What are the minimal conditions required to define a SIC POVM?
arXiv:2007.10483 · doi:10.1103/PhysRevLett.126.100401
Abstract
Symmetric informationally complete (SIC) POVMs are a class of quantum measurements which, in addition to being informationally complete, satisfy three conditions: 1) every POVM element is rank one, 2) the Hilbert-Schmidt inner product between any two distinct elements is constant, and 3) the trace of each element is constant. The third condition is often overlooked, since it may give the impression that it follows trivially from the second. We show that this condition cannot be removed, as it leads to two distinct values for the trace of an element of the POVM. This observation has led us to define a broader class of measurements which we call semi-SIC POVMs. In dimension two we show that semi-SIC POVMs exist, and we construct the entire family. In higher dimensions, we characterize key properties and applications of semi-SIC POVMs, and note that the proof of their existence remains open.
arXiv comment5 pages, 1 figure, comments are welcome!
References in corpus (25)
- Symmetric Informationally Complete Quantum Measurements
- Quantum-Bayesian Coherence: The No-Nonsense Version
- SIC-POVMs: A new computer study
- Tight informationally complete quantum measurements
- The SIC Question: History and State of Play
- Minimal qubit tomography
- Constructing exact symmetric informationally complete measurements from numerical solutions
- Experimental characterization of qutrits using SIC-POVMs
- Symmetric Informationally Complete Measurements of Arbitrary Rank
- Wigner tomography of two qubit states and quantum cryptography
- Quasiprobability representations of quantum mechanics with minimal negativity
- Minimum tomography of two entangled qutrits using local measurements of one-qutrit SIC-POVM
- Quantum Conical Designs
- Fibonacci-Lucas SIC-POVMs
- SICs and Algebraic Number Theory
- SICs: Extending the list of solutions
- Generating Ray Class Fields of Real Quadratic Fields via Complex Equiangular Lines
- QBism: Quantum Theory as a Hero's Handbook
- Exploring the geometry of qutrit state space using symmetric informationally complete probabilities
- On the Brukner-Zeilinger approach to information in quantum measurements
- Compounds of symmetric informationally complete measurements and their application in quantum key distribution
- Simplified exact SICs
- SICs: Some explanations
- Detecting EPR steering via two classes of local measurements
- Squeezing Quantum Information through a Classical Channel: Measuring the "Quantumness" of a Set of Quantum States
Cited by in corpus (4)
- Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario
- Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
- Non-projective Bell state measurements
- All classes of informationally complete symmetric measurements in finite dimensions