Geometry of faithful entanglement
arXiv:2008.05961 · doi:10.1103/PhysRevLett.126.140503
Abstract
A typical concept in quantum state analysis is based on the idea that states in the vicinity of some pure entangled state share the same properties; implying that states with a high fidelity must be entangled. States whose entanglement can be detected in this way are also called faithful. We prove a structural result on the corresponding fidelity-based entanglement witnesses, resulting in a simple condition for faithfulness of a two-party state. For the simplest case of two qubits faithfulness can directly be decided and for higher dimensions accurate analytical criteria are given. Finally, our results show that faithful entanglement is, in a certain sense, useful entanglement; moreover, they establish connections to computational complexity and simplify several results in entanglement theory.
arXiv comment8 pages, no figures. v2: extended and final version
References in corpus (32)
- Quantum entanglement
- Entanglement detection
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- A simple formula for the average gate fidelity of a quantum dynamical operation
- Optimization of entanglement witnesses
- Witnessing multipartite entanglement
- Direct Fidelity Estimation from Few Pauli Measurements
- Induced measures in the space of mixed quantum states
- Entanglement Certification From Theory to Experiment
- Quantum certification and benchmarking
- Entanglement as precondition for secure quantum key distribution
- Further results on the cross norm criterion for separability
- Some Properties of the Computable Cross Norm Criterion for Separability
- Schmidt number witnesses and bound entanglement
- Entanglement witnesses: construction, analysis and classification
- Entanglement Witnesses in Spin Models
- Local environment can enhance fidelity of quantum teleportation
- Optimal teleportation with a mixed state of two qubits
- Toolbox for entanglement detection and fidelity estimation
- Theory of quantum system certification: a tutorial
- Nonlinear entanglement witnesses
- On the fidelity of mixed states of two qubits
- Entanglement criteria based on local uncertainty relations are strictly stronger than the computable cross norm criterion
- All quantum states useful for teleportation are nonlocal resources
- Class of PPT bound entangled states associated to almost any set of pure entangled states
- Fidelity witnesses for fermionic quantum simulations
- Entanglement Detection Beyond Measuring Fidelities
- Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
- Spectral properties of entanglement witnesses
- Lower bounds for the fidelity of entangled state preparation
- Detecting mixed-unitary quantum channels is NP-hard
- Lower bounds on concurrence and negativity from a trace inequality
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