Process positive-operator-valued measure: A mathematical framework for the description of process tomography experiments

2008/02/29 by Mário Ziman, Mario Ziman · 78 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Calculus (dental) #Computer science #Data mining #Formalism (music) #Mathematics #Measure (data warehouse) #Operator (biology) #POVM #Physics #Process (computing) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum measurement #Quantum mechanics #Quantum process #Theoretical computer science #quant-ph

paper · pdf · doi:10.1103/physreva.77.062112

published in Physical Review A 77(6) (American Physical Society) · 4 pages, comments are welcome

openalex publication_date 2008/06/24 · arxiv created 2008/07/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We introduce a mathematical framework for the description of measurements of quantum processes. Using this framework, process estimation problems can be treated in a similar way as state estimation problems, only replacing the concept of positive-operator-valued measure (POVM) by the concept of process POVM (PPOVM). In particular, we will show that any measurement of qudit channels can be described by a collection of effects (positive operators) defined on a two-qudit system. However, the effects forming a PPOVM are not normalized in the usual sense. We will demonstrate the use of this formalism in discrimination problems by showing that perfect channel discrimination is equivalent to a specific unambiguous state discrimination.

Citations

• The Quantum Theory of Measurement
• Statistical Distinguishability between Unitary Operations
• Quantum detection and estimation theory
• Completely positive linear maps on complex matrices
• Quantum Theory: Concepts and Methods

Cited by

• Optimal quantum networks and one-shot entropies
• Optimal Quantum Tomography of States, Measurements, and Transformations
• Incomplete quantum process tomography and principle of maximal entropy
• Uncertainty principle of quantum processes
• Necessary condition for incompatibility of observables in general probabilistic theories
• Popescu-Rohrlich box implementation in general probabilistic theory of processes
• Theoretical framework for quantum networks
• Quantum memory in spontaneous emission processes

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• Unified Framework for Direct Characterization of Kraus Operators, Observables, Density Matrices, and Weak Values Without Weak Interaction
• On single qubit quantum process tomography for trace-preserving and nontrace-preserving maps
• Quantum filtering using POVM measurements
• Non-completely positive maps: properties and applications