Experimental verification of threshold quantum state tomography on a fully-reconfigurable photonic integrated circuit

Reconstructing the state of a quantum system represents a pivotal task for quantum information applications. The standard approach based on quantum state tomography requires a number of measurements that scales exponentially with the number of qubits. Other methods have been proposed and tested to reduce the number of measurements, or to focus on specific properties of the output state rather than on its complete reconstruction. Here, we show experimentally the application of an approach, called threshold quantum state tomography, in an advanced hybrid photonic platform with states up to n = 4 qubits. This method does not require prior knowledge and selects only the informative projectors starting from the measurement of the density matrix diagonal. We demonstrate its effectiveness by showing that a consistent reduction in the number of measurements is obtained for relevant states, with only very limited loss of information. These results open perspective for its application in larger systems.