Gene

Quantum mechanics

Algorithm

Statistics

Variety (cybernetics)

Eigenvalues and eigenvectors

Set (abstract data type)

Biochemistry

Computer science

Statistical physics

Physics

Transpose

Quantum entanglement

Mathematics

Transcription factor

Geometry

Quantum

Moment (physics)

Repressor

Chemistry

Programming language

Symmetry (geometry)

Operator (biology)

Quantum state

State (computer science)

npj Quantum Information

We propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The $k$-th condition involves comparing moments of the partially transposed density operator up to order $k$. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

Symmetry-resolved entanglement detection using partial transpose moments