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arXiv:2306.14666

Quantum squeezing cannot beat the standard quantum limit

Liam Paul McGuinness

Published Jun 26, 2023• 0 citations
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Abstract

Quantum entanglement between particles is expected to allow one to perform tasks that would otherwise be impossible. In quantum sensing and metrology, entanglement is often claimed to enable a measurement precision that cannot be attained with the same number of particles and time, forgoing entanglement. Two distinct approaches exist: creation of entangled states that either i) respond quicker to the signal, or ii) are associated with lower noise and uncertainty. The second class of states are generally called squeezed states. Here we show that if our definition of success is a precision that is impossible to achieve using the same resources but without entanglement then squeezed states cannot succeed. In doing so we show that a single non-separable squeezed state provides fundamentally no better precision, per unit time, than a single particle.

DOI
10.48550/arxiv.2306.14666

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Quantum entanglement between particles is expected to allow one to perform tasks that would otherwise be impossible. In quantum sensing and metrology, entanglement is often claimed to enable a measurement precision that cannot be attained with the same number of particles and time, forgoing entanglement. Two distinct approaches exist: creation of entangled states that either i) respond quicker to the signal, or ii) are associated with lower noise and uncertainty. The second class of states are generally called squeezed states. Here we show that if our definition of success is a precision that is impossible to achieve using the same resources but without entanglement then squeezed states cannot succeed. In doing so we show that a single non-separable squeezed state provides fundamentally no better precision, per unit time, than a single particle.
We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing , which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the DS states are more robust to decoherence and give better measurement precision under typical experimental noise.
It is widely accepted that quantum entanglement between otherwise independent sensors can yield a measurement precision beyond that achievable when the same resources are employed without entanglement \cite{Helstrom1969, Holevo1973a, Caves1980a, Caves1981, Wootters1981, Yurke1986, Wu1986, Xiao1987, Slusher1987, Shapiro1989, Wineland1992, Polzik1992, Kitagawa1993, Braunstein1994, Wineland1994, Sanders1995, Bollinger1996, Ou1997, Dowling1998,Soerensen1998, Brif1999, Childs2000, Fleischhauer2000, Meyer2001, Geremia2003, Giovannetti2004, Kok2004, Leibfried2004, Leibfried2005, Giovannetti2006, Nagata2007, Appel2009, Gross2010, Leroux2010, Zwierz2010,DemkowiczDobrzanski2012, Zwierz2012,Aasi2013,Pezze2018,Tse2019,Casacio2021}. Here we show that theoretical proofs of entanglement enhanced metrology are based on a misinterpretation of \emph{can't} theorems as \emph{can} theorems. In concert, we dissect claims of an experimental precision beyond the classical limits and detail where comparisons are misleading, incomplete or incorrect to show that the precision of optimised measurements which forgo entanglement has not been surpassed. In doing so, we highlight a significant discrepancy between experimentally reported uncertainties and the current predictions of quantum measurement theory. The discrepancy can be resolved by introducing a simple physical principle which demonstrates better agreement to empirical evidence. We thus provide viable avenues as to where standard interpretations of quantum mechanics should be modified in order to better predict measurement outcomes.
Precision measurement plays a vital role in metrology. To achieve the ultimate precision predicted by quantum theory, one can leverage quantum entanglement—correlations between particles of light or matter that cannot be explained in classical physics. The use of quantum entanglement in probing an object enhances measurement precision by a factor of √N beyond what is attainable with classical resources, where precision is typically limited by Poisson noise. Here, N represents the number of entangled particles. To date, most research efforts have focused on understanding and characterizing non-classical correlations between two particles. For instance, in 2022, optical clocks were synchronized using quantum entanglement, achieving frequency uncertainties of √2 lower than what is possible with non-entangled clocks. However, despite rapid advancements in single-particle sensing technologies, the generation and characterization of quantum correlation involving three or more particles remain an ongoing challenge. The absence of rigorous measurement standards for multi-particle entanglement, coupled with the lack of photon-number-resolving (PNR) detection capabilities, can lead to faulty measurements and reduced metrological accuracy and precision. It is therefore essential to establish robust methodologies and standards for the creation and validation of multi-particle entanglement to enable quantum-limited precision measurements. These developments will provide significant impacts in various fields, including optical astronomy, frequency standards, microscopy, and secure communication. The integration of entanglement-assisted sensors with PNR detection will enhance imaging resolution in applications such as astronomy and biological sample analysis. Additionally, standardized metrological frameworks for quantum entanglement and hardware evaluation will enhance the security level of quantum communication by mitigating vulnerabilities associated with inconsistencies arising from the use of dissimilar characterization methodologies. These fundamental research efforts will have far-reaching implications, not only improving the quality of quantum measurements but also guiding national metrology institutes in developing standardized quantum measurement protocols.
Quantum metrology exploits entangled states of particles to improve sensing precision beyond the limit achievable with uncorrelated particles. All previous methods required detection noise levels below this standard quantum limit to realize the benefits of the intrinsic sensitivity provided by these states. We experimentally demonstrate a widely applicable method for entanglement-enhanced measurements without low-noise detection. The method involves an intermediate quantum phase magnification step that eases implementation complexity. We used it to perform squeezed-state metrology 8 decibels below the standard quantum limit with a detection system that has a noise floor 10 decibels above the standard quantum limit.
We introduce a super-sensitive phase measurement technique that yields the Heisenberg limit without using either a squeezed state or a many-particle entangled state. Instead, we use a many-particle separable quantum state to probe the phase and we then retrieve the phase through single-particle interference. The particles that physically probe the phase are never detected. Our scheme involves no coincidence measurement or many-particle interference and yet exhibits phase super-resolution. We also analyze in detail how the loss of probing particles affects the measurement sensitivity and find that the loss results in the generation of many-particle entanglement and the reduction of measurement sensitivity. When the loss is maximum, the system produces a many-particle Greenberger-Horne-Zeilinger (GHZ) state, and the phase measurement becomes impossible due to very high phase uncertainty. In striking contrast to the super-sensitive phase measurement techniques that use entanglement involving two or more particles as a key resource, our method shows that having many-particle entanglement can be counterproductive in quantum metrology.