Quantum limits on phase-shift detection using multimode interferometers
  Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work, the limits are found to be independent of the number of interfering modes. However, the reported bounds are consistent with the Heisenberg limit. A short discussion on the concept of well-defined relative phase is also included. 
Jonas Soderholm, Gunnar Bjork, Bjorn Hessmo, and Shuichiro Inoue