A solution to two party typicality using representation theory of the symmetric group

Abstract

We give a proof of the multi-party typicality conjecture for the first nontrivial case when there are only two parties. The conjecture itself is motivated by the study of multi-party state merging protocols on quantum systems. Our approach is based on fundamental group-theoretical properties, thereby providing an opportunity to study the problem from a more systematic perspective. Our proof also covers an extended multiparty typicality conjecture that we state in this work. This extended multiparty typicality conjecture is formulated using arbitrary $k$-norms instead of only the $2$-norm as in the original conjecture.

17 pages, no figures. Typos removed, extended introduction. Generalized problem statement

References in corpus (6)

• The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography
• The Spectra of Density Operators and the Kronecker Coefficients of the Symmetric Group
• Applications of coherent classical communication and the Schur transform to quantum information theory
• On simultaneous min-entropy smoothing
• Multiparty quantum protocols for assisted entanglement distillation
• Network information theory for classical-quantum channels

Cited by in corpus (5)

• Hypothesis Testing on Invariant Subspaces of the Symmetric Group, Part I - Quantum Sanov's Theorem and Arbitrarily Varying Sources
• On simultaneous min-entropy smoothing
• The Classical-Quantum Channel with Random State Parameters Known to the Sender
• A Quantum Multiparty Packing Lemma and the Relay Channel
• The depolarising channel and Horns problem