Incompatibility robustness of quantum measurements: a unified framework

@article{Designolle2019IncompatibilityRO,
  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},
  year={2019}
}
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… 

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References

SHOWING 1-10 OF 54 REFERENCES
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.
TLDR
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.
TLDR
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.
TLDR
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.
TLDR
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
TLDR
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
TLDR
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
...
1
2
3
4
5
...