Quantum entanglement from random measurements

We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states, which can be directly experimentally assessed if two copies of the state are available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarizers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run, access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and, in fact, observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasize how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilized randomness and should find practical applications in experimental confirmation of multiphoton entanglement or space experiments.

Figure 1

Entanglement detection with minimal independent reference frames. In every experimental run, each observer, enumerated from 1 to $N$, receives one qubit from a principal system (violet) and takes one qubit from the ensemble of identically aligned reference qubits (orange). The reference qubits are all in the same unknown random state obtained, e.g., by cooling a magnetic material below the Curie temperature. Different observers have independent reference qubits so they can be placed even in far away arms of the galaxy. We show that correlations between results of local total-spin measurements with outcomes denoted by $S$ and $T$ detect quantum entanglement for the principal system in an arbitrary pure state and some mixed ones. In principle, this requires infinitely many experimental runs in order to average over random directions and in order to estimate correlation functions for fixed directions, but we also demonstrate that this technique is useful in the presence of finite resources.