We uncover a form of quantum contextuality that connects maximal contextuality to boson indistinguihability in a similar way maximal nonlocality with respect to the Clauser-Horne-Shimony-Holt Bell inequality is connected to maximal entanglement. Unlike previous forms of photonic contextuality, this form cannot be simulated with classical light, as it relies on indistinguishability and higher-order interference. Ideal measurements on the bosonic system can be performed by means of dispersive coupling with an ancillary qubit. This allows us delaying at will the ending of each measurement and targeting high-dimensional contextual correlations, which are features which cannot be achieved with existing platforms.
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This allows us to consider a new ontology in order to study properties of quantum systems.
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable y…
Bosonic bunching occurs within quantum physics and can be mimicked classically by noncontextual hidden-variable models, which excludes this phenomenon as a means to prove stronger-than-quantum contextuality.
We show that under certain assumptions one can derive a variant of Specker's non-contextual inequality for a system of three indistinguishable bosonic particles. The inequality states that the sum of probabilities of three pairwise exclusive events is bounded by one. This inequality cannot be violated using standard quantum mechanical projectors. On the other hand, due to bosonic properties this bound is violated up to 3/2. We also argue that the violation of this inequality can be considered as a test of bosonic nature.
It has been recently conjectured that the state-independency of quantum contextuality may be lost when the indistinguishability of identical particles is taken into account. Here, we show that quantum state-independent contextuality exists for any system of more than one identical bosonic qudits, and for most systems of fermionic qudits. The only exception is the case of d fermionic qudits, since there the dimension of the antisymmetric subspace is 1, which is insufficient for contextuality. For all the other cases, either the symmetry precludes the existence of physical states, or we provide …
In a recent paper, Kurzynski et al. present a gedanken experiment that, they claim, violates the Klyachko-Can-Binicioglu-Shumovsky (KCBS) noncontextuality (NC) inequality beyond its maximum quantum value, and a similar experiment that, they claim, violates Specker's NC inequality, which is not violated by quantum mechanics. We argue that these claims are baseless, since these experiments do not satisfy the conditions required for any observation of contextuality through the experimental violation of a NC inequality. Moreover, the physical events in the experiments of Kurzynski et al. do not ha…
The dynamics of bosons in generic multimode systems, such as Bose-Hubbard models, is not only determined by interactions among the particles, but also by their mutual indistinguishability manifested in many-particle interference. We introduce a measure of indistinguishability for Fock states of bosons whose mutual distinguishability is controlled by an internal degree of freedom. We demonstrate how this measure emerges both in the non-interacting and interacting evolution of observables. In particular, we find an unambiguous relationship between our measure and the variance of single-particle …
In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.
Most of the paradoxical, for the classical intuition, features of quantum theory were formulated for situations which involve a fixed number of particles. While one can now find a formulation of Bell's theorem for quantum fields, a Kochen-Specker-type reasoning is usually formulated for just one particle, or like in the case of Peres-Mermin square for two. A question emerges. Is it possible to formulate a contextuality proof for situation in which the numbers of particles are fundamentally undefined? We address this problem for bosonic fields. We introduce a representation of the $\mathfrak{su…
The non-classicality of single quantum systems can be formalised using the notion of contextuality. But can contextuality be convincingly demonstrated in an experiment, without reference to the quantum formalism? The operational approach to contextuality due to Spekkens requires finding operationally equivalent preparation procedures. Previously these have been obtained by demanding indistinguishability under a set of measurements taken to be tomographically complete. In the language of generalised probability theories, this requires the ability to explore all the dimensions of the system's st…
Quantum contextuality in systems of identical bosonic particles is explicitly exhibited via the maximum violation of a suitable inequality of Clauser-Horne-Shimony-Holt type. Unlike the approaches considered so far, which make use of single-particle observables, our analysis involves collective observables constructed using multi-boson operators. An exemplifying scheme to test this violation with a quantum optical setup is also discussed.
The link of two concepts, indistinguishability and entanglement, with the energy-time uncertainty principle is demonstrated in a system composed of two strongly coupled bosonic modes. Working in the limit of a short interaction time, we find that the inclusion of the antiresonant terms to the coupling Hamiltonian leads the system to relax to a state which is not the ground state of the system. This effect occurs passively by just presence of the antiresonant terms and is explained in terms of the time-energy uncertainty principle for the simple reason that at a very short interaction time, the…
We show how to characterize the indistinguishability of up to four identical, bosonic or fermionic particles, which are rendered partially distinguishable through their internal degrees of freedom prepared in mixed states. This is accomplished via their counting statistics when subjected to a highly symmetric unitary acting upon their external (i.e., dynamical) degrees of freedom. For pure internal states, we further extract information on the particles' collective phases, which ultimately allows for an experimental reconstruction of the full many-particle density operator up to complex conjug…
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 multi-boson indistinguishability, for which we also provide a novel intuitive model using set theory. We experimenta…
We explore the multiparticle transition probabilities in Gaussian unitaries effected by a two-mode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the transition probabilities can be characterized by remarkably simple, yet unsuspected recurrence equations involving a linear combination of probabilities. The recurrence exhibits an interferometric suppression term - a negative probability - which generalizes the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons impinging on a beam splitter of rational transmittance. Unexpecte…
Interference at a beam splitter reveals both classical and quantum properties of electromagnetic radiation. When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou, and Mandel (HOM) [1]. Here, we present the observation of the HOM effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a co…
Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or anti-bunching. In presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al. recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multi-port beam splitters. Here we study the case in which $2^q$ particles (eith…
Modelling quantum measurement dynamics: from decoherence to redundancy with site-hopping indistinguishable particles
Institute for Theoretical Physics, TU Wien（维也纳工业大学理论物理研究所）；Atominstitut, TU Wien（维也纳工业大学原子研究所）；Vienna Center for Quantum Science and Technology (VCQ), TU Wien（维也纳大学量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
