Entanglement-induced sub-Planck phase-space structures

We show that entanglement of two superposed coherent states produces sub-Planck structures in phase space. The origin of these structures depends entirely on entanglement, unlike those in Zurek Nature (London) 412 712 (2001), where the effect of entanglement was not considered. The constituent states are sensitive enough to carry out the Heisenberg sensitive measurements. However, their usefulness is limited in providing high sensitivity in either the position (x) direction or in the momentum (p) direction of the phase-space. Interestingly, the entanglement causes the proposed states to be sensitive in both x and p directions. This state offers a better sensitivity compared to the single partite compass state in Zurek Nature (London) 412 712 (2001) in carrying out precision measurements. It is also argued that such states are easy to create and are better suited for carrying out precision measurements.