Quantum Smoothing Measurement is Two Times Better than standard quantum limit.

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Researchers at LSU have invented an optical sensor that surpasses a quantum limit to sensitivity previously believed to be unbeatable. The breakthrough has a broad array of applications, from gravity wave observatories seeking to observe distant and bizarre astrophysical phenomena, to optical gyroscopes used in commercial navigation. This work exploits quantum properties of light to design of the most sensitive optical interferometer ever devised.

Physics Review Letters – Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

The precision of any measurement is fundamentally limited by the standard quantum limit. Often there are classical quantities related to the dynamical evolution of a quantum system one would like to measure, a process known as quantum parameter estimation. This kind of estimation is useful in delicate measurements ranging from gravitational wave detection to quantum computation. Recently, Tsang considered the case of quantum estimation for dynamical systems and proposed a method called quantum smoothing that combines past observations with “future” measurements (that is, a signal is inferred from measurements both before and after a chosen point in time).

As reported in Physical Review Letters, Trevor Wheatley at the University of New South Wales in Canberra, Australia, and co-workers in Australia, Japan, and Canada now have experimentally tested these ideas by considering the problem of estimating the phase of a continuous optical field in the presence of classical noise. The authors use optical modulators to prepare a laser beam in a known state with a predetermined noise signature and then apply an adaptive measurement technique to estimate the optical phase. By including data obtained after time t with data collected before t along with Tsang’s theory, the researchers were able to estimate the phase at t with a mean-square error more than a factor of 2 smaller than the standard quantum limit.

Combining quantum smoothing with adaptive measurements gives the maximum improvement over the standard (perfect non-adaptive, filtering) quantum limit. The experimental improvement of a factor of 2.24 +/ 0.14 in the mean-square error compares well with the theoretical maximum (using phase diffused coherent states) of 2p2. These insights and techniques will be applicable to the even more interesting case of estimation using non-classical states, where the improvement can be arbitrarily large.

A version of the full article is in arxiv (5 pages)

Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation. We consider both adaptive and nonadaptive quantum smoothing, and show that both are better than their filtered counterparts. For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2√2 times smaller than nonadaptive filtering (the standard quantum limit). The experimentally measured improvement is 2.24±0.14.

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