PERSPECTIVES
Quantum sensors
Among these, N00N states represent a particularly interesting example [ 4 ]. A N00N state corresponds to a quantum superposition of the form | N, 0 〉 + | 0, N 〉, where N particles( typically photons) are simultaneously in one or the other of two possible modes. The metrological interest of these states lies in their increased sensitivity to perturbations: a N00N state accumulates a phase N times faster than a classical state containing the same number of particles.
To illustrate this phenomenon, let us consider an entangled two-photon state | 2,0 〉 + | 0,2 〉 passing through a medium inducing a phase shift ϕ. While a classical two-photon state would acquire a global phase of 2Δϕ, the entangled state develops a phase of 4Δϕ, thus doubling the sensitivity of the measurement [ 5 ]. More generally, for an incident N00N state, the probability of finding the state | N, 0 〉 + exp( iNϕ)| 0, N 〉 is given by q( ϕ)= cos 2( Nϕ / 2). The error on the phase is then obtained by Δϕ = Δq /( ∂q / ∂ϕ)= 1 / N, the Heisenberg limit. This amplification of sensitivity constitutes the very signature of the quantum advantage in metrology.
PERSPECTIVES: CIRCUIT QUANTUM ELECTRODYNAMICS A particularly promising platform for the development of advanced quantum sensors is circuit quantum electrodynamics( cQED) [ 6 ]. This approach, which transposes the concepts of traditional quantum electrodynamics to superconducting circuits, allows for extraordinarily strong and controllable light-matter interactions. In these systems, superconducting qubits play the role of artificial atoms, while superconducting resonators replace optical cavities. The decisive advantage of this architecture lies in the extreme confinement of electromagnetic fields, leading to couplings several orders of magnitude greater than in conventional optical systems.
These strong interactions facilitate the preparation and
Figure 2. Phase-space diagram depicting the fluctuations, in photon number Δn and phase Δϕ, of coherent and squeezed states. While the coherent state has equal fluctuations in intensity and phase, the squeezed state can present decreased phase fluctuations at the expense of increased intensity fluctuations.
manipulation of non-classical quantum states, including squeezed states, large-photon-number Fock states, and even more complex states such as Gottesman-Kitaev- Preskill( GKP) states [ 7 ]. This ability to generate advanced quantum resources paves the way for a new generation of quantum sensors capable of operating at the fundamental Heisenberg limit. Recent work has demonstrated the use of displaced cat states, more robust than squeezed states or Fock states, with a sensitivity for phase and amplitude estimation very close to the Heisenberg limit [ 8 ]. Looking forward, GKP states are extremely promising in the context of quantum sensors as they are inherently resilient to photon loss. Furthermore, these states have been at the centre of important effort in quantum computing for their application in quantum error correction and protocols have already been successfully implemented experimentally. For quantum sensing, quantum error correction opens an interesting avenue as it would allow for maintaining complex quantum states that can approach the Heisenberg limit.
THE PRACTICAL DILEMMA: COMPLEX QUANTUM STATES VERSUS MULTIPLICATION OF CLASSICAL SENSORS Examining only the fundamental limits of quantum metrology seems to suggest that the use of quantum sensors constitutes the best way to improve sensitivity. However, the fundamental question faced by experimenters is that of the compromise between complexity and the real cost-benefit of advanced quantum approaches. On one hand, theory clearly demonstrates that a sensor using N resources in an optimal quantum state can achieve a precision proportional to 1 / N, surpassing the classical limit of 1 / √N. On the other hand, this theoretical improvement must be weighted by the considerable technical challenges associated with the preparation and maintenance of these quantum states, which are often extremely fragile. The N00N state is a perfect example: although it does indeed allow reaching the Heisenberg limit, this type of state is particularly sensitive to losses, making its practical use very difficult. In general, the production of large non-classical states requires sophisticated experimental setups( indistinguishable photon sources, low-loss optical elements, cryogenic environments) and generally suffers from a success probability that decreases exponentially with N. In parallel, a classical approach simply consisting of multiplying the number of independent sensors by a factor of N 2 would effectively achieve the same metrological precision as an optimal quantum sensor using N resources. This brute force strategy has the advantage of being technically simpler to implement and of increased robustness to noise. In many current practical cases, the distributed classical approach remains competitive, even superior, due to its technological maturity. However, in contexts where resources are inherently limited( spatial, energy, or material
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