Estimating the Schmidt numbers of quantum states via symmetric measurements
arXiv:2505.02297 · doi:10.1002/andp.202500259
Abstract
The Schmidt numbers quantify the entanglement degree of quantum states. Quantum states with high Schmidt numbers provide a larger advantage in various quantum information processing tasks compared to quantum states with low Schmidt numbers. We derive a Schmidt number criterion based on the trace norm of the correlation matrix obtained from symmetric measurements. We show that our result is more effective than and superior to existing Schmidt number criteria by detailed examples.
References in corpus (22)
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Separability criterion and inseparable mixed states with positive partial transposition
- Universal state inversion and concurrence in arbitrary dimensions
- A Schmidt number for density matrices
- Further results on the cross norm criterion for separability
- Concurrence of arbitrary dimensional bipartite quantum states
- Schmidt number witnesses and bound entanglement
- Entanglement witnesses: construction, analysis and classification
- Mutually unbiased measurements in finite dimensions
- Enhanced entanglement criterion via symmetric informationally complete measurements
- Characterizing multipartite entanglement without shared reference frames
- Entanglement Detection Beyond Measuring Fidelities
- More entanglement implies higher performance in tailored channel discrimination tasks
- Characterizing entanglement dimensionality from randomized measurements
- Bounding entanglement dimensionality from the covariance matrix
- Construction of efficient Schmidt number witnesses for high-dimensional quantum states
- Enhanced Schmidt number criteria based on correlation trace norms
- Entanglement criterion via general symmetric informationally complete measurements
- Schmidt number criterion via general symmetric informationally complete measurements
- Symmetric measurement-induced lower bounds of concurrence
- Only-phase Popov action: thermodynamic derivation and superconducting electrodynamics