Five Open Problems in Quantum Information Theory

2022/03/03 by Paweł Horodecki, Łukasz Rudnicki, Karol Życzkowski · 1 voice · 10 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications

paper · pdf · doi:10.1103/prxquantum.3.010101

openalex publication_date 2022/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We identify five selected open problems in the theory of quantum information, which are rather simple to formulate, are well studied in the literature, but are technically not easy. As these problems enjoy diverse mathematical connections, they offer a huge breakthrough potential. The first four concern existence of certain objects relevant for quantum information, namely a family of symmetric informationally complete generalized measurements in an infinite sequence of dimensions, mutually unbiased bases in dimension six, measurements saturating multiparameter Cramr-Rao bound and bound entangled states with negative partial transpose. The fifth problem requires checking whether a certain state of a two-ququart system is two-copy distillable.

Citations

• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Quantum Computation and Quantum Information
• Quantum entanglement

Cited by

• Equivalence of mutually unbiased bases via orbits: general theory and a d=4 case study
• Partial transpose as a space-time swap
• Maximally non-projective measurements are not always symmetric informationally complete
• Partial trace relations beyond normal matrices
• Symmetry reduction for testing k-block-positivity via extendibility
• Sharp Plucker Geometry for Three-Copy Werner Distillation
• A Reproducible Software Workflow for Unanchored Approximate MUB Optimization: A Case Study in Dimension Six
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Thirty-six officers, artisanally entangled
• Multiparameter estimation for qubit states with collective measurements: a case study
• Unlimited quantum correlation advantage from bound entanglement

Discussions

• A recent review provides answers to the OP's questions, to be found in Mutually Unbiased Bases in Composite Dimensions -- A Review. Daniel McNulty and Stefan Weigert. arXiv:2410.23997 (2024). In short [stackexchange, 1 points]

Related

• Five open problems in quantum information
• Some Open Problems in Quantum Information Theory
• Some Open Problems in Quantum Information Theory
• Distinguishability and Accessible Information in Quantum Theory
• Quantum information theory