Symmetric Localizable Multipartite Quantum Measurements from Pauli Orbits

Abstract

While the structure of entangled quantum states is relatively well understood, the characterization of entangled measurements, especially in multipartite and high-dimensional settings, remains far less developed. In this work, we introduce a general approach to construct highly symmetric, locally encodable orthonormal measurement bases, as orbits of a single fiducial state under tensor-product actions of Pauli subgroups. This framework recovers the Elegant Joint Measurement-a two-qubit measurement whose local marginals form a regular tetrahedron on the Bloch sphere-as a special case, and we extend the construction to both more systems and higher dimensions. We analyze the entanglement cost required to implement these measurements locally via the Clifford hierarchy and use this criterion to classify them. We show how the symmetry of our constructions allows us to characterize their localizability, which is generally a challenging problem, and to identify certain classes of measurement bases that are efficiently localizable. Our approach offers a systematic toolkit for designing entangled measurements with rich symmetry and implementability properties.

15 + 3 pages, 3 figures. v2: minor changes

References in corpus (28)

• Quantum entanglement
• Quantum Teleportation is a Universal Computational Primitive
• Symmetric Informationally Complete Quantum Measurements
• On the role of entanglement in quantum computational speed-up
• Fully device independent quantum key distribution
• Hudson's Theorem for finite-dimensional quantum systems
• Entanglement Detection in the Stabilizer Formalism
• Distributed Quantum Computing: a Survey
• Instantaneous measurement of non-local variables
• Entanglement 25 years after Quantum Teleportation: testing joint measurements in quantum networks
• Bilocal Bell inequalities violated by the quantum Elegant Joint Measurement
• Diagonal gates in the Clifford hierarchy
• Multipartite Entanglement and Global Information
• Covariant quantum measurements which maximize the likelihood
• Causality Constraints on Nonlocal Quantum Measurements
• Entanglement-assisted quantum communication with simple measurements
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Linear Dependencies in Weyl-Heisenberg Orbits
• Extremal covariant measurements
• Iso-entangled bases and joint measurements
• Bipartite quantum measurements with optimal single-sided distinguishability
• Quantum stochastic communication via high-dimensional entanglement
• Correspondence between entangled states and entangled bases under local transformations
• Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
• Local encoding of classical information onto quantum states
• Classification of joint quantum measurements based on entanglement cost of localization
• Noise-robust proofs of quantum network nonlocality
• Multipartite Nonlocality in Clifford Networks