Monogamy relations of quantum coherence between multiple subspaces

TL;DR

This paper establishes trade-off relations for quantum coherence shared among multiple subspaces, revealing limitations and criteria for genuine multisubspace coherence in quantum systems.

Contribution

It introduces new trade-off relations for coherence between subspaces using various norms and entropy, advancing understanding of coherence monogamy.

Findings

Derived coherence trade-off relations for trace norm, Hilbert-Schmidt norm, and von Neumann entropy.

Established criteria for detecting genuine multisubspace coherence.

Provided bounds illustrating the limitations of coherence sharing among subspaces.

Abstract

Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity constraint on the density matrix. On the level of multipartite systems, this gives rise to what is known as monogamy of entanglement. On the level of single systems this leads to a bound, and hence, a trade-off in coherence that can exist between different orthogonal subspaces. In this work we derive trade-off relations for the amount of coherence that can be shared between a given subspace and all other subspaces based on trace norm, Hilbert-Schmidt norm and von Neumann relative entropy. From this we derive criteria detecting genuine multisubspace coherence.