Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.Quantum entanglement offers the possibility of making measurements beyond the classical limit, however some issues still need to be overcome before it can be applied in realistic lossy systems. Recent work has used the quantum Fisher information (QFI) to show that entangled coherent states (ECSs) may be useful for this purpose as they combine sub-classical phase precision capabilities with robustness (Joo et al., 2011). However, to date no effective scheme for measuring a phase in lossy systems using an ECS has been devised. Here we present a scheme that does just this. We show how one could measure a phase to a precision significantly better than that attainable by both unentangled "classical" states and highly-entangled NOON states over a wide range of different losses. This brings quantum metrology closer to being a realistic and practical technology.

arXiv:1401.3969Jan 16, 20140 citations

Optical Phase Measurement Using Entangled Photons

Ryo Okamato, Shigeki Takeuchi

光学Oct 10, 20130 citations

Phase Tracking and Correction for Quantum Measurements of Coherent States

M. T. DiMario, Elohim Becerra

Bulletin of the American Physical SocietyMay 30, 20180 citations

Loss-induced limits to phase measurement precision with maximally entangled states

Mark A. Rubin, Sumanth Kaushik

The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values $L$ of the loss, phase measurement precision degrades with increasing number $N$ of entangled photons for $N$ sufficiently large. For $L$ above a critical value of approximately 0.785, phase measurement precision degrades with increasing $N$ for all values of $N$ . For $L$ near zero, phase measurement precision improves with increasing $N$ down to a limiting precision of approximately $1.018L\phantom{\rule{0.3em}{0ex}}\text{radians}$ , attained at $N$ approximately equal to $2.218∕L$ , and degrades as $N$ increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons ${N}_{T}$ is also examined. For $L$ above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing $N$ , the number of entangled photons employed in a single measurement, for all values of $N$ . For $L$ near zero this ratio is optimized by using approximately $N=1.279∕L$ entangled photons in each measurement, yielding a precision of approximately $1.340\sqrt{L∕{N}_{T}}\phantom{\rule{0.3em}{0ex}}\text{radians}$ .The presence of loss limits the precision of an approach to phase measurement using maximally entangled states, also referred to as NOON states. A calculation using a simple beam-splitter model of loss shows that, for all nonzero values $L$ of the loss, phase measurement precision degrades with increasing number $N$ of entangled photons for $N$ sufficiently large. For $L$ above a critical value of approximately 0.785, phase measurement precision degrades with increasing $N$ for all values of $N$. For $L$ near zero, phase measurement precision improves with increasing $N$ down to a limiting precision of approximately $1.018L\phantom{\rule{0.3em}{0ex}}\text{radians}$, attained at $N$ approximately equal to $2.218∕L$, and degrades as $N$ increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons ${N}_{T}$ is also examined. For $L$ above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing $N$, the number of entangled photons employed in a single measurement, for all values of $N$. For $L$ near zero this ratio is optimized by using approximately $N=1.279∕L$ entangled photons in each measurement, yielding a precision of approximately $1.340\sqrt{L∕{N}_{T}}\phantom{\rule{0.3em}{0ex}}\text{radians}$.

arXiv:quant-ph/0612080Physical Review AMay 7, 2007100 citations

Effectiveness of entangled coherent state in quantum metrology

Osamu Hirota, Kentaro Kato, Dan Murakami

This Letter verifies the potential of several classes of entangled coherent state in well known quantum metrology which includes detection of classical external force, and shows that there is a class of entangled coherent state for the external force detection system without the quantum limit in the detection of the light. In the case of the precision measurement of continuos parameter like phase measurement, the entangled coherent state with perfect entanglement does not provide remarkable benefit, but we provide a concrete example that certain class of entangled coherent state gives a remarkable sensitive detection scheme in the discrimination of digital signal affected by external force.This Letter verifies the potential of several classes of entangled coherent state in well known quantum metrology which includes detection of classical external force, and shows that there is a class of entangled coherent state for the external force detection system without the quantum limit in the detection of the light. In the case of the precision measurement of continuos parameter like phase measurement, the entangled coherent state with perfect entanglement does not provide remarkable benefit, but we provide a concrete example that certain class of entangled coherent state gives a remarkable sensitive detection scheme in the discrimination of digital signal affected by external force.

arXiv:1108.1517Aug 6, 20113 citations

Quantum disentanglement and phase measurements

Vladimír Bužek, Mark S. Hillery

Czechoslovak Journal of PhysicsSep 1, 19958 citations

L

of the loss, phase measurement precision degrades with increasing number

N

of entangled photons for

N

sufficiently large. For

L

above a critical value of approximately 0.785, phase measurement precision degrades with increasing

N

for all values of

N

. For

L

near zero, phase measurement precision improves with increasing

N

down to a limiting precision of approximately

1.018L\phantom{\rule{0.3em}{0ex}}\text{radians}

, attained at

N

approximately equal to

2.218∕L

, and degrades as

N

increases beyond this value. Phase measurement precision with multiple measurements and a fixed total number of photons

{N}_{T}

is also examined. For

L

above a critical value of approximately 0.586, the ratio of phase measurement precision attainable with NOON states to that attainable by conventional methods using unentangled coherent states degrades with increasing

N

, the number of entangled photons employed in a single measurement, for all values of

N

. For

L

near zero this ratio is optimized by using approximately

N=1.279∕L

entangled photons in each measurement, yielding a precision of approximately

1.340\sqrt{L∕{N}_{T}}\phantom{\rule{0.3em}{0ex}}\text{radians}