  The Pancharatnam phase deficit is defined as the difference between the
Pancharat- nam phase acquired by the global system and the sum of the
Pancharatnam phases acquired by subsystems during local unitary evolutions. We
show that a non-zero value of the Pancharatnam phase deficit for a composite
quantum system can be a signature of quantum entanglement. In the context of
macroscopic quantum systems, we illustrate how the Pancharatnam phase deficit
can be used to detect macroscopically entangled states. In particular, we use
the Pancharatnam phase deficit to detect the entanglement for macroscopic
superposition of coherent states. Furthermore, we show that by measuring the
Pancharatnam phase deficit one can measure the concurrence of two spin singlets
between distant boundaries.

Quantum Physics