No Arabic abstract
The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. It is shown that the resulting measurement-induced non-linear dynamics of the two-qubit state exhibits strong sensitivity to initial conditions and also true chaos. For a special class of initially prepared two-qubit states two types of islands characterize the asymptotic limit. They correspond to a separable and a maximally entangled two-qubit state, respectively, and their boundaries form fractal-like structures. In the presence of incoherent noise an additional stable asymptotic cycle appears.
The problem of demonstrating entanglement is central to quantum information processing applications. Resorting to standard entanglement witnesses requires one to perfectly trust the implementation of the measurements to be performed on the entangled state, which may be an unjustified assumption. Inspired by the recent work of F. Buscemi [Phys. Rev. Lett. 108, 200401 (2012)], we introduce the concept of Measurement-Device-Independent Entanglement Witnesses (MDI-EWs), which allow one to demonstrate entanglement of all entangled quantum states with untrusted measurement apparatuses. We show how to systematically obtain such MDI-EWs from standard entanglement witnesses. Our construction leads to MDI-EWs that are loss-tolerant, and can be implemented with current technology.
It has been extensively shown in past literature that Bayesian Game Theory and Quantum Non-locality have strong ties between them. Pure Entangled States have been used, in both common and conflict interest games, to gain advantageous payoffs, both at the individual and social level. In this paper we construct a game for a Mixed Entangled State such that this state gives higher payoffs than classically possible, both at the individual level and the social level. Also, we use the I-3322 inequality so that states that arent helpful as advice for Bell-CHSH inequality can also be used. Finally, the measurement setting we use is a Restricted Social Welfare Strategy (given this particular state).
We propose a classical to quantum information encoding system using non--orthogonal states and apply it to the problem of searching an element in a quantum list. We show that the proposed encoding scheme leads to an exponential gain in terms of quantum resources and, in some cases, to an exponential gain in the number of runs of the protocol. In the case where the output of the search algorithm is a quantum state with some particular physical property, the searched state is found with a single query to the introduced oracle. If the obtained quantum state must be converted back to classical information, our protocol demands a number of repetitions that scales polynomially with the number of qubits required to encode a classical string.
A cavity quantum electrodynamical scenario is proposed for implementing a Schrodinger microscope capable of amplifying differences between non orthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum transformation, which exhibits measurement-induced chaos, allows approximate orthogonalization of atomic states by purification after a few iterations of the protocol, and thus the application of the scheme for quantum state discrimination.
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this article, we exploit the classical Fisher information induced by quantum measurements, and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc.