Experimental entanglement entropy without twin copy

We show that it is possible to estimate experimentally the von Neuman entanglement entropy SAvN of a symmetric bi-partite quantum system $AB$ by using the basic measurement counts for a *single* copy of a prepared state. We use the entropy SABX associated with the experimental measurements for this state and the reduced entropy SAX obtained by tracing the experimental probabilities over the B half of the system. We conjecture that SAvN∝ (2SAX-SABX) and demonstrate that it is verified in good approximation using exact diagonalization and analog calculations performed with the publicly available QuEra facilities for chains and ladders of Rydberg atoms. The approximate proportionality constant is of order one for the examples considered. 2SAX-SABX can be calculated easily for many other qubit platforms and appears to be generically robust under measurement errors, although a general proof remains to be found. Similar results are found for the second order R\'enyi entanglement entropy.