We show how quantum correlations allow us to break the local speed limits of physical processes using only local measurements and classical communication between two parties that share an entangled state. Inequalities that bound the minimal time of evolution of a quantum state by energy fluctuations can be violated in the presence of steering by conditioning on the measurement outcomes of a remote system. Our results open up pathways for studying how quantum correlations influence the dynamical properties of states and observables. Published by the American Physical Society 2024
We show how quantum correlations allow us to break the local speed limits of physical processes using only local measurements and classical communication between two parties that share an entangled state. Inequalities that bound the minimal time of evolution of a quantum state by energy fluctuations can be violated in the presence of steering by conditioning on the measurement outcomes of a remote system. Our results open up pathways for studying how quantum correlations influence the dynamical properties of states and observables. Published by the American Physical Society 2024
Quantum entanglement is a key resource for foundational quantum information and communication tasks, such as teleportation, entanglement swapping and quantum key distribution [1]. Quantum steering is a quantum correlation that is distinct from other nonclassical correlations such as Bell nonlocality [2] and entanglement. Steering describes the effect of measuring one system, let's say Alice, and affecting the measurement results on the other system, let's say Bob. Moving through the hierarchy of nonlocal classes, from Bell nonlocality towards nonsepa-rability, requires an increasing number of parties and apparatus that need to be trusted but gives access to protocols which are more robust to noise for projective measurements [3,4]. In a quantum steering task [5] the correlations of Alice and Bob's measurement outcomes are tested against a classical probability bound which can be only violated if the state shared between the parties is quantum steerable.
Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by dynamically exploiting quantum correlations. In this study, speed limits in interacting quantum systems are derived by comparing the rates of change in actual quantum dynamics with the quasiclassical evolution confined to the manifold of nonentangled separable states. The utility of the resulting bounds on entanglement-assisted speedup is demonstrated on bipartite qubit systems, bipartite qudit systems, as well as a complex multimode systems. Specifically, the proposed speed limits provide a tight bound on quantum speed advantage, including a quantum gain that can scale exponentially with the system's size. Extensions of the results to open systems and measurable witnesses are discussed.
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.
Harnessing the advantages of shared entanglement for sending quantum messages often requires the implementation of complex two-particle entangled measurements. We investigate entanglement advantages in protocols that use only the simplest two-particle measurements, namely, product measurements. For experiments in which only the dimension of the message is known, we show that robust entanglement advantages are possible but that they are fundamentally limited by Einstein-Podolsky-Rosen steering. Subsequently, we propose a natural extension of the standard scenario for these experiments and show that it circumvents this limitation. This leads us to prove entanglement advantages from every entangled two-qubit Werner state, evidence its generalization to high-dimensional systems, and establish a connection to quantum teleportation. Our results reveal the power of product measurements for generating quantum correlations in entanglement-assisted communication and they pave the way for practical semi-device-independent entanglement certification well beyond the constraints of Einstein-Podolsky-Rosen steering. Published by the American Physical Society 2024
Quantum steering captures the ability of one party, through local measurements on a shared entangled state, to affect the conditional states held by distant parties in a way that admits no local explanation. Its device-independent (DI) quantification -- requiring no characterization of any state or measurement -- has been developed in the bipartite setting, notably through the framework of assemblage moment matrices (AMMs) [Phys. Rev. Lett. 116, 240401 (2016)], but has remained largely unexplored beyond it. Here, we extend the AMM framework to tripartite steering, covering both the scenario in which two parties jointly steer a third one (2-steer-1) and that in which a single party steers the remaining two (1-steer-2). For each scheme, we construct a semidefinite program that, from the observed correlations -- or merely from the violation of a Bell inequality -- yields lower bounds on the steering robustness of the underlying assemblage. As a by-product, our bounds also certify, in a DI manner, the incompatibility of the measurements performed by the steering parties.
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.