Dr Aonan Zhang

Abstract:

In quantum mechanics, geometry has been demonstrated as a useful tool for inferring nonclassical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the quantum state space onto the Euclidean space via measurements of observables on the system. Despite the great success of this method in studying two-level quantum systems (qubits) with the celebrated Bloch sphere representation, it is still difficult to reveal the geometry of multidimensional quantum systems. Here we report the first experiment measuring the geometry of such projections beyond the qubit. Specifically, we observe the joint numerical ranges of a triple of observables in a three-level photonic system, providing a complete classification of these ranges. We further show that the geometry of different classes reveals ground-state degeneracies of a Hamiltonian as a linear combination of the observables, which is related to quantum phases in the thermodynamic limit. Our results offer a versatile geometric approach for exploring the properties of higher-dimensional quantum systems.

Abstract:

The accurate and reliable description of measurement devices is a central problem in both observing uniquely nonclassical behaviors and realizing quantum technologies from powerful computing to precision metrology. To date quantum tomography is the prevalent tool to characterize quantum detectors. However, such a characterization relies on accurately characterized probe states, rendering reliability of the characterization lost in circular argument. Here we report a self-characterization method of quantum measurements based on reconstructing the response range-the entirety of attainable measurement outcomes, eliminating the reliance on known states. We characterize two representative measurements implemented with photonic setups and obtain fidelities above 99.99% with the conventional tomographic reconstructions. This initiates range-based techniques in characterizing quantum systems and foreshadows novel device-independent protocols of quantum information applications.