Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation.Finding reliable and effective methods for assessing its presence is then highly desirable.Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis.Here, we experimentally measure a type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way.Our experiment uses a single interferometric setup to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests.Aside from coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness.Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.
Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation.Finding reliable and effective methods for assessing its presence is then highly desirable.Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis.Here, we experimentally measure a type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way.Our experiment uses a single interferometric setup to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests.Aside from coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness.Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.
Suppose we have N quantum systems in unknown states $\left|{\ensuremath{\psi}}_{i}\right\ensuremath{\rangle}$, but we know the value of some pairwise overlaps ${\left|\ensuremath{\langle}{\ensuremath{\psi}}_{k}|{\ensuremath{\psi}}_{l}\ensuremath{\rangle}\right|}^{2}$. What can we say about the values of the unknown overlaps? We provide a complete answer to this problem for three pure states and two given overlaps and a way to obtain bounds for the general case. We discuss how the answer contrasts from that of a classical model featuring only coherence-free, diagonal states, and we describe three applications: basis-independent coherence witnesses, dimension witnesses, and characterization of multiphoton indistinguishability.
Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. In the standard formulation, a quantum state is said to have "imaginarity" if the associated density matrix is not real-valued in a given, fixed basis. If instead we consider a set of states, it is possible to devise tests that guarantee imaginarity of some state in the set, independently of the basis chosen. Here we propose such basis-independent witnesses for imaginarity that rely on measurements of unitary-invariant properties of sets of states. For three pure states, we completely characterize the invariant values attainable by quantum theory, and give a partial characterization for four pure states. We show that simple pairwise overlap measurements suffice to witness imaginarity of sets of four states, but not for sets of three. Our witnesses are experimentally friendly, opening up a new path for measuring and using imaginarity as a resource.
Multiphoton indistinguishability is a key resource for photonic quantum technologies, yet its characterization typically relies on resource-intensive methods. In this work, we develop two efficient and experimentally friendly protocols to estimate or bound the fidelity Find of an N-photon state to the closest perfectly indistinguishable state. The first protocol applies to sources preparing separable states, uses a single Fourier interferometer together with photon-number-resolving detection, and yields tight two-sided bounds on Find. The second protocol combines randomized implementations of linear-optical interferometers with photon counting, enabling direct estimation of Find for arbitrary N-photon states. Both protocols can certify Find=1−O(ε) using provably optimal O(1/ε) samples, in contrast to previous approaches which required prior assumptions on the model of partial distinguishability. Our methods, based on a multiphoton generalization of the Hong-Ou-Mandel test, bring the rigorous and operationally meaningful certification of multiphoton indistinguishability within reach of current photonic technologies.
Quantum coherence, present whenever a quantum system exists in a superposition of multiple classically distinct states, marks one of the fundamental departures from classical physics.Quantum coherence has recently been investigated rigorously within a resource-theoretic formalism.However, the finer-grained notion of multilevel coherence, which explicitly takes into account the number of superposed classical states, has remained relatively unexplored.A comprehensive analysis of multilevel coherence, which acts as the singleparty analogue to multipartite entanglement, is essential for understanding natural quantum processes as well as for gauging the performance of quantum technologies.Here, we develop the theoretical and experimental groundwork for characterizing and quantifying multilevel coherence.We prove that nontrivial levels of purity are required for multilevel coherence, as there is a ball of states around the maximally mixed state that do not exhibit multilevel coherence in any basis.We provide a simple, necessary, and sufficient analytical criterion to verify the presence of multilevel coherence, which leads to a complete classification of multilevel coherence for three-level systems.We present the robustness of multilevel coherence, a bona fide quantifier, which we show to be numerically computable via semidefinite programming and experimentally accessible via multilevel coherence witnesses, which we introduce and characterize.We further verify and lower bound the robustness of multilevel coherence by performing a semi-device-independent phase discrimination task, which is implemented experimentally with four-level quantum probes in a photonic setup.Our results contribute to understanding the operational relevance of genuine multilevel coherence, also by demonstrating the key role it plays in enhanced phase discrimination-a primitive for quantum communication and metrology-and suggest new ways to reliably and effectively test the quantum behavior of physical systems.
Bosonic interference is a fundamental physical phenomenon, and it is believed to lie at the heart of quantum computational advantage. It is thus necessary to develop practical tools to witness its presence, both for a reliable assessment of a quantum source and for fundamental investigations. Here we describe how linear interferometers can be used to unambiguously witness genuine n-boson indistinguishability. The amount of violation of the proposed witnesses bounds the degree of multiboson indistinguishability, for which we also provide a novel intuitive model using set theory. We experimentally implement this test to bound the degree of three-photon indistinguishability in states we prepare using parametric down-conversion. Our approach results in a convenient tool for practical photonic applications, and may inspire further fundamental advances based on the operational framework we adopt.
Certification is important to guarantee the correct functioning of quantum devices. A key certification task is verifying that a device has produced a desired output state. In this work, we study this task in the context of photonic platforms, where single photons are propagated through linear optical interferometers to create large, entangled resource states for metrology, communication, quantum advantage demonstrations and for so-called linear optical quantum computing (LOQC). This setting derives its computational power from the indistinguishability of the photons, i.e., their relative overlap. Therefore, standard fidelity witnesses developed for distinguishable particles (including qubits) do not apply directly, because they merely certify the closeness to some fixed target state. We introduce a measure of fidelity suitable for this setting and show several different ways to witness it, based on earlier proposals for measuring genuine multi-photon indistinguishability. We argue that a witness based upon the discrete Fourier transform is an optimal choice. We experimentally implement this witness and certify the fidelity of several multi-photon states.