In recent years, examining the information processing aspects of nature has received significant attention. In particular, entanglement has been shown to exhibit what is arguably the most distinctive and unique aspect of quantum information science. In this note, a numerical method is applied to the Bell inequalities for examining the range of nonlocality when imperfect measurements are performed at each end. A two-qubit direct protocol is also examined such that, unlike the Bell-type inequalities, the approach is not as stable as the indirect one against measurement errors in yielding the nonlocality. On the other hand, since many applications of quantum technology involve a particular type of entanglement, it is important to have a technique to manipulate correlations. In this paper, five chained 2-level entanglements are also examined with swapping protocols applied at each joint. It is numerically shown that there exists a class of states that approximate the optimal result, i.e., the weakest link.
In recent years, examining the information processing aspects of nature has received significant attention. In particular, entanglement has been shown to exhibit what is arguably the most distinctive and unique aspect of quantum information science. In this note, a numerical method is applied to the Bell inequalities for examining the range of nonlocality when imperfect measurements are performed at each end. A two-qubit direct protocol is also examined such that, unlike the Bell-type inequalities, the approach is not as stable as the indirect one against measurement errors in yielding the nonlocality. On the other hand, since many applications of quantum technology involve a particular type of entanglement, it is important to have a technique to manipulate correlations. In this paper, five chained 2-level entanglements are also examined with swapping protocols applied at each joint. It is numerically shown that there exists a class of states that approximate the optimal result, i.e., the weakest link.
The subjectivity seen in quantum theory has been the topic of major debate ever since the theory was first introduced about a century ago. The idea of treating the subject and the object independently has been difficult to accept in the science community; however, the subjective limit of knowledge has been discussed in philosophy for centuries. On the other hand, one of the important outcomes of recent studies of quantum theory is developing useful and practical applications from often controversial and philosophical debates such as the simultaneous existence of multiple states or superluminal influencing, which appears to violate the locality imposed by relativity. Establishing a long-distance correlation may be effective in a number of applications in quantum information technology. In this paper, an entanglement swapping scheme for three 2-level states is examined using numerical methods. In particular, it is studied that there is a class of non-maximal states that approximate the optimal outcome, namely, the weakest link.
Recent successes in quantum technology have provided a number of powerful tools for viewing nature in terms of information. In particular, quantum information science has proved to be a useful way to greatly simplify the way the universe is viewed as well as treating the subject, an observer, and the object, the observed universe, on an equal footing. Several important applications in quantum technology such as communication, information processing, etc., use a distinctive property of entanglement. In this article, a numerical simulation is applied to a swapping measurement protocol involving two 3-level entangled states. A different condition, in non-maximal states, that approximates the optimal result (i.e., the weaker link between the two initial states) will be shown through a numerical method. This different class of states is distributed just as wide as the class yielding the optimal result. The result may be useful in establishing a long distance maximal entanglement that is often fragile and unstable due to noise.
Abstract: Entanglement has been one of the dominant aspects distinguishing quantum theory from its classical counterpart. Indeed, entanglement has played a central role in recent developments in quantum technology, such as quantum computing, key distribution, etc. In order to use entanglement in these situations, a particular form is often needed, namely the maximal case. Various techniques have been used to manipulate entangled states, especially between distant parties. Generating long-distance entanglement from multiple shorter states has been studied, and it has been shown that there exists a class of states that can achieve optimal entanglement resources. In this paper, the particular class of states that yields the weakest link is numerically examined. The findings reveal that the range of this class is limited but substantial. Keywords: Quantum entanglement, Numerical methods, Maximal states.
The quantum information network is important in establishing next-generation technology. In particular, maximal and long-distance entangled states are important in realizing a number of quantum information technologies, such as teleportation, key distribution and so forth. Entanglement swapping is a scheme that creates a long-distance network by using multiple short ones. Entanglement swapping protocols applied to non-maximal correlations have been thoroughly investigated by various people. Rather than providing any new analytic results, some examples of a numerical approach will be provided in this paper. In particular, the paper reveals the existence of different classes of coefficients that approximate the optimal outcome ( i.e. , the weaker average maximal entanglement between the two initial states). The new class of states is non-trivial in the sense that their coefficients are just as widely distributed as the coefficients of states satisfying optimality conditions are. Moreover, we will numerically examine entanglement swapping methods and show the distribution of optimal and general coefficients for three and four 2-level correlations.
Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, Gisin's Theorem ), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio R = 1/Tr(ρ 2 ) or their maximum eigenvalue λ max . This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so-called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four-qubit systems, where nonlocality for generalized Greenberger–Horne–Zeilinger states of arbitrary number of parties is computed.
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. There are however some complications with Bell inequalities. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an ambiguity stemming from the choice of the normalization of the Bell coefficients. An alternative measure of nonlocality with a direct information-theoretic interpretation is the minimal amount of classical communication required for simulating nonlocal correlations. In the case of many instances simulated in parallel, the minimal communication cost per instance is called nonlocal capacity, and its computation can be reduced to a convex-optimization problem. This quantity can be computed for a higher number of measurements and turns out to be useful for finding the optimal experimental setup. Focusing on the bipartite case, we present a simple method for maximizing the nonlocal capacity over a given configuration space and, in particular, over a set of possible measurements, yielding the corresponding optimal setup. Furthermore, we show that there is a functional relationship between Bell violation and nonlocal capacity. The method is illustrated with numerical tests and compared with the maximization of the violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed by qutrits turns out to be even stronger if the nonlocal capacity is employed as a measure of nonlocality.