Abstract
Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything. This requires quantum process tomography, which demands an informationally-complete set of probe states. It is very convenient if this set is group-covariant -- i.e., each element is generated by applying an element of the quantum system's natural symmetry group to a single fixed fiducial state. In this paper, we consider metrology with 2-photon ("biphoton") states, and report experimental studies of different states' sensitivity to small, unknown collective SU(2) rotations ("SU(2) jitter"). Maximally entangled N00N states are the most sensitive detectors of such a rotation, yet they are also among the worst at fully characterizing an a-priori unknown process. We identify (and confirm experimentally) the best SU(2)-covariant set for process tomography; these states are all less entangled than the N00N state, and are characterized by the fact that they form a 2-design.
Highlights
The goal of quantum metrology is to measure or detect physical phenomena with surprising precision by exploiting quantum resources
quantum process tomography (QPT) requires a diverse set of probe states, and the overall accuracy of estimation depends on the properties of the entire set
If the process is pure SUð2Þ depolarization, and the input state is given by Eq (3), d will be real. (We check that this is the case by performing quantum state tomography on ρ for several depolarization strengths.) In this case, the expectation value of the projection onto jψxi is hjψxihψxji 1⁄4 TrðjψxihψxjρÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Summary
The goal of quantum metrology is to measure or detect physical phenomena with surprising precision by exploiting quantum resources. Optical mode, Lobino et al [11] showed that it is sufficient to (1) prepare a single Glauber coherent state and (2) displace it by a variety of phase space translations. This approach, in which a single “fiducial” state is multiplied into a complete set of probe states by implemented group transformations, has the great merit of experimental ease. We prepare a wide range of probe states and quantify their performance at two opposite extremes of the metrology spectrum: (1) their ability to detect random SUð2Þ phase shifts, and (2) their ability to characterize an unknown process, 2160-3308=14=4(4)=041025(9). Subsystems [18,19] were designed against this noise model
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