Confident entanglement detection via separable numerical range
arXiv:2107.04365 · doi:10.1103/PhysRevA.104.042420
Abstract
We investigate the joint (separable) numerical range of multiple measurements, i.e., the regions of expectation values accessible with (separable) quantum states for given observables. This not only enables efficient entanglement detection, but also sheds light on the geometry of the set of quantum states. More precisely, in an experiment, if the confidence region for the obtained data and the separable numerical range are disjoint, entanglement is reliably detected. Generically, the success of such an experiment is more likely the smaller the separable numerical range is compared to the standard numerical range of the observables measured. We quantify this relation using the ratio between these two volumes and show that it cannot be arbitrarily small, giving analytical bounds for any number of particles, local dimensions as well as number of measurements. Moreover, we explicitly compute the volume of separable and standard numerical range for two locally traceless two-qubit product observables, which are of particular interest as they are easier to measure in practice. Furthermore, we consider typical volume ratios for generic observables and extreme instances.
arXiv comment21 pages, 8 figures, 4 tables
References in corpus (26)
- Quantum entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Bell nonlocality
- Entanglement detection
- On the volume of the set of mixed entangled states
- Quantum Steering
- Largest separable balls around the maximally mixed bipartite quantum state
- Maximally entangled mixed states of two qubits
- Geometry of entangled states
- Maximally entangled mixed states in two qubits
- Nonlinear entanglement witnesses
- Hilbert--Schmidt volume of the set of mixed quantum states
- Determining lower bounds on a measure of multipartite entanglement from few local observables
- Restricted numerical range: a versatile tool in the theory of quantum information
- Better bound on the exponent of the radius of the multipartite separable ball
- Ultrafine Entanglement Witnessing
- Entangled states close to the maximally mixed state
- Cones of ball-ball separable elements
- Iterations of nonlinear entanglement witnesses
- A Concise Formula for Generalized Two-Qubit Hilbert-Schmidt Separability Probabilities
- Invariance of separability probability over reduced states in 4x4 bipartite systems
- Numerical Computations of Separability Probabilities
- Separability gap and large deviation entanglement criterion
- Formulas for Rational-Valued Separability Probabilities of Random Induced Generalized Two-Qubit States
- The structure of ultrafine entanglement witnesses
- Joint separable numerical range and bipartite entanglement witness