Two parts of an entangled quantum state can have a correlation, in their joint behavior under measurements, that is unexplainable by shared classical information. Such correlations are called nonlocal and have proven to be an interesting resource for information processing. Since nonlocal correlations are more useful if they are stronger, it is natural to ask whether weak nonlocality can be amplified. We give an affirmative answer by presenting the first protocol for distilling nonlocality in the framework of generalized nonsignaling theories. Our protocol works for both quantum and nonquantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a Clauser-Horne-Shimony-Holt inequality is not a good measure for the usefulness of nonlocality. A more meaningful measure follows from our results.
Two parts of an entangled quantum state can have a correlation, in their joint behavior under measurements, that is unexplainable by shared classical information. Such correlations are called nonlocal and have proven to be an interesting resource for information processing. Since nonlocal correlations are more useful if they are stronger, it is natural to ask whether weak nonlocality can be amplified. We give an affirmative answer by presenting the first protocol for distilling nonlocality in the framework of generalized nonsignaling theories. Our protocol works for both quantum and nonquantum correlations. This shows that in many contexts, the extent to which a single instance of a correlation can violate a Clauser-Horne-Shimony-Holt inequality is not a good measure for the usefulness of nonlocality. A more meaningful measure follows from our results.
Nonlocality is one of the most important resources for quantum information protocols.The observation of nonlocal correlations in a Bell experiment is the result of appropriately chosen measurements and quantum states.We quantify the minimal purity to achieve a certain Bell value for any Bell operator.Since purity is the most fundamental resource of a quantum state, this enables us also to quantify the necessary coherence, discord, and entanglement for a given violation of two-qubit correlation inequalities.Our results shine a light on the Clauser-Horne-Shimony-Holt inequality by showing that for a fixed Bell violation an increase in the measurement resources does not always lead to a decrease of the minimal state resources.
Non-local correlations are not only a fascinating feature of quantum theory, but an interesting resource for information processing, for instance in communication-complexity theory or cryptography. An important question in this context is whether the resource can be distilled: Given a large amount of weak non-local correlations, is there a method to obtain strong non-locality using local operations and shared randomness? We partly answer this question by no: CHSH-type non-locality, the only possible non-locality of binary systems, which is not super-strong, but achievable by measurements on certain quantum states, has at best very limited distillability by any non-interactive classical method. This strongly extends and generalizes what was previously known, namely that there are two limits that cannot be overstepped: The Bell and Tsirelson bounds. Moreover, our results imply that there must be an infinite number of such bounds. A noticeable feature of our proof of this purely classical statement is that it is quantum mechanical in the sense that (both novel and known) facts from quantum theory are used in a crucial way to obtain the claimed results. One of these results, of independent interest, is that certain mixed entangled states cannot be distilled without communication. Weaker statements, namely limited distillability, have been known for Werner states.
Nonlocality is one of the main characteristic features of quantum systems involving more than one spatially separated subsystem. It is manifested theoretically as well as experimentally through violation of some local realistic inequality. On the other hand, classical behavior of all physical phenomena in the macroscopic limit gives a general intuition that any physical theory for describing microscopic phenomena should resemble classical physics in the macroscopic regime, the so-called macrorealism. In the 2-2-2 scenario (two parties, with each performing two measurements and each measurement having two outcomes), contemplating all the no-signaling correlations, we characterize which of them would exhibit classical (local realistic) behavior in the macroscopic limit. Interestingly, we find correlations which at the single-copy level violate the Bell-Clauser-Horne-Shimony-Holt inequality by an amount less than the optimal quantum violation (i.e., Cirel'son bound 22), but in the macroscopic limit gives rise to a value which is higher than 22. Such correlations are therefore not considered physical. Our study thus provides a sufficient criterion to identify some of unphysical correlations.
The stronger nonlocality than that allowed in quantum theory can provide an advantage in information processing and computation. Since quantum entanglement is distillable, can nonlocality be distilled in the nonsignalling condition? The answer is positive in the bipartite case. In this article the distillability of the multipartite nonlocality is investigated. We propose a distillation protocol solely exploiting xor operations on output bits. The probability-distribution vectors and matrix are introduced to tackle the correlators. It is shown that only the correlators with extreme values can survive the distillation process. As the main result, the amplified nonlocality cannot maximally violate any Bell-type inequality. Accordingly, a distillability criterion in the postquantum region is proposed.
Abstract Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by quantifying entanglement using a family of generalized Clauser–Horne–Shimony–Holt-type Bell inequalities. Given a Bell-inequality violation, we derive analytical lower bounds on the entanglement of formation, a measure related to entanglement dilution. The bounds also lead to an analytical estimation of the negativity of entanglement. In addition, we consider one-way distillable entanglement tied to entanglement distillation and derive tight numerical estimates. With the additional assumptions of qubit-qubit systems, we find that the relationship between entanglement and measurement incompatibility is not simply a trade-off under a fixed nonlocal behavior. Furthermore, we apply our results to two realistic scenarios—non-maximally entangled and Werner states. We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.
Non-local correlations are among the most fascinating features of quantum theory from the point of view of information: Such correlations, although not allowing for signaling, are unexplainable by pre-shared information. The correlations have applications in cryptography, communication complexity, and sit at the very heart of many attempts of understanding quantum theory -- and its limits -- in terms of classical information. In these contexts, the question is crucial whether such correlations can be amplified or distilled, i.e., whether and how weak correlations can be used for generating (a smaller amount of) stronger. Whereas the question has been studied quite extensively for bipartite correlations (yielding both pessimistic and optimistic results), only little is known in the multi-partite case. We introduce a general framework of reductions between multi-party input-output systems. Within this formalism, we show that a natural n-party generalization of the well-known Popescu-Rohrlich box can be distilled, by an adaptive protocol, to the algebraic maximum.We use this result further to show that a much broader class of correlations, including all purely threepartite correlations, can be distilled from arbitrarily weak to almost maximal strength with partial communication, i.e., using only a subset of the channels required for the creation of the same correlation from scratch. Alternatively, this means that arbitrarily weak non-local correlations can have a "communication value" in the context of the generation of maximal non-locality.