Related papers: On the compatibility of quantum instruments
Quantum resources are certain features of the quantum world that provide advantages in certain information-theoretic, thermodynamic, or any other useful operational tasks that are outside the realm of what classical theories can achieve.…
Incompatible, i.e. non-jointly measurable quantum measurements are a necessary resource for many information processing tasks. It is known that increasing the number of distinct measurements usually enhances the incompatibility of a…
Quantum coherence, incompatibility, and quantum correlations are fundamental features of quantum physics. A unified view of those features is crucial for revealing quantitatively their intrinsic connections. We define the relative quantum…
Quantum instruments describe both the classical output and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure.…
Incompatible quantum channels cannot be jointly and exactly realized, meaning that any approximate joint realization inevitably entails a tradeoff in implementation accuracy. While this notion of channel incompatibility unifies fundamental…
We connect two key concepts in quantum information: compatibility and divisibility of quantum channels. Two channels are compatible if they can be both obtained via marginalization from a third channel. A channel divides another channel if…
Three notions of complementarity - operational, probabilistic, and value complementarity - are reanalysed with respect to the question of joint measurements and compared with reference to some examples of canonically conjugate observables.…
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that,…
In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Due to the information gain of classical measurement outputs non-unitary dynamical processes can take place on…
We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy…
In this contribution I review rigorous formulations of a variety of limitations of measurability in quantum mechanics. To this end I begin with a brief presentation of the conceptual tools of modern measurement theory. I will make precise…
Given two quantum channels, we examine the task of determining whether they are compatible - meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting…
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection…
The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker…
We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…
We introduce the notion of incompatibility witness for quantum channels, defined as an affine functional that is non-negative on all pairs of compatible channels and strictly negative on some incompatible pair. This notion extends the…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
A typical bipartite quantum protocol, such as EPR-steering, relies on two quantum features, entanglement of states and incompatibility of measurements. Noise can delete both of these quantum features. In this work we study the behavior of…
Central to the power of quantum computing is the concept of quantum parallelism: quantum systems can explore and process multiple computational paths simultaneously. In this paper, we discuss the elusive nature of quantum parallelism,…
General quantum measurements are represented by instruments. In this paper the mathematical formalization is given of the idea that an instrument is a channel which accepts a quantum state as input and produces a probability and an a…