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Register a new userSpatial Orientation using Quantum Telepathy
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Added by
Fabio Antonio Bovino
Publication date
2006
fields
Physics
and research's language is
English
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We implemented the protocol of entanglement assisted orientation in the space proposed by Brukner et al (quant-ph/0603167). We used min-max principle to evaluate the optimal entangled state and the optimal direction of polarization measurements which violate the classical bound.
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Quantum pseudo-telepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum non-locality games. The setting of these games is as follows: the players are separated so that no communication between them is possible and are given a certain computational task. When the players have access to a quantum resource called entanglement, they can accomplish the task: something that is impossible in a classical setting. To an observer who is unfamiliar with the laws of quantum mechanics it seems that the players employ some sort of telepathy; that is, they somehow exchange information without sharing a communication channel. This paper provides a formal framework for specifying, implementing, and analysing quantum non-locality games.
We study the quantum walk search algorithm of Shenvi, Kempe and Whaley [PRA 67 052307 (2003)] on data structures of one to two spatial dimensions, on which the algorithm is thought to be less efficient than in three or more spatial dimensions. Our aim is to understand why the quantum algorithm is dimension dependent whereas the best classical algorithm is not, and to show in more detail how the efficiency of the quantum algorithm varies with spatial dimension or accessibility of the data. Our numerical results agree with the expected scaling in 2D of $O(sqrt{N log N})$, and show how the prefactors display significant dependence on both the degree and symmetry of the graph. Specifically, we see, as expected, the prefactor of the time complexity dropping as the degree (connectivity) of the structure is increased.
Motivated by the engineering applications of uncertainty quantification, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural probability distributions that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case, and fortunately there are many existing techniques for inference and sampling that exist for these distributions. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation.
We introduce spatial deformations to an array of light sources and study how the estimation precision of the interspacing distance, d, changes with the sources of light used. The quantum Fisher information (QFI) is used as the figure of merit in this work to quantify the amount of information we have on the estimation parameter. We derive the generator of translations, G, in d due to an arbitrary homogeneous deformation applied to the array. We show how the variance of the generator can be used to easily consider how different deformations and light sources can effect the estimation precision. The single parameter estimation problem is applied to the array and we report on the optimal state that maximises the QFI for d. Contrary to what may have been expected, the higher average mode occupancies of the classical states performs better in estimating d when compared with single photon emitters (SPEs). The optimal entangled state is constructed from the eigenvectors of the generator and found to outperform all these states. We also find the existence of multiple optimal estimators for the measurement of d. Our results find applications in evaluating stresses and strains, fracture prevention in materials expressing great sensitivities to deformations, and selecting frequency distinguished quantum sources from an array of reference sources.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g. wave plates for polarisation. However for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations when the number of phase modulation planes is comparable to the number of modes. More importantly, we experimentally implement several high-dimensional quantum gates for up to 5-dimensional states encoded in the full-field mode structure of photons. In particular, we realise cyclic and quantum Fourier transformations, known as Pauli $hat{X}$-gates and Hadamard $hat{H}$-gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect unitarity by means of quantum process tomography unveiling a process purity of 99%. Lastly, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e. azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation and sensing schemes.
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