Monogamy of entanglement and other correlations
Masato Koashi, Andreas Winter
TL;DR
The paper investigates how quantum entanglement cannot be freely shared among multiple parties, formalizing a complementarity between entanglement cost and distillable common randomness as a measure of classical correlation. It proves a central identity $E_f(\rho_{AB})+I^\leftarrow(\rho_{AB'})=S(\rho_A)$ and its analogue with $E_C$, linking quantum and classical resources and establishing monogamy inequalities that extend to one-way distillable entanglement, secret key, and squashed entanglement. It also provides a counterexample showing that entanglement cost does not obey the same template, and discusses additivity implications and the equivalence $E=E_C$, along with corollaries relating different distillation and secrecy measures. Overall, the work offers a unified, operational framework for understanding monogamy of correlations across multiple quantum-information-theoretic tasks, with implications for additivity questions and practical limits on distributing correlations in multipartite systems.
Abstract
It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.