Interferometric Mass Spectrometry

Accelerator mass spectrometry (AMS) is a widely used technique with multiple applications, including geology, molecular biology, and archeology. In order to achieve a high dynamic range, AMS requires tandem accelerators and large magnets, which thus confines it to big laboratories. Here we propose interferometric mass spectrometry (Interf-MS), a novel method of mass separation which uses quantum interference. Interf-MS employs the wave-like properties of the samples and as such is complementary to AMS, in which samples are particle-like. This complementarity has two significant consequences: (i) in Interf-MS separation is performed according to the absolute mass m, and not to the mass-to-charge ratio m/q, as in AMS; (ii) in Interf-MS the samples are in the low-velocity regime, in contrast to the high-velocity regime used in AMS. Potential applications of Interf-MS are compact devices for mobile applications, sensitive molecules that break at the acceleration stage and neutral samples which are difficult to ionize.

Cyclic permutations for qudits in d dimensions

One of the main challenges in quantum technologies is the ability to control individual quantum systems. This task becomes increasingly difficult as the dimension of the system grows. Here we propose a general setup for cyclic permutations Xd in d dimensions, a major primitive for constructing arbitrary qudit gates. Using orbital angular momentum states as a qudit, the simplest implementation of the Xd gate in d dimensions requires a single quantum sorter Sd and two spiral phase plates. We then extend this construction to a generalised Xd(p) gate to perform a cyclic permutation of a set of d, equally spaced values {|[Formula: see text]〉, |[Formula: see text] + p〉, …, |[Formula: see text] + (d - 1)p〉} [Formula: see text] {|[Formula: see text] + p〉, |[Formula: see text] + 2p〉, …, |[Formula: see text]〉}. We find compact implementations for the generalised Xd(p) gate in both Michelson (one sorter Sd, two spiral phase plates) and Mach-Zehnder configurations (two sorters Sd, two spiral phase plates). Remarkably, the number of spiral phase plates is independent of the qudit dimension d. Our architecture for Xd and generalised Xd(p) gate will enable complex quantum algorithms for qudits, for example quantum protocols using photonic OAM states.

Sorting quantum systems efficiently

Measuring the state of a quantum system is a fundamental process in quantum mechanics and plays an essential role in quantum information and quantum technologies. One method to measure a quantum observable is to sort the system in different spatial modes according to the measured value, followed by single-particle detectors on each mode. Examples of quantum sorters are polarizing beam-splitters (PBS) – which direct photons according to their polarization – and Stern-Gerlach devices. Here we propose a general scheme to sort a quantum system according to the value of any d-dimensional degree of freedom, such as spin, orbital angular momentum (OAM), wavelength etc. Our scheme is universal, works at the single-particle level and has a theoretical efficiency of 100%. As an application we design an efficient OAM sorter consisting of a single multi-path interferometer which is suitable for a photonic chip implementation.

Determinism, independence, and objectivity are incompatible

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we study the mutual compatibility of apparently reasonable classical assumptions. We analyze a version of the delayed-choice experiment which ostensibly combines determinism, independence of hidden variables on the conducted experiments, and wave-particle objectivity (the assertion that quantum systems are, at any moment, either particles or waves, but not both). These three ideas are incompatible with any theory, not only with quantum mechanics.

Is wave-particle objectivity compatible with determinism and locality?

Wave–particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies, we can test experimentally the predictions of quantum theory versus HV theories and put strong restrictions on their key assumptions. Here, we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions.

Arguably, the most counterintuitive aspects of quantum mechanics are indeterminacy of physical quantities and ambiguity of wave/particle behaviour prior to measurement. Terno et al. propose an experiment to test hidden-variable models that aim to restore objectivity and determinism in quantum theory.

Proposal for a quantum delayed-choice experiment

Gedanken experiments help to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behavior of the controlling devices in such experiments. We propose a framework to analyze quantum-controlled experiments and illustrate it by discussing a quantum version of Wheeler's delayed-choice experiment. Using a quantum control has several consequences. First, it enables us to measure complementary phenomena with a single experimental setup, pointing to a redefinition of complementarity principle. Second, it allows us to prove there are no consistent hidden-variable theories having "particle" and "wave" as realistic properties. Finally, it shows that a photon can have a morphing behavior between particle and wave. The framework can be extended to other experiments (e.g., Bell inequality).