Post-processing of quantum instruments

Abstract

Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the concatenation of quantum instruments into a sequence of certain length. In general, the choice of instrument at any given step in the sequence can be conditionally chosen based on the classical results of all preceding instruments. For two instruments in a sequence we consider the conditional second instrument as an effective way of post-processing the first instrument into a new one. This is similar to how a measurement described by a positive operator-valued measure (POVM) can be post-processed into another by way of classical randomization of its outcomes using a stochastic matrix. In this work we study the post-processing relation of instruments and the partial order it induces on their equivalence classes. We characterize the greatest and the least element of this order, give examples of post-processings between different types of instruments and draw connections between post-processings of some of these instruments and their induced POVMs.

References in corpus (26)

• Measurement-based quantum computation with cluster states
• An Invitation to Quantum Incompatibility
• Simulating positive-operator-valued measures with projective measurements
• Clean Positive Operator Valued Measures
• Non-disturbing quantum measurements
• Extracting information from a qubit by multiple observers: Toward a theory of sequential state discrimination
• Operational framework for quantum measurement simulability
• Distinguishability Measures and Entropies for General Probabilistic Theories
• Informationally complete joint measurements on finite quantum systems
• Simulating all quantum measurements using only projective measurements and postselection
• Invertible Quantum Operations and Perfect Encryption of Quantum States
• Simulability of observables in general probabilistic theories
• Sequential decoding of a general classical-quantum channel
• Approximate simulation of quantum channels
• Quantum correlations are stronger than all nonsignaling correlations produced by n-outcome measurements
• Qualitative Noise-Disturbance Relation for Quantum Measurements
• Observation of stronger-than-binary correlations with entangled photonic qutrits
• Universality of Sequential Quantum Measurements
• Extremal quantum protocols
• Minimal sufficient positive-operator valued measure on a separable Hilbert space
• Operational restrictions in general probabilistic theories
• Proposed experiment to test fundamentally binary theories
• Saturation of repeated quantum measurements
• Sequential measurement-based quantum computing with memories
• The unavoidable information flow to environment in quantum measurements
• Quantum state tomography via sequential uses of the same informationally incomplete measuring apparatus

Cited by in corpus (9)

• Incompatibility of observables, channels and instruments in information theories
• Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel
• On the compatibility of quantum instruments
• Characterizing and quantifying the incompatibility of quantum instruments
• Incompatibility of quantum instruments
• Multi-object operational tasks for measurement incompatibility
• Entropic partial orderings of quantum measurements
• Minimal operational theories: classical theories with quantum features
• Measurement disturbance tradeoffs in three-qubit unsupervised quantum classification