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arXiv:0708.1385 · Science

Beating the Standard Quantum Limit with Four-Entangled Photons

Tomohisa Nagata, Ryo Okamoto, Jeremy L. O’Brien, Keiji Sasaki, Shigeki Takeuchi

Published May 3, 2007• 805 citations
arXivHTMLPDF

Abstract

Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit-the limit attainable without entanglement. These results open the way for new high-precision measurement applications.

DOI
10.1126/science.1138007

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Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit-the limit attainable without entanglement. These results open the way for new high-precision measurement applications.
Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here, we present a theory of the phase sensitivity for the general case where the detection probability is given by an N photon interference fringe. We find that the phase sensitivity has a complicated dependence on both the intrinsic efficiency of detection η and the interference fringe visibility V . Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previously been assumed. We determine the parameter range where quantum enhanced sensitivity can be achieved. In order to illustrate these theoretical results, we perform a four-photon experiment with η=3/4 and V =82±6% (an extension of our previous work (Nagata et al 2007 Science 316 726)) and find a phase sensitivity 1.3 times greater than the standard quantum limit at a phase different to that which gives maximum slope of the interference fringe.
We propose and demonstrate experimentally a projection scheme to measure the quantum phase with a precision beating the standard quantum limit. The initial input state is a twin Fock state | N , N ⟩ proposed by Holland and Burnett ( Phys. Rev. Lett. , 71 (1993) 1355) but the phase information is extracted by a quantum state projection measurement. The phase precision is about 1.4/ N for large photon number N , which approaches the Heisenberg limit of 1/ N . Experimentally, we employ a four-photon state from type-II parametric down-conversion and achieve a phase uncertainty of 0.291±0.001 beating the standard quantum limit of for four photons.
With the rapid advancement of science and technology, phase measurement plays a crucial role in various fields such as optics, communication, and radar. Traditional phase measurement methods, relying on classical light sources, produce results following the central limit theorem, limiting measurement precision to the standard quantum limit. However, recent in-depth studies of quantum theory and quantum enhanced experimental techniques are breaking this barrier. The use of specially designed non-classical light sources for phase measurement not only provides the possibility of breaking through the limits of measurement precision but also meets the growing demand for high-precision measurements.This paper started from a statistical perspective, introduced key indicators for evaluating measurement precision, including the Cramér-Rao Boundary (CRB) and Fisher Information, and extends to experimental approaches beyond the standard quantum limit. Subsequently, by introducing quantum light sources such as squeezed states, entangled states, and methods like harmonic amplification to achieve amplifier the phase and optical detection, the paper provides a comprehensive review of recent research achievements in super-resolution phase measurement techniques. Finally, we select several technological categories with a promising engineering outlook, analyze the technical challenges limiting their maturity, and provide a prospective outlook.
Entangled photons can be used to make measurements with an accuracy beyond that possible with classical light. While most implementations of quantum metrology have used states made up of a single color of photons, we show that entangled states of two colors can show supersensitivity to optical phase and path length by using a photonic crystal fiber source of photon pairs inside an interferometer. This setup is relatively simple and robust to experimental imperfections. We demonstrate sensitivity beyond the standard quantum limit and show superresolved interference fringes using entangled states of two, four, and six photons.
Quantum-enhanced measurements use highly non-classical quantum states in order to enhance the precision of the measurement of classical quantities, like the length of an optical cavity. The major goal is to beat the standard quantum limit (SQL), i.e. a precision of order 1/N1/\sqrt{N}1/N​, where NNN is the number of quantum resources (e.g. the number of photons or atoms used), and to achieve a scaling 1/N1/N1/N, known as the Heisenberg limit. Doing so would have tremendous impact in many areas, but so far only three experiments have demonstrated a slight improvement over the SQL. The required quantum states are generally difficult to produce, and very prone to decoherence. Here we show that decoherence itself may be used as an extremely sensitive probe of system properties. This should allow for a new measurement principle with the potential to achieve the Heisenberg limit without the need to produce highly entangled states.
Quantum entanglement can help to increase the precision of optical phase measurements beyond the standard quantum limit (SQL) to the ultimate Heisenberg limit [1, 2]. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N + 1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SQL for two[3–5] and four[6–9] photons have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investigate the achievable phase sensitivity of the simple and efficient single interference fringe detection technique. We show that the maximally-entangled NOON[10] state does not achieve optimal phase sensitivity when N > 4, rather, the Holland-Burnett state[11] is optimal. We experimentally demonstrate this enhanced sensitivity using a single photon-counted fringe of the six-photon Holland-Burnett state. Specifically, our single-fringe six-photon measurement achieves a phase variance three times below the SQL.