensor networks and informationally-complete measurements
- Quantum Tomography and Schwinger's Picture of Quantum Mechanics
- Any DOF All at Once: Single Photon State Tomography in a Single Measurement Setup
- Minimal covariant observables identifying all pure states
- Quantum indirect estimation theory and joint estimate of all moments of two incompatible observables
- Holevo Cramér-Rao bound: How close can we get without entangling measurements?
- Conditional SIC-POVMs
- Improving shadow estimation with locally-optimal dual frames