Uesli Alushi

Quantum phenomena offer the possibility of measuring physical quantities with precision beyond classical limits. However, current progress is constrained by scalability, environmental noise, and challenges in practical integration. This highlights the necessity for novel approaches. An emerging paradigm in this direction is , which harnesses the enhanced susceptibility and nonclassical correlations that naturally occur near quantum phase transitions as resources for quantum-enhanced precision. This tutorial provides a pedagogical introduction to key concepts and a detailed overview of prominent quantum sensing strategies that exploit critical phenomena in metrology. Through examples of increasing complexity, the reader is guided through various critical quantum sensing protocols applied to different critical systems. Special emphasis is placed on the optimal scaling of estimation precision with respect to fundamental resources. Finally, we discuss how critical quantum metrology extends from idealized models to realistic open-system, dissipative regimes, and strongly correlated fermionic systems, outlining both the challenges and opportunities for future quantum technologies.

Quantum teleportation uses a shared entangled resource, local operations, and a digitally error-corrected classical channel to transfer quantum states between distant parties. We introduce a hybrid teleportation-direct transmission protocol for state transfer that still exploits entanglement, but replaces classical communication and digital error correction with an feedforward through a noisy quantum channel. We show that quantum teleportation outperforms this protocol if the communication channel reduces the entanglement of all bipartite states having the same amount of entanglement as the resource; otherwise, the hybrid protocol is optimal. We apply our result to the state transfer of a uniformly distributed coherent-states codebook, highlighting experimentally relevant scenarios where our protocol is most effective. Our findings are directly relevant to both optical and superconducting microwave channels, where analog feedforward techniques have been recently implemented.

Critical systems represent a valuable resource in quantum sensing and metrology. Critical quantum sensing (CQS) protocols can be realized using finite-component phase transitions, where criticality arises from the rescaling of system parameters rather than the thermodynamic limit. Here, we show that a collective quantum advantage can be achieved in a multipartite CQS protocol using a chain of parametrically coupled critical resonators in the weak-nonlinearity limit. We derive analytical solutions for the low-energy spectrum of this unconventional quantum many-body system, which is composed of locally critical elements. We then assess the scaling of the quantum Fisher information with respect to fundamental resources. We demonstrate that the coupled chain outperforms an equivalent ensemble of independent critical sensors, achieving quadratic scaling in the number of resonators. Finally, we show that even with finite Kerr nonlinearity or Markovian dissipation, the critical chain retains its advantage, making it relevant for implementing quantum sensors with current microwave superconducting technologies.

We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.

Quadratic light-matter interactions are nonlinear couplings such that quantum emitters interact with photonic or phononic modes exclusively via the exchange of excitation pairs. Implementable with atomic and solid-state systems, these couplings lead to a plethora of phenomena that have been characterized in the context of cavity QED, where quantum emitters interact with localized bosonic modes. Here, we explore quadratic interactions in a waveguide QED setting, where quantum emitters interact with propagating fields confined in a one-dimensional environment. We develop a general scattering theory under the Markov approximation and discuss paradigmatic examples for spontaneous emission and scattering of biphoton states. Our analytical and semianalytical results unveil fundamental differences with respect to conventional waveguide QED systems, such as the spontaneous emission frequency-entangled photon pairs or the full transparency of the emitter to single-photon inputs. This unlocks new opportunities in quantum information processing with propagating photons. As a striking example, we show that a single quadratically coupled emitter can implement a two-photon logic gate with unit fidelity, circumventing a no-go theorem derived for conventional waveguide-QED interactions.