Abstract
While classical correlations can be freely distributed among many systems, this is not true for entanglement and quantum correlations. If a quantum system Sa is entangled with another quantum system Sb, then its entanglement with any third quantum system Sc cannot be arbitrary. This is the celebrated monogamy of entanglement. Implicit in this general statement is the plausible belief that only entanglement between the systems Sa and Sb constrains the entanglement between Sa and the third system Sc. We demonstrate that even classical correlations between Sa and Sb may impose surprisingly stringent restrictions on the possible entanglement between Sa and Sc. In particular, perfect bipartite classical correlations and full entanglement cannot coexist in any tripartite state. An intuitive explanation of this monogamy of hybrid classical and quantum correlations might be that the system Sa has a correlating capability, which cannot be used to establish any entanglement with a third system (but can still be used to establish classical correlations) if it is exhausted when correlated with Sb (in either a classical or quantum fashion). This may be interpreted as an alternate version of monogamy.
Published Version
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