Quantum Noise as an Entanglement Meter

Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to condensed matter theory and quantum information. The universal appeal of the entanglement entropy concept is related, in part, to the fact that it is defined solely in terms of the many-body density matrix of the system, with no relation to any particular observables. However, for the same reason, it has not been clear how to access this quantity experimentally. Here we derive a universal relation between entanglement entropy and the fluctuations of current flowing through a quantum point contact (QPC) which opens a way to perform a direct measurement of entanglement entropy. In particular, by utilizing space-time duality of 1d systems, we relate electric noise generated by opening and closing the QPC periodically in time with the seminal S = 1/3 log L prediction of conformal field theory.