Related papers: On the compatibility of quantum instruments

On the compatibility of quantum instruments

URL: http://arxiv.org/abs/2110.00932v3
Date: Mon, 7 Mar 2022 15:51:09 GMT
Title: On the compatibility of quantum instruments
Authors: Arindam Mitra, M\'at\'e Farkas
Abstract summary: We argue that the notion of traditional compatibility is incomplete, and prove that while parallel compatibility captures measurement and channel compatibility, traditional compatibility does not. We propose parallel compatibility as the conceptually complete definition of compatibility of quantum instruments.
Score: 5.1398743023989555
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Incompatibility of quantum devices is a useful resource in various quantum information theoretical tasks, and it is at the heart of some fundamental features of quantum theory. While the incompatibility of measurements and quantum channels is well-studied, the incompatibility of quantum instruments has not been explored in much detail. In this work, we revise a notion of instrument compatibility introduced in the literature that we call traditional compatibility. Then, we introduce the new notion of parallel compatibility, and show that these two notions are inequivalent. Then, we argue that the notion of traditional compatibility is incomplete, and prove that while parallel compatibility captures measurement and channel compatibility, traditional compatibility does not. Hence, we propose parallel compatibility as the conceptually complete definition of compatibility of quantum instruments.

Related papers

The incompatibility of quantum channels in general probabilistic theories [0.0]
In quantum theory, there exist sets of operations that cannot be performed simultaneously. In GPTs, composite systems are not uniquely defined, and the set of states can vary from the minimal tensor to the maximal tensor. We show that the set of all almost quantum compatible channel pairs is strictly narrower than the set of all min-tensor-compatible channel pairs.
arXiv Detail & Related papers (2024-03-03T04:28:25Z)
Witnessing the Hierarchy of Quantum Incompatibility Resources in High-Dimensional Systems [10.661961857558106]
Quantum incompatibility is a phenomenon that some quantum measurements cannot be performed simultaneously. We propose a modified quantum state discrimination protocol that decomposes complex compatibility structures into pair-wise ones. Our approach is able to witness incompatibility structures, i.e., the hierarchy of quantum incompatibility resources.
arXiv Detail & Related papers (2023-06-21T09:12:51Z)
Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication [60.18814584837969]
We introduce the notion of q-compatibility, which unifies different notions of POVMs, channels, and instruments incompatibility. We are able to pinpoint exactly what each notion of incompatibility consists of, in terms of information-theoretic resources.
arXiv Detail & Related papers (2022-11-16T21:33:31Z)
Characterizing and quantifying the incompatibility of quantum instruments [5.1398743023989555]
We introduce -- similarly to the case of measurements and channels -- the incompatibility of quantum instruments and derive universal bounds on it. We prove that post-processing of quantum instruments is a free operation for parallel compatibility. We provide families of instruments for which our bounds are tight, and families of compatible indecomposable instruments.
arXiv Detail & Related papers (2022-09-06T16:19:14Z)
Incompatibility of observables, channels and instruments in information theories [68.8204255655161]
We study the notion of compatibility for tests of an operational probabilistic theory. We show that a theory admits of incompatible tests if and only if some information cannot be extracted without disturbance.
arXiv Detail & Related papers (2022-04-17T08:44:29Z)
Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
arXiv Detail & Related papers (2021-09-06T14:35:15Z)
Self-adjointness in Quantum Mechanics: a pedagogical path [77.34726150561087]
This paper aims to make quantum observables emerge as necessarily self-adjoint, and not merely hermitian operators. Next to the central core of our line of reasoning, the necessity of a non-trivial declaration of a domain to associate with the formal action of an observable.
arXiv Detail & Related papers (2020-12-28T21:19:33Z)
Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks [48.7576911714538]
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. We experimentally verify detailed and integral fully quantum fluctuation theorems for heat exchange using two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup.
arXiv Detail & Related papers (2020-12-11T12:55:17Z)
Quantum Incompatibility of a Physical Context [0.0]
We characterize quantum incompatibility as a resource encoded in a physical context, involving both the quantum state and observables. We derive a measurement-incompatibility quantifier that is easily computable, admits a geometrical interpretation, and is maximum only if the eigenbases of the involved observables are mutually unbiased.
arXiv Detail & Related papers (2020-04-02T14:00:39Z)
From a quantum theory to a classical one [117.44028458220427]
We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
arXiv Detail & Related papers (2020-04-01T09:16:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.