Detecting Entanglement with Partial State Information

Abstract

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the form of linear constraints on the density matrix, the sequence of tests can prove that either all states satisfying the constraints are entangled, or there is at least one separable state that satisfies them. The algorithm works even if the values of the constraints are only known to fall in a certain range. If the states are entangled, an entanglement witness is constructed and lower bounds on entanglement measures and related quantities are provided; if a separable state satisfies the constraints, a separable decomposition is provided to certify this fact.

7 pages, 1 figure, v2; title changed, expanded description of the approach, extension to multipartite case, figure added, references added and corrected. Published version

References in corpus (9)

• On the Measurement of Qubits
• Robustness of entanglement
• A complete family of separability criteria
• Distinguishing separable and entangled states
• Quantifying Entanglement with Witness Operators
• Detecting multipartite entanglement
• Witnessed entanglement and the geometric measure of quantum discord
• The power of symmetric extensions for entanglement detection
• A complete criterion for separability detection

Cited by in corpus (5)

• Entanglement in a quantum annealing processor
• Reexamination of the evidence for entanglement in the D-Wave processor
• Entanglement detection on an NMR quantum information processor using random local measurements
• Rényi formulation of entanglement criteria for continuous variables
• Ground-state entanglement in coupled qubits