Implementation of quantum measurements using classical resources and only a single ancillary qubit

Abstract We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension d using only classical resources and single ancillary qubit. Our method is based on probabilistic implementation of -outcome measurements which followed by postselection some the received outcomes. conjecture that success probability our larger than constant independent for all POVMs . Crucially, this implies possibility realizing arbitrary nonadaptive measurement protocol -dimensional system auxiliary qubit with overhead sampling complexity. show holds typical rank-one Haar-random dimensions. Furthermore, we carry out extensive numerical computations showing above variety extremal POVMs, including SIC-POVMs up 1299. Finally, argue can be favorable experimental realization noise compounding circuits required typically substantially lower standard directly uses Naimark’s dilation theorem.