Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes: Sequential correlations can outperform spatial correlations. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.
Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes: Sequential correlations can outperform spatial correlations. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.
Information Causality was introduced as a physical principle for constraining the set of nonlocal correlations. In recent work, we proposed an extension of Information Causality that allows correlations among Alice's inputs. This extended principle yields tighter constraints than the original formulation and recovers part of the quantum boundary in certain Bell scenarios. In this work, we further investigate the implications of extended Information Causality and apply it to scenarios beyond binary inputs and outputs. We derive a family of quantum Bell inequalities that strengthen previously known constraints on quantum correlations. Using these inequalities, we obtain an improved analytical bound for the Collins-Gisin family of Bell inequalities. We also apply Information Causality to entanglement-assisted random access codes and derive new theory-independent analytical bounds on the winning probability. For this latter task, we prove that, despite being stronger in general, the extended principle does not improve the bounds obtained from the original Information Causality principle. This suggests that the existing Information Causality bounds are optimal for this class of random access codes.
Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication protocol, based on a quantum random access code. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations that return both a classical and quantum outcome, and the latter is measured by the third party. We demonstrate a nearly optimal sequential quantum random access code that outperforms both the best possible classical protocol and any quantum protocol that utilizes only projective measurements. Furthermore, while only assuming that the involved devices operate on qubits and that detected events constitute a fair sample, we demonstrate the noise-robust characterization of unsharp measurements based on the sequential quantum random access code. We apply this characterization towards quantifying the degree of incompatibility of two sequential pairs of quantum measurements.
Complications in preparing and preserving quantum correlations stimulate recycling of a single quantum resource in information processing and communication tasks multiple times. Here, we consider a scenario involving multiple independent pairs of observers acting with unbiased inputs on a single pair of spatially separated qubits sequentially. In this scenario, we address whether more than one pair of observers can demonstrate quantum advantage in some specific $2\ensuremath{\rightarrow}1$ and $3\ensuremath{\rightarrow}1$ random access codes. Interestingly, we not only address these in the affirmative but also illustrate that unbounded pairs can exhibit quantum advantage. Furthermore, these results remain valid even when all observers perform suitable projective measurements and an appropriate separable state is initially shared.
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.
The algebraic derivation of the numerical limits of Bell inequalities in either three or four random variables is independent of the assumption of randomness. The limits of the inequalities follow as mathematical consequences of their created algebraic structures independently of application to random or deterministic variables. The inequalities should be called identity-inequalities. A final correlation re-uses data from the previous correlations and thus leads to the inequality limits. It generally has a different functional form from the previous correlations, whether derived as a counterfactual mathematical result, or in a way enabling comparison with experiment. These algebraic facts and their consequences are central to understanding the inequalities’ use, but have not been widely recognized. Logically consistent application of the inequalities to Bell experiments is challenging, given that the number of mathematically assumed random variables is greater than the number of physical variables produced per experimental realization. Given Bell’s rejection of the use of sequential, alternative paths, three experimental runs are here considered to enable acquisition of data to be rearranged for computation of statistical cross-correlations. Predicted quantum mechanical correlations then satisfy the inequality. Since mathematically inconsistent use is sufficient to cause inequality violation, the conclusion that violation implies the nonexistence of underlying variables in the entanglement process does not follow.
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.