Experimental hierarchy of two-qubit quantum correlations without state tomography

Abstract

A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.

Asymmetric bidirectional quantum controlled teleportation via a seven-qubit Werner-like mixed state

“…producing a two-qubit Werner-like mixed state [48,52]. In a Kraus representation [53], the operation can be expressed as with elements E m are ( ) where σ x , σ y , and σ z are the Pauli matrices.…”