Resolving the phase space

Abstract: Quantum tomography can reconstruct fine phase-space structures that are not necessarily resolved by measurement itself. We show that the effective resolution of tomography is determined by a sampling operator linked to the Gram matrix of the measurement, which defines the experimentally accessible degrees of freedom and reconstruction bandwidth of the quantum state. Acting analogously to a transfer function in imaging, this operator provides an operational criterion for distinguishing genuinely resolved quantum features from artefacts induced by incomplete sampling or reconstruction assumptions. Reconstruction in the Gram eigenbasis emerges as an efficient measurement-adapted compression of the tomographic problem. Within finite frame theory, the same structure appears naturally as the frame operator. Our results establish a resolution-based framework for quantum tomography relevant for contemporary experiments probing highly structured nonclassical states.