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
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
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.
Probing the quantum nature of gravity is one of the most profound open challenges in physics. A promising direction is the Gravitationally Induced Entanglement (GIE) protocol, where two initially unentangled probes become entangled solely through local interactions with a mediator of interaction, the gravitational field. Such entanglement would imply that gravity must carry quantum features, namely, it must possess at least a couple of incompatible observables. This thesis further expands the GIE protocol and its Theory-Independent argument by introducing a general, dynamics-independent inequality: the quantum correlation gain between the probes is upper-bounded by the non-commutativity of the mediator’s observables and its Hilbert space dimension. This bound holds for arbitrary interactions and any finite-dimensional systems. A decoherence analysis shows the bound vanishes when the mediator becomes classical. These results provide a quantitative, operational tool for observing the non-classicality of mediators, thereby expanding the conceptual and experimental reach of GIE-based tests of gravity.
Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the nonclassicality of the inaccessible objects as characterized by quantum discord. We consider two probes individually interacting with the inaccessible object but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly, as it allows the probes and the object to be open systems and makes no assumptions about the initial state, dimensionality of involved Hilbert spaces, and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as nonclassicality of the environment, and we foresee potential benefits for the inference of the nonclassical nature of gravity.
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.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
One of the most relevant problems in the quantum theory is the question whether the appropriate state of the system can be described within a classical theory. The famous examples of nonclassical states are Schrodinger-cats states or entanglement states. In spite of many practical applications of entanglement as a special kind of nonclassicality (like quantum teleportation [1], dense coding [2], or implementation of super-fast [3] and fast algorithms [4]), we still have difficulties with describing and specifying it. One cannot find such an operational optimal method, which would allow us to maximally use the technological and scientific potential arising from the adaptation properties of quantum correlations. Thus, my thesis is focused on giving a proposal of a theoretical recipe for constructing experimentally achievable procedures for the study of quantum correlations. In my thesis I have focused on quantum correlations described in terms of nonclassicality (quantumness) and specific kind of it,i.e., entanglement. The nonclassicality definition, used by me in the thesis, is based on the Glauber-Sudarshan function (P -function). One can assume, that a state is nonclassical, if its P -function is negative or more singular than Dirac’s delta [5]. As follows, the state is nonclassical, when its P -function cannot be treated as a “real” probabilistic distribution. Based on specific properties of the P -function, Agarwal and Tara [6], as well as, Shchukin, Richter and Vogel [7, 8] proposed nonclassicality and entanglement [9] criteria based on matrices of moments of annihilation and creation operators. The operational procedures for analyzing nonclassicality and an efficient method for measuring such moments developed by Shchukin and Vogel [10] creates basis for my thesis. It can be seen that the nonclassicality criteria based on matrices of moments offer an effective way of deriving specific inequalities, which might be useful in the verification of nonclassicality of particular states generated in experiments. Therefore, criteria constructed based on the above definition of nonclassicality can be used to find practical and effective methods of generating and testing nonclassicality and, therefore, also quantum entanglement of optical fields. The results presented in my thesis can be divided into three main groups: 1. Finding operational and practical criteria to classify states in terms of nonclassicality and entanglement based on fundamental classical inequalities like Cauchy-Schwarz inequality. It was also shown how some known entanglement inequalities can be derived as nonclassicality inequalities or as sums of more than one inequality [Bartkowiak2010a]. 2. Describing properties and behaviour of quantum correlations for different optical fields (e.g. for multiand single-mode systems, for interacting and noninteracting modes). In particular, general occurrence of sudden vanishing of nonclassicality, which can be observed not only for twoor multimode but also for single-mode fields, was proven [Bartkowiak2011]. 3. Finding the methods of generating and testing of quantum correlations, which would be practical and easy to implement with available resources in both linear and nonlinear optics.