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Physical Review A

Quantum phase amplification

Giacomo Mauro D’Ariano, Chiara Macchiavello, Nicoletta Sterpi, Horace P. Yuen

Published Dec 1, 1996• 24 citations
Publisher

Abstract

A scheme for amplifying phase shifts is presented, based on ideal photon number deamplification. For high-sensitivity measurements phase amplification sizeably reduces the bit-error rate and enhances the mutual information retrieved from the measurement. Phase-coherent states preserve their coherence under amplification, and achieve the best amplifier performance. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.4712

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A scheme for amplifying phase shifts is presented, based on ideal photon number deamplification. For high-sensitivity measurements phase amplification sizeably reduces the bit-error rate and enhances the mutual information retrieved from the measurement. Phase-coherent states preserve their coherence under amplification, and achieve the best amplifier performance. \textcopyright{} 1996 The American Physical Society.
Quantum interferometers offer phase measurement capabilities that surpass the standard quantum limit (SQL), with phase sensitivity and quantum enhancement factor serving as key performance metrics. However, practical implementations face severe degradation of both metrics due to unavoidable losses, representing the foremost challenge in advancing quantum interferometry toward real-world applications. To address this challenge, we propose a coherent-amplifier-empowered quantum interferometer. The coherent amplifier dramatically suppresses the decay of both sensitivity and quantum enhancement under high-loss conditions, maintaining phase sensitivity beyond the original SQL even for losses exceeding 90%. Using an injected 4.2 dB squeezed-vacuum state in experimental demonstration, our scheme reduces the quantum enhancement degradation under 90% loss from 3.7 dB in a conventional quantum interferometer (CQI) to only 1.5 dB. More importantly, the phase sensitivity degradation under the same loss is limited to 4.0 dB, markedly outperforming the 11.2 dB degradation observed in a CQI. This improvement is enabled by the coherent amplifier's phase-sensitive photon amplification and its protection of the quantum state. This breakthrough in amplifier-empowered quantum interferometry overcomes the critical barrier to practical deployment, enabling robust quantum-enhanced measurements in lossy environments.
Fundamental laws of quantum mechanics impose that arbitrary quantum states cannot be perfectly cloned or amplified without introducing some unavoidable noise in the process. The quantum noise intrinsic to the functioning of a linear phase-insensitive amplifier can however be avoided by relaxing the requirement of a deterministic operation. Non-deterministic noiseless linear amplifiers that do not violate any fundamental quantum law are therefore possible and here we present the first experimental realization of a scheme that allows noiseless amplification of coherent states at the best level of effective gain and final state fidelity ever reached. This scheme, based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, may become a useful tool for quantum communications and metrology, by enhancing the discrimination between partially overlapping quantum states or by recovering the information transmitted over lossy channels.
We study statistical properties of quantum superposition states (Schr\"odinger-cat states) amplified by phase-sensitive (squeezed) amplifiers. We show that the phase-sensitive amplifier with a properly chosen phase can preserve quantum coherences and nonclassical behavior of the Schr\"odinger-cat-state input even for a gain factor G larger than 2. In particular, we show that for an even coherent state (CS) phase-sensitive amplifiers can preserve squeezing for G>2 but simultaneously in the process of amplification the noise added by the amplifier leads to a rapid increase of fluctuations in the photon number. Because of the finite maximum degree of squeezing obtainable for the even CS the maximum gain factor Gm{\mathit{G}}_{\mathit{m}}Gm​ for which squeezing can still be observed in the output state is finite. The phase-sensitive amplifier with a properly chosen phase can also reduce fluctuations in the photon number of the initial even CS. Nevertheless, one cannot amplify the initial even CS with super-Poissonian photon statistics into the state with sub-Poissonian photon statistics.
Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.