Dynamics-based certification of quantumness is an approach to witnessing the nonclassical character of some continuous-variable states, under the assumption that their dynamics is known. Contrary to other tests of nonclassicality for single systems, it does not require sequential measurements. This family of protocols was introduced for harmonic dynamics. In this work we discuss dynamics-based certification for one degree of freedom evolving under a generic time-independent Hamiltonian. We characterize the conditions under which such a certification is possible. Several examples are explicitly studied, some that are approximately harmonic in the limits of low energy (Kerr nonlinearities, the pendulum, and the Morse potential) and one that is not (the particle in an infinite well).
Dynamics-based certification of quantumness is an approach to witnessing the nonclassical character of some continuous-variable states, under the assumption that their dynamics is known. Contrary to other tests of nonclassicality for single systems, it does not require sequential measurements. This family of protocols was introduced for harmonic dynamics. In this work we discuss dynamics-based certification for one degree of freedom evolving under a generic time-independent Hamiltonian. We characterize the conditions under which such a certification is possible. Several examples are explicitly studied, some that are approximately harmonic in the limits of low energy (Kerr nonlinearities, the pendulum, and the Morse potential) and one that is not (the particle in an infinite well).
We introduce a family of entanglement witnesses for continuous variable systems, which rely on the sole assumption that their dynamics is that of coupled harmonic oscillators at the time of the test. Entanglement is inferred from the Tsirelson nonclassicality test on one of the normal modes, without any knowledge about the state of the other mode. In each round, the protocol requires measuring only the sign of one coordinate (e.g., position) at one among several times. This dynamic-based entanglement witness is more akin to a Bell inequality than to an uncertainty relation: in particular, it does not admit false positives from classical theory. Our criterion detects non-Gaussian states, some of which are missed by other criteria.
A dynamics-based test, originally proposed by Tsirelson for the harmonic oscillator, provides a method for certifying quantumness under the assumption of a known Hamiltonian. These tests, however, are typically proposed for isolated systems, an assumption that breaks down in experimental implementation. In this paper, we extend the protocol to the harmonic oscillator coupled to standard models of dissipation: thermal relaxation, pure dephasing, and the Caldeira--Leggett model. Using the Moyal-Wigner formalism of quantum mechanics in phase space, we show that the introduction of dissipation requires a dissipation-dependent shift of the classical bound, and provide the threshold under which the nonclassicality witness retains its validity.
Secure and reliable certification of quantum resources is a fundamental challenge in the advancement of next-generation quantum technologies, particularly as devices become more complex and integrated into practical applications, where parts of the system may be untrusted or inaccessible by users. Addressing this challenge requires certification methods that rely on minimal assumptions and limited trust while still faithfully and reliably verifying the quantum resources in question. For infinite-dimensional bosonic systems, existing certification methods rely on fully trusted and well-calibrated measurement systems, leaving significant security vulnerabilities open. In this work, we present the first experimental demonstration of measurement-device-independent (MDI) certification schemes for infinite-dimensional bosonic systems, where the certification process is conducted using entirely untrusted measurement devices and assuming only the trusted preparation of coherent states. Specifically, we implement schemes for the MDI certification of continuous-variable (CV) entanglement and the operation of an elementary optical CV quantum memory. We leverage techniques of Bayesian metrology and exploit the practicality and accessibility of Gaussian quantum optics to achieve secure and efficient certification. These results demonstrate the potential of the MDI framework to enhance trust in quantum technologies with applications in quantum communication and quantum computing.
Abstract Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case, it corresponds to having a time-dependent Hamiltonian. Designing quantum algorithms for time-dependent Hamiltonian is generally much more complicated than time-independent Hamiltonian problems, due to the challenge in handling the time-ordering; moreover, almost all existing such algorithms are developed for qubit-based quantum devices. Here we propose an alternative formalism based on Sambe-Howland’s clock that turns any non-autonomous unitary dynamical system into an autonomous unitary system, i.e. quantum system with a time-independent Hamiltonian, in one higher dimension, while keeping time continuous. This makes the simulation with time-dependent Hamiltonians not much more difficult than that of time-independent Hamiltonians, and can also be framed in terms of an analogue quantum system evolving continuously in time. We show how our new quantum protocol for time-dependent Hamiltonians can be performed in a resource-efficient way and without measurements, and can be made possible on either continuous-variable, qubit or hybrid systems. Combined with a technique called Schrödingerisation, this dilation technique can be applied to the quantum simulation of any linear ODEs and PDEs, and nonlinear ODEs and certain nonlinear PDEs, with time-dependent coefficients.
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
This PhD thesis contains results about two different main topics. The first part deals with the application of continuously monitored quantum systems to high precision quantum metrology. A continuous in time measurement on a quantum system is a kind indirect measurement, which only weakly perturbs the system and leaves room for it to evolve under its dynamics. This time-continuous measurement allows one to collect information about some interesting parameter characterizing the dynamics. In this thesis we show how to apply the theory of quantum parameter estimation to continuously monitored quantum systems. In particular, we study the estimation of a magnetic field applied to an ensemble of two level atoms; we show that by continuously monitoring the system we can obtain a quadratic scaling of the precision with the number of atoms, in two different physical settings (dynamically generated entanglement or initial entanglement). In the second part we study different aspects of nonclassicality of continuous variable quantum systems (bosonic degree of freedoms). They can be described by distributions (in particular, the Wigner function) on a classical phase space, which however can take negative values, the hallmark of nonclassicality. In this context, states with a Gaussian distribution are very useful and very well studied; however, on a fundamental level they must be considered classical. We present several studies connected to the vast topic of non-Gaussian states, starting from an application to parameter estimation, as a link to the first part. We study the relationships between anharmonic Hamiltonians and the nonclassicality of their ground states; we also explore the connection between a quantum effect called `backflow of probability' and the negativity of the Wigner function. We end by showing that quantum operations made out of Gaussian building blocks give rise to a well-defined resource theory of Wigner negativity and non-Gaussianity.