Incompatibility robustness of quantum measurements: a unified framework

  title={Incompatibility robustness of quantum measurements: a unified framework},
  author={S{\'e}bastien Designolle and M{\'a}t{\'e} Farkas and J Kaniewski},
  journal={New Journal of Physics},
In quantum mechanics performing a measurement is an invasive process which generally disturbs the system. Due to this phenomenon, there exist incompatible quantum measurements, i.e., measurements that cannot be simultaneously performed on a single copy of the system. It is then natural to ask what the most incompatible quantum measurements are. To answer this question, several measures have been proposed to quantify how incompatible a set of measurements is, however their properties are not… 

Figures and Tables from this paper

Amount of quantum coherence needed for measurement incompatibility
A pair of quantum observables diagonal in the same “incoherent” basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that
Joint measurability in non-equilibrium quantum thermodynamics
Quantum work and fluctuation theorems are mostly discussed in the framework of projective two-point measurement (TPM) schemes. According to a well known no-go theorem, there is no work observable
Incompatibility as a resource for programmable quantum instruments
This work identifies an incompatibility partial ordering of PIDs based on whether one can be transformed into another using processes that do not require additional quantum memory, and offers tests for incompatibility in the most general types of quantum instruments.
Complete Resource Theory of Quantum Incompatibility as Quantum Programmability.
This Letter characterize incompatibility in terms of programmable measurement devices and the general notion of quantum programmability, which refers to the temporal freedom a user has in issuing programs to a quantum device.
Order preserving maps on quantum measurements
We study the partially ordered set of equivalence classes of quantum measurements endowed with the post-processing partial order. The post-processing order is fundamental as it enables to compare
Device-independent quantification of measurement incompatibility
This work provides a device-independent framework to lower bound any quantifier of measurement incompatibility that can be defined in terms of the measurement effects as a semidefinite program, including quantifiers such as the incomp compatibility robustness and the genuine-multipartite incompatibility robustness.
Robust genuine high-dimensional steering with many measurements
This work develops, for more than two measurements, universal bounds on the incompatibility robustness, turned into meaningful dimension certificates that often offer an increased resistance to noise and could then be advantageously employed in experiments.
Symmetries between measurements in quantum mechanics
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of
Testing incompatibility of quantum devices with few states
When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called
A Fisher information-based incompatibility criterion for quantum channels
. We introduce a new incompatibility criterion for quantum channels, based on the notion of (quantum) Fisher information. Our construction is based on a similar criterion for quantum measurements put


Noise robustness of the incompatibility of quantum measurements
The existence of incompatible measurements is a fundamental phenomenon having no explanation in classical physics. Intuitively, one considers given measurements to be incompatible within a framework
All Sets of Incompatible Measurements give an Advantage in Quantum State Discrimination.
It is shown that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination task and that if the authors take a resource-theory perspective of measurement incompatibility, then the guessing probability in discrimination tasks of this type forms a complete set of monotones that completely characterize the partial order in the resource theory.
Quantifying Measurement Incompatibility of Mutually Unbiased Bases.
This work quantifies precisely the degree of incompatibility of mutually unbiased bases (MUB) using the notion of noise robustness using the standard construction for d being a prime power, and provides upper and lower bounds on this quantity for sets of k MUB in dimension d.
Simulating Positive-Operator-Valued Measures with Projective Measurements.
This work proves that every measurement on a given quantum system can be realized by classical randomization of projective measurements on the system plus an ancilla of the same dimension, and shows that deciding whether it is PM simulable can be solved by means of semidefinite programming.
Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory.
It is shown that for arbitrary dimension the Clauser-Horne-Shimony-Holt inequality provides the Lagrangian dual of the characterization of joint measurability, which leads to a simple criterion for joint measURability beyond the known qubit case.
Most incompatible measurements for robust steering tests
It is shown that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not the most incompatible ones nor are they optimal for steering the isotropic states.
Operational relevance of resource theories of quantum measurements
It is proved that every resource measurement offers advantage for some quantum state discrimination task, and an operational interpretation of robustness is given, which quantifies the minimal amount of noise that must be added to a measurement to make it free.
Simultaneous measurement of two quantum observables: Compatibility, broadcasting, and in-between
One of the central features of quantum theory is that there are pairs of quantum observables that cannot be measured simultaneously. This incompatibility of quantum observables is a necessary
Quantum resource theories
Quantum resource theories (QRTs) offer a highly versatile and powerful framework for studying different phenomena in quantum physics. From quantum entanglement to quantum computation, resource
Dynamics of incompatibility of quantum measurements in open systems
The non-classical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the non-classicality