Activation of indistinguishability-based quantum coherence for enhanced metrological applications with particle statistics imprint

Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.

A quantum system can reside in coherent superpositions of states, which have a role in the interpretation of quantum mechanics (1–4), lead to nonclassicality (5, 6), and imply the intrinsically probabilistic nature of predictions in the quantum realm (7, 8). Besides this fundamental role, quantum coherence is also at the basis of quantum algorithms (9–14) and, from a modern information-theoretic perspective, constitutes a paradigmatic basis-dependent quantum resource (15–17), providing a quantifiable advantage in certain quantum information protocols.For a single quantum particle, coherence manifests itself when the particle is found in a superposition of a reference basis, for instance, the computational basis of the Hilbert space. Formally, any quantum state whose density matrix contains nonzero diagonal elements when expressed in the reference basis is said to display quantum coherence (16). This is the definition of quantum coherence employed in our work. For multiparticle compound systems, the physics underlying the emergence of quantum coherence is richer and strictly connected to the nature of the particles, with fundamental differences for nonidentical and identical particles. A particularly intriguing observation is that the states of identical particle systems can manifest coherence even when no particle resides in superposition states, provided that the wave functions of the particles overlap (18–20). In general, a special contribution to quantum coherence arises thanks to the spatial indistinguishability of identical particles, which cannot exist for nonidentical (or distinguishable) particles (18). Recently, it has been found that the spatial indistinguishability of identical particles can be exploited for entanglement generation (21), applicable even for spacelike-separated quanta (22) and against preparation and dynamical noises (23–26). The presence of entanglement is a signature that the bipartite system as a whole carries coherence even when the individual particles do not, the amount of this coherence being dependent on the degree of indistinguishability. We name this specific contribution to quantumness of compound systems “indistinguishability-based coherence,” in contrast to the more familiar “single-particle superposition-based coherence.” Indistinguishability-based coherence qualifies in principle as an exploitable resource for quantum metrology (18). However, it requires sophisticated control techniques to be harnessed, especially in view of its nonlocal nature. Moreover, a crucial property of identical particles is the exchange statistics, while its experimental study requiring operating both bosons and fermions in the same setup is generally challenging.In the present work, we investigate the operational contribution of quantum coherence stemming from the spatial indistinguishability of identical particles. The main aim of our experiment is to prove that elementary states of two independent spatially indistinguishable particles can give rise to exploitable quantum coherence, with a measurable effect due to particle statistics. By utilizing our recently developed photonic architecture capable of tuning the indistinguishability of two uncorrelated photons (27), we observe the direct connection between the degree of indistinguishability and the amount of generated coherence and show that indistinguishability-based coherence can be concurrent with single-particle superposition-based coherence. In particular, we demonstrate its operational implications, namely, providing a quantifiable advantage in a phase discrimination task (28, 29), as depicted in Fig. 1. Furthermore, we design a setup capable of testing the impact of particle statistics in coherence production and phase discrimination for both bosons and fermions; this is accomplished by compensating for the exchange phase during state preparation, simulating fermionic states with photons, which leads to statistics-dependent efficiency of the quantum task.Open in a separate windowFig. 1.Illustration of the indistinguishability-activated phase discrimination task. A resource state ρin that contains coherence in a computational basis is generated from spatial indistinguishability. The state then enters a black box which implements a phase unitary U^k=eiG^ϕk,k∈{1,…,n} on ρin. The goal is to determine the ϕk actually applied through the output state ρout: indistinguishability-based coherence provides an operational advantage in this task.