Quantum sensors PERSPECTIVES what distinguishes quantum sensors from their classical counterparts is not so much their size or microscopic nature, but rather the exploitation of fundamental principles of quantum mechanics in the measurement process itself.
QUANTUM ADVANTAGES IN METROLOGY Quantum sensors do not merely exploit the properties of microscopic systems; they take advantage of the very principles of quantum mechanics to achieve superior performance. Several fundamental advantages can be identified [ 1 ]:
• The quantization of energy levels offers an absolute reference for measurements, unlike classical systems that often require external calibration. Although not a sensor in the strict sense of the term, atomic clocks exploit the transition frequency between two energy levels of an atom, thus providing a time reference of remarkable stability. This is actually a quantum technology that we use daily since it is an integral part of the satellite positioning system.
• Quantum superposition allows for simultaneously exploring multiple configurations of the system. This superposition enables the implementation of quantum measurement algorithms, such as the quantum phase algorithm, which offer algorithmic advantages over classical approaches.
• Quantum entanglement allows for non-classical correlations between different parts of the measurement system, enabling the surpassing of precision limits accessible to classical strategies. This approach notably allows for surpassing the standard quantum limit.
FUNDAMENTAL LIMITS OF QUANTUM METROLOGY From a formal point of view, the precision of estimation of a parameter ϕ is bounded by the quantum Cramér-Rao inequality [ 2 ] by Δϕ ≥ 1 / √( n FQ), where n is the number of independent measurements and FQ is the quantum Fisher information, which quantifies the maximum sensitivity achievable for a given quantum state. Due to the additivity of quantum Fisher information, an important fundamental limit follows directly from this inequality: the standard quantum limit( SQL) with a dependence on 1 / √n. This limit, known as shot noise in quantum optics, assumes nothing more than classical statistical correlations between different measurements. It therefore does not allow for fully exploiting the quantum nature of the system and probes. An obvious strategy to exceed this limit is therefore to use quantum effects such as entanglement to introduce correlations. Nevertheless, quantum mechanics still sets ultimate precision limits through Heisenberg-type uncertainty relations, which are sometimes referred to as Heisenberg bounds with a dependence on 1 / n.
An emblematic example of the application of these concepts is the Advanced LIGO gravitational interferometer, designed for the detection of gravitational waves. In its initial configuration, this instrument operated at the standard quantum limit. The use of squeezed states of light allowed for redistributing the quantum noise between different complementary observables, thus reducing the noise in the quadrature of interest and allowing for crossing the SQL barrier over a wide frequency range [ 3 ].
ADVANCED QUANTUM STATES FOR METROLOGY While the coherent state-- considered as the most classical-like quantum state-- present equal fluctuations for phase and intensity, squeezed states on the other hand can have much smaller fluctuation for one of the quadrature to the expense of the other( see Fig. 2). This reduction of the fluctuation is essential to overcome the SQL as it allows to greatly reduce the uncertainty for a well-chosen observable. Yet, while quantum squeezing allows for exceeding the SQL, other more sophisticated quantum states are better suited to approach the ultimate Heisenberg limit.
Figure 1. Transition energies for the first 4 levels as a function of the charge offset n g, normalized to the 0 → 1 transition n g = 0( E 01). The left panel illustrates the case when the charging and Josephson energies are equal, and the right panel illustrates the case when the Josephson energy is 50 times larger than the charging energy( transmon regime).
Finally, the discrete nature of quantum interactions( for example, the absorption or emission of individual photons) allows in some cases ultimate sensitivity to extremely weak signals, up to the detection of single events.
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