Coarse-grained quantum state tomography with optimal POVM construction

Donghun Jung, Young‐Wook Cho, Yosep Kim +1 more

In a multiqubit system, when a detector's resolution is insufficient to distinguish between qubits, individual qubit measurement becomes impractical. This limitation results in coarse-grained (CG) measurements that dilute system information and, more critically, hinder accurate assessment of qubit correlations, making quantum state tomography (QST) infeasible. To address this issue, we propose a scheme to utilize CG measurements for QST by integrating two-qubit gates and optimizing their corresponding positive operator-valued measures (POVMs) using parametrized quantum circuits. Specifically, we focus on constructing generalized symmetric informationally complete POVMs by maximizing the von Neumann entropy of the Gram matrix of these CG POVMs. Our numerical simulations demonstrate the effectiveness of this approach for QST using a two-qubit model and further verify the scalability of our scheme toward N -qubit systems.

Shun Umekawa, Koki Ono, Hayato Arai

We identify an operational principle that singles out Projection-Valued Measures (PVMs) among general Positive Operator-Valued Measures (POVMs), bridging the modern quantum measurement theory and the traditional formulation based on projective measurements of physical observables. We reformulate Ozawa's intersubjectivity condition, which requires inter-observer agreement of the measurement outcomes, in a quantitative manner within the framework of generalized probabilistic theories. We prove that (i) a POVM is a PVM if and only if its every coarse-graining is intersubjective, and (ii) a system is classical if and only if intersubjectivity is preserved under any coarse-graining, establishing a complete characterization of the physical observables and the classical theory. Furthermore, measurements with intersubjectivity are sufficiently rich for the informational tasks of state tomography and state discrimination, testifying to its operational significance in quantum and beyond information processing.

M. Cramer, Martin Bodo Plenio, Steven T. Flammia +6 more

Gregory S. Kanter, Prem Kumar

Yong Siah Teo, Jaroslav Řeháček, Z. Hradil

We introduce a numerical coarse-graining scheme to reliably estimate the quantum state of a source given a set of noisy measurement outcomes that are not well calibrated. This scheme requires no additional knowledge or assumptions about the structures of the noisy outcomes and is, thus, applicable for very general tomography experiments with arbitrary noise perturbations. Further, this scheme involves an optimization procedure that is straightforward to implement and can readily be extended to any number of ill-calibrated noisy outcomes in a measurement setup. Compared with the standard estimation strategy where noise is neglected, coarse graining performed on simulated and experimental data for two-qubit quantum states and on simulated data from continuous-variable tomography shows that this scheme can significantly improve the accuracies of state estimators for noise levels ranging from low to moderately high values.

Xuanmin Zhu, Dezheng Zhang, Runping Gao +3 more