PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
August 7, 2024Journal of Physics A Mathematical and Theoretical16 citationsOpen Access

How much symmetry do symmetric measurements need for efficient operational applications?

View Full Paper
KSKatarzyna Siudzińska

Key Points

Key points are not available for this paper at this time.

Abstract

Abstract We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). This provides a uniform description of objects that are more general than symmetric, informationally complete POVMs and mutually unbiased bases, but at the same time less destructive and more noise tolerant. For informationally complete sets, we propose construction methods from orthonormal Hermitian operator bases. The correspondence between operator bases and measurements can be as high as one-to-four, with a one-to-one correspondence following only under additional assumptions. Importantly, it turns out that some of the symmetry properties, lost in the process of generalization, can be recovered without fixing the same number of elements for all POVMs. In particular, for a wide class of unequinumerous symmetric measurements that are conical 2-designs, we derive the index of coincidence, entropic uncertainty relations, and separability criteria for bipartite quantum states.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Katarzyna Siudzińska (2024) studied this question.

synapsesocial.com/papers/68e5d23bb6db6435875680f9https://doi.org/10.1088/1751-8121/ad6cb8
Ask AI
Helpful
Bookmark
Share
View Full Paper

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1All classes of informationally complete symmetric measurements in finite dimensions2021 · 46 citations
  2. 2Non-Markovian quantum dynamics from symmetric measurements2024 · 5 citations
  3. 3Characterizing Entanglement via Uncertainty Relations2003 · 310 citations
  4. 4Security of Quantum Key Distribution Using d -Level Systems2002 · 1,348 citations
  5. 5The Brukner-Zeilinger invariants in terms of (N, M) − POVMs2023 · 5 citations