RQC Seminar

150th RQC Seminar

• Speaker

  Prof. Michał Oszmaniec
  ( Center for Theoretical Physics, Polish Academy of Sciences )

• Date

  14:00-15:00, September 4, 2024 (Wednesday)

• Venue

  Hybrid(ZOOM・ Wako Main Research 3F 345-347 Seminar Room/ 研究本館3階 セミナー室(345-347) C01）

• Title

  Ancilla-Free Implementation of Quantum Measurements

• Inquiries

  rqc_info[at]ml.riken.jp

Abstract
In quantum theory general measurements are described by so-called Positive Operator-Valued Measures (POVMs). In this work we show that in d-dimensional quantum systems an application of depolarizing noise with constant (independent of d) visibility parameter makes any POVM simulable by a randomized implementation of projective measurements that do not require any auxiliary systems to be realized.

This result significantly limits the asymptotic advantage that POVMs can offer over projective measurements in various information-processing tasks, including state discrimination, shadow tomography or quantum metrology. We also apply our findings to questions originating from quantum foundations. First, we asymptotically improve the range of parameters for which Werner and isotropic states have local models for generalized measurements (by factors of d and log(d) respectively). Second, we give asymptotically tight (in terms of dimension) bounds on critical visibility for which all POVMs are jointly measurable.

On the technical side we use recent advances in POVM simulation, the solution to the celebrated Kadison-Singer problem, and a new method of approximate implementation of a class of "nearly projective" POVMs by a convex combination of projective measurements, which we call dimension-deficient Naimark extension theorem.

The talk will be based on joint work with Michał Kotowski (MIM UW)