QUANTUM INCOMPATIBILITY
WHAT IS IT?

When you start to learn about quantum mechanics, one of the first pieces of quantum ‘weirdness’ that you come across is the notion of incompatibility; this concept arises in multiple situations, but in its loosest terms it deals with things that cannot occur together on the same system. The standard example of this is the measurement of position and momentum of a particle: if one accurately performs a measurement of one, then all information about the other is lost, making it impossible to measure. This is an example of a strictly nonclassical phenomenon that provides significant benefits within quantum information theory, in particular within quantum cryptography.
Related to the notion of incompatibility is that of noise and disturbance: noise can be either in terms of the statistical noise that may arise when performing and measuring an experiment, or can be intrinsic to the quantity that is measured; disturbance relates to how a physical system is altered by the act of measurement. These two notions are intrinsically linked: a noisy version of a measurement is less disturbing than its more accurate counterparts, and a measurement that does not disturb any system necessarily provides no information. As such, there is a tradeoff between the amount of information we can obtain from a system and how much we unavoidably alter it. The same ideas can be applied to the notion of incompatibility, as a sequential measurement of two incompatible quantities will leave the second disturbed, and such a disturbance can be reduced by making the first more noisy. 
OUR RESEARCH

We consider not only incompatibility in the context of measured quantities (socalled ‘observables’), but also between quantum channels, which describe the evolution of a system. Further to this, incompatibility between observables and channels is investigated. In particular, we aim to provide a characterisation of the compatibility of qubit channels and observables.
In addition to this, we work on the concept of sequential measurement schemes, in which repeated application of a small number of measurements and operations lead to more informative observables. 
RECENT ARTICLES

T. Bullock, P. Busch: Measurement uncertainty relations: characterising optimal error bounds for qubits. J. Phys. A: Math. Theor. 51, 283001 (2018) [arXiv].
C. Carmeli, T. Heinosaari, A. Toigo: State discrimination with postmeasurement information and incompatibility of quantum measurements. Phys. Rev. A 98, 0120126 (2018) [arXiv]. T. Heinosaari, D. Reitzner, T. Rybár, M. Ziman: Incompatibility of unbiased qubit observables and Pauli channels. Phys. Rev. A 97, 022112 (2017) [arXiv]. 
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