General measurements with limited resources and their application to quantum unambiguous state discrimination

Abstract

In this report, we present a framework for implementing an arbitrary $n$-outcome generalized quantum measurement (POVM) on an $m$-qubit register as a sequence of two-outcome measurements requiring only single ancillary qubit. Our procedure offers a particular construction for the two-outcome partial measurements which can be composed into a full implementation of the measurement on any gate architecture. This implementation in general requires classical feedback; we present specific cases when this is not the case. We apply this framework on the unambiguous state discrimination and analyze possible strategies. In the simplest case, it gives the same construction as is known, if we opt for performing conclusiveness measurement first. However, it also offers possibility of performing measurement for one of the state outcomes first, leaving conclusiveness measurement for later. This shows flexibility of presented framework and opens possibilities for further optimization. We present discussion also on biased qubit case as well as general case of unambiguous quantum state discrimination in higher dimension.

arXiv comment27 pages, 8 figures

References in corpus (27)

• Quantum Computing in the NISQ era and beyond
• Symmetric Informationally Complete Quantum Measurements
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Simulating positive-operator-valued measures with projective measurements
• Optimal randomness certification from one entangled bit
• Realization of single-qubit positive operator-valued measurement via a one-dimensional photonic quantum walk
• Ancilla-Driven Universal Quantum Computation
• Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
• Binary search trees for generalized measurement
• Quantum Channel Construction with Circuit Quantum Electrodynamics
• Spherical Code Key Distribution Protocols for Qubits
• Device-Independent Certification of a Nonprojective Qubit Measurement
• A two-qubit Bell inequality for which POVM measurements are relevant
• General implementation of all possible positive-operator-value measurements of single photon polarization states
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
• Simulating all quantum measurements using only projective measurements and postselection
• Implementation of a general single-qubit positive operator-valued measure on a circuit-based quantum computer
• Implementing general measurements on linear optical and solid-state qubits
• All possible bipartite positive-operator-value measurements of two-photon polarization states
• Optimal quantum state discrimination via nested binary measurements
• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• Implementing generalized measurements with superconducting qubits
• Implementation of discrete positive operator valued measures on linear optical systems using cosine-sine decomposition
• Simulation of positive operator-valued measures and quantum instruments via quantum state preparation algorithms
• Optimal minimum-cost quantum measurements for imperfect detection