Gaussian systems for quantum-enhanced multiple phase estimation

Christos N. Gagatsos, Dominic Branford, Animesh Datta

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cramér-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We prove that this bound can be saturated. In spite of the Gaussian nature of the problem, the calculation of non-Gaussian integrals is required, which we accomplish analytically. We find our simultaneous strategy to yield no more than a factor-of-2 improvement in total precision, possibly because of a fundamental performance limitation of Gaussian states. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.

Original languageEnglish (US)
Article number042342
JournalPhysical Review A
Issue number4
StatePublished - Oct 28 2016
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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