Abstract In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bell-cat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.
Abstract In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations between discrete and continuous variable quantum systems, where visualizing the full phase space has proven difficult in the past due to the high number of degrees of freedom. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bell-cat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in these hybrid discrete-continuous variable quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.
In this work we construct Wigner functions for hybrid continuous and discrete variable quantum systems. We demonstrate new capabilities in the visualization of the interactions and correlations within hybrid quantum systems. Specifically, we show how to clearly distinguish signatures that arise due to quantum and classical correlations in an entangled Bell-cat state. We further show how correlations are manifested in different types of interaction, leading to a deeper understanding of how quantum information is shared between two subsystems. Understanding the nature of the correlations between systems is central to harnessing quantum effects for information processing; the methods presented here reveal the nature of these correlations, allowing a clear visualization of the quantum information present in hybrid quantum systems. The methods presented here could be viewed as a form of quantum state spectroscopy.
Entanglement is a key resource for fundamental tests of physics and emerging quantum technologies. In quantum optics, two perspectives on entanglement coexist. In the continuous-variable framework, entanglement is understood as holding between optical modes. In contrast, discrete-variable quantum optics focuses on quantum correlations in degrees of freedom such as polarization that label fixed numbers of photons. In this paper, we show that entanglement can transcend this separation. Spontaneous parametric down-conversion inherently generates correlations in optical phase space, photon number, and labelling degrees of freedom simultaneously. In polarization, this structure is traditionally described by macroscopic Bell states. Existing witnesses, however, fail to detect the genuine hybrid entanglement of these states, which goes beyond the continuous-discrete-variable categorization. Here, we lay the groundwork for a general framework unifying continuous- and discrete-variable notions of entanglement. In particular, we derive an operational witness providing a sufficient criterion for genuine hybrid number-polarization entanglement and outline its experimental implementation. Finally, we discuss exemplary states which, together with our results on macroscopic Bell states, motivate a broader classification of genuine hybrid quantum correlations.
The main topic of this thesis revolves around quantum measurement. We illustrate how two different views of quantum objects, the discrete-and continuous-variable views, can be combined to more effectively distinguish between orthogonal states. Such combined measurements are referred to as hybrid. The discrete-variable view is more appropriate to probe energy eigenstates. However, when two or more energy eigenstates are superposed, accurate measurements in the energy eigenbasis require rotations in phase space which are very unwieldy as they require strong nonlinearities and elaborate interactions between light and matter. On the other hand, energy eigenstate superpositions carry a continuous relative phase which is easily probed by continuous-variable interference measurements such as homodyning. The tradeoff between photon counting and homodyning is in practice determined by feasibility studies. This is what we do for two particular applications of quantum measurements: Bell tests and the amplication of Schrödinger cat states. This project also had an experimental component which was supposed to produce high-fidelity Schrödinger cat states. This goal turned out to be hampered by noise from the laser as well as a series of anomalous behavior of the nonlinear crystal whereby no classical de-amplification, and therefore no squeezing, could be observed.
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations (entanglement) between spin and spatial degrees of freedom (spin-orbit coupling) and between spin degrees of freedom, as well as more complex combinations of spin and spatial entanglement. This is important as there is growing recognition that such properties affect the physical characteristics, and chemistry, of atoms and molecules. Our visualizations are sufficiently accessible that, with some preparation, those with a nontechnical background can gain an appreciation of subtle quantum properties of atomic and other systems. By providing insights and modeling capability, our phase-space representation will be of great utility in understanding aspects of atomic physics and chemistry not available with current techniques.
The dimensionality of entanglement, quantified by the Schmidt number, is a core resource for quantum information processing. While its certification is well-established in finite-dimensional systems, many platforms harnessing high Schmidt numbers are natively continuous-variable (CV) systems, which are usually truncated to a finite subspace before canonical discrete-variable techniques are applied. For those instances, a core question is whether directly utilizing a genuinely CV toolbox leads to better and more robust characterisations. We answer this question by introducing Schmidt-number witnesses built directly from correlations and covariances of phase-space observables, accessible through characteristic- or Wigner-function measurements. They hold for arbitrary mixed states, including non-Gaussian ones, and only require correlations along a slice of phase space. We show that this direct estimation is more robust and versatile than first discretizing the system and using canonical discrete variable techniques. Moreover, we apply our method to certify arbitrarily-large Schmidt numbers of a bound-entangled Gaussian state. These results motivate genuine CV methods for characterizing high-dimensional entanglement across CV quantum technologies.
We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.