Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles

TL;DR

This paper demonstrates that in systems of indistinguishable qubits, the monogamy of entanglement can be maximally violated using measures that are monogamous for distinguishable particles, challenging previous assumptions about entanglement shareability.

Contribution

It introduces a formulation of the trace-out rule for indistinguishable particles and shows maximum violation of monogamy of entanglement without contradicting no-cloning.

Findings

Maximum violation of monogamy in indistinguishable particles

Formulation of trace-out rule for indistinguishable particles

Entanglement shareability restrictions are removed for indistinguishable particles

Abstract

Two important results of quantum physics are the \textit{no-cloning} theorem and the \textit{monogamy of entanglement}. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results imply the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually), a maximum violation of the monogamy of entanglement is possible by the measures that are monogamous for distinguishable particles. To derive this result, we formulate the degree of freedom trace-out rule for indistinguishable particles corresponding to a spatial location where each degree of freedom might be entangled with the other degrees of freedom. Our result removes the restriction on the shareability of quantum entanglement for indistinguishable particles, without contradicting the no-cloning theorem.