Morphophoric POVMs, generalised qplexes, and 2-designs

@article{Somczyski2020MorphophoricPG,
  title={Morphophoric POVMs, generalised qplexes, and 2-designs},
  author={Wojciech Słomczyński and Anna Szymusiak},
  journal={Quantum},
  year={2020},
  volume={4},
  pages={338}
}
We study the class of quantum measurements with the property that the image of the set of quantum states under the measurement map transforming states into probability distributions is similar to this set and call such measurements morphophoric. This leads to the generalisation of the notion of a qplex, where SIC-POVMs are replaced by the elements of the much larger class of morphophoric POVMs, containing in particular 2-design (rank-1 and equal-trace) POVMs. The intrinsic geometry of a… 
View via Publisher
quantum-journal.org
2 Citations
Background Citations
1

2 Citations

Citation Type

Citation Type

QBians Do Not Exist
Philosophers pride themselves on being careful readers and analyzers. In a recent article in The Monist, “Quantum Bayesianism Assessed” [2], John Earman analyzes a position he ascribes to a group of…
Operational Detection of Entanglement via Quantum Designs
From an operational point of view, several new entanglement detection criteria are proposed using quantum designs. These criteria are constructed by considering the correlations defined with quantum…

References

SHOWING 1-10 OF 80 REFERENCES
Introducing the Qplex: a novel arena for quantum theory
Abstract We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, “Unperformed experiments have no results.” The tools of quantum information theory, and in particular…
Highly symmetric POVMs and their informational power
TLDR
In this case, it is proved that the entropy is minimal, and hence, the relative entropy is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM.
Multiqubit Clifford groups are unitary 3-designs
Unitary $t$-designs are a ubiquitous tool in many research areas, including randomized benchmarking, quantum process tomography, and scrambling. Despite the intensive efforts of many researchers,…
Geometry of the set of quantum correlations
It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually…
(Non-)Contextuality of Physical Theories as an Axiom
We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure…
t-Designs in Projective Spaces
Symmetric informationally complete measurements identify the irreducible difference between classical and quantum systems
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely…
Properties of QBist State Spaces
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states.…
Quantifying non-classical and beyond-quantum correlations in the unified operator formalism
Acin et al (2010 Phys. Rev. Lett. 104 140404) introduced a unified framework for the study of no-signalling correlations. Such a framework is based on the notion of local quantum measurements, but,…
The SIC Question: History and State of Play
TLDR
Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844.
...
...