The study of nonclassicality is essential to understand the quantum-to-classical transition in physical systems. Recently, a witness of nonclassicality has been proposed, linking the ability of a system (the mediator) to create quantum correlations between two quantum probes with its nonclassicality, intended as the existence of at least two noncommuting variables. Here we propose an inequality that quantitatively links the increase in quantum correlations between the probes to a function of the noncommutativity of the mediator's observables. We test the inequality for various degrees of nonclassicality of the mediator, from fully quantum to fully classical. This quantum-to-classical transition is simulated via a phase-flip channel applied to the mediator, inducing an effective reduction of the noncommutativity of its variables. Our results provide a general framework for witnessing nonclassicality, assessing the nonclassicality of a system via its intrinsic properties, independently of the specific chosen interaction dynamics.
The study of nonclassicality is essential to understand the quantum-to-classical transition in physical systems. Recently, a witness of nonclassicality has been proposed, linking the ability of a system (the mediator) to create quantum correlations between two quantum probes with its nonclassicality, intended as the existence of at least two noncommuting variables. Here we propose an inequality that quantitatively links the increase in quantum correlations between the probes to a function of the noncommutativity of the mediator's observables. We test the inequality for various degrees of nonclassicality of the mediator, from fully quantum to fully classical. This quantum-to-classical transition is simulated via a phase-flip channel applied to the mediator, inducing an effective reduction of the noncommutativity of its variables. Our results provide a general framework for witnessing nonclassicality, assessing the nonclassicality of a system via its intrinsic properties, independently of the specific chosen interaction dynamics.
In a plethora of physical situations, one can distinguish a mediator—a system that couples other, noninteracting, systems. Often, the mediator itself is not directly accessible to experimentation, yet it is interesting and sometimes crucial to understand if it admits nonclassical properties. An example of this sort that has recently been enjoying considerable attention is that of two quantum masses coupled via a gravitational field. It has been argued that the gain of quantum entanglement between the masses indicates nonclassicality of the states of the whole tripartite system. Here, we focus on the nonclassical properties of the involved interactions rather than the states. We derive inequalities the violation of which indicates noncommutativity and nondecomposability (open-system generalization of noncommuting unitaries) of interactions through the mediators. The derivations are based on properties of general quantum formalism and make minimalistic assumptions about the studied systems; in particular, the interactions can remain uncharacterized throughout the assessment. Furthermore, we also present conditions that solely use correlations between the coupled systems, excluding the need to measure the mediator. Next, we show that the amount of violation places a lower bound on suitably defined degree of nondecomposability. This makes the methods quantitative and at the same time experiment ready. We give applications of these techniques in two different fields: for detecting the nonclassicality of gravitational interaction and in bounding the Trotter error in quantum simulations. Published by the American Physical Society 2024
We propose a general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be nonclassical. Remarkably, we do not assume any classical or quantum formalism to describe the mediating physical system: our result follows from general information-theoretic principles, drawn from the recently proposed constructor theory of information. This argument provides a broader theoretical basis for recently proposed tests of nonclassicality in gravity, based on witnessing gravitationally induced entanglement in quantum probes, making them applicable in the context where quantum theory may not apply.
Noncommutativity is one of the most elementary nonclassical features of quantum observables. Here we propose a method to detect noncommutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals nondecomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.
The universality of quantum theory has been questioned ever since it was proposed. Key to this long-unsolved question is to test whether a given physical system has non-classical features. Here we connect recently proposed witnesses of non-classicality, based on information-theoretic ideas, with the theory of temporal entanglement. We provide a protocol to witness the non-classicality of a system by probing it with a qubit: we show that, assuming a general conservation law, violating temporal Bell inequalities on the qubit probe implies the non-classicality of the system under investigation. We also perform proof-of-principle experimental emulations of the proposed witness of non-classicality, using a three qubit Nuclear Magnetic Resonance quantum computer. Our result is robust, as it relies on minimal assumptions, and remarkably it can be applied in a broad range of contexts, from quantum biology to quantum gravity.
Nonclassicality encompasses all of quantum physics that cannot be explained with classical theories. Fundamentally, studying nonclassicality promises to give better insight into the structure of quantum theory and what makes it unique in comparison to classical theories. Moreover, nonclassical effects can be exploited in technologies that can perform tasks that are impossible or perform worse classically. Understanding nonclassicality is thus crucial both from a foundational and an application level. Despite its importance, it is not fully understood what exactly constitutes nonclassicality and how it should be properly defined. Nonclassicality is defined differently in different contexts and thus remains a contested term. The present cumulative thesis aims to give a better understanding of the concept of nonclassicality. It is based on three publications (I)–(III) (Tschaffon et al. 2023, Tschaffon and Seiler 2024, Tschaffon and Freyberger 2025) which were written under the supervision of Prof. Matthias Freyberger at the Institut für Quantenphysik at Ulm University. Nonclassicality is the common theme of all three publications presented here and the central theme of this thesis. Since the definitions of nonclassicality are manifold, we restrict ourselves to just one precise definition. In this work, we focus on nonclassical correlations of bipartite states, and more specifically, on the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality. We will use this definition of nonclassicality in the main part of this work, Chapters 2 and 3, to study bipartite quantum states with discrete (DV) and continuous variables (CV). In Chapter 2, we discuss publications (I) and (II) that deal with nonclassicality of DV states, in particular with qubits. For this purpose, we revisit Bell’s original inequality and the CHSH inequality and, with their help, motivate average correlation as a novel indicator for nonclassicality. Average correlation is an operational quantity based on the expectation value present in many Bell inequalities, such as the CHSH inequality. Unlike Bell inequalities, it is not based on specific measurements but rather on infinitely many uniform measurements. With average correlation, we can formulate a necessary and sufficient condition for nonclassicality and even inseparability, constituting new Bell-like inequalities. In Chapter 3, we expound on publication (III) where we focus on nonclassicality for CV states. We again examine the CHSH inequality with the help of a pseudo-spin and use it to define nonclassicality. Negative values of Wigner functions are typically associated with nonclassicality. For this reason, we look at the sum of all negative values of the Wigner function, Wigner negativity, and examine how it correlates with nonclassicality for two classes of states. This helps us understand that Wigner negativity is related to nonclassicality quantitatively but varies for different classes of states. Furthermore, for each class of state, a different amount of Wigner negativity is necessary to find nonclassicality. Thus, we find that a nonzero Wigner negativity is not sufficient to observe nonclassicality.
Quantum theory is one of the most successful theories in modern physics. It has been extensively tested in the microscopic domain, always with remarkable success. Yet, these tests do not currently extend in a conclusive way to all physical systems and across all scales. This leaves open the question of whether quantum theory provides a truly universal description of reality, especially in regimes where direct experimental access is limited, such as the gravitational field or complex macroscopic biological systems. This Thesis addresses this question through the study of hybrid systems, where a well-controlled quantum sector interacts with an unknown sector whose underlying description may or may not be quantum. It contributes to the emerging framework of information-theoretical witnesses of non-classicality, where the quantum sector is used as a probe to test the nature of the unknown system under minimal assumptions. We first examine spatial entanglement-based witnesses, in which the ability of an unknown system to mediate entanglement between two quantum probes by local means provides a sufficient condition for its non-classicality. We extend this framework by quantitatively showing that locally mediated quantum correlations lower bound the non-commutativity of the observables of the mediator, within quantum theory. We then introduce a novel class of single-probe temporal witnesses, where non-classicality is inferred from the temporal evolution of a probe under a global conservation law. We prove that quantum coherent evolution under such a constraint can only be mediated by a non-classical system, and propose an application to light-harvesting processes in photosynthetic complexes. Finally, we develop a temporal entanglement-based witness. Here, the sufficient condition for the non-classicality of the unknown system is the ability to mediate temporal entanglement relative to the probe's local conserved quantity and a non-commuting observable. This result provides a temporal extension of the spatial entanglement-based witness, representing a promising route for the development of the next generation of tests to probe the universality of quantum theory in previously inaccessible fields such as gravity and biology.