Bulletin of the American Physical Society

Information Processing Structure of Quantum Gravity

László Gyöngyösi

Published Jan 26, 2014• 0 citations

Abstract

The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework.The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics.In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable.In this work, we provide a model for the information processing structure of quantum gravity.We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted.We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry.We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel.We reveal that the quantum gravity space acts as a background noise on the local environment states.We characterize the properties of the noise of the quantum gravity space and show that it allows the separate local parties to simulate remote outputs from the local environment state, through the process of remote simulation.We characterize the information transfer of the gravity space and the correlation measure functions of the gravity channel.We investigate the process of stimulated storage for quantum gravity memories, a phenomenon that exploits the information resource-pool property of quantum gravity.The results confirm the perception that the benefits of the quantum gravity space can be exploited in quantum computations, particularly in the development of quantum computers.

Related papers

Theory of quantum gravity information processing

Laszlo Gyongyosi, Sándor Imre

The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. The space of quantum gravity provides both the nonfixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite, and the processes are causally nonseparable. Here, we provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We reveal that the quantum gravity space acts as a background noise on the local environment states. We characterize the properties of the noise of the quantum gravity space and show that it allows the separate local parties to simulate remote outputs from the local environment state, through the process of remote simulation.

arXiv:1401.6706Quantum EngineeringOct 18, 201913 citations

Correlation measure equivalence in dynamic causal structures of quantum gravity

László Gyöngyösi

We prove an equivalence transformation between the correlation measure functions of the causally unbiased quantum gravity space and the causally biased standard space. The theory of quantum gravity fuses the dynamic (nonfixed) causal structure of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity space, the events are causally nonseparable and all time bias vanishes, which make it no possible to use the standard causally biased entropy and the correlation measure functions. Since a corrected causally unbiased entropy function leads to an undefined, obscure mathematical structure, in our approach, the correction is made in the data representation of the causally unbiased space. Here, we prove that the standard causally biased entropy function with a data correction can be used to identify correlations in dynamic causal structures. As a corollary, all mathematical properties of the causally biased correlation measure functions are preserved in the causally unbiased space. The equivalence transformation allows us to measure correlations in a quantum gravity space with the stable, well-defined mathematical background and apparatus of the causally biased functions of quantum Shannon theory.

arXiv:1603.02416Quantum EngineeringJan 7, 202011 citations

Correlation Measure Equivalence in Dynamic Causal Structures

László Gyöngyösi

We prove an equivalence transformation between the correlation measure functions of the causally-unbiased quantum gravity space and the causally-biased standard space. The theory of quantum gravity fuses the dynamic (nonfixed) causal structure of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity space, the events are causally nonseparable and all time bias vanishes, which makes it no possible to use the standard causally-biased entropy and the correlation measure functions. Since a corrected causally-unbiased entropy function leads to an undefined, obscure mathematical structure, in our approach the correction is made in the data representation of the causally-unbiased space. We prove that the standard causally-biased entropy function with a data correction can be used to identify correlations in dynamic causal structures. As a corollary, all mathematical properties of the causally-biased correlation measure functions are preserved in the causally-unbiased space. The equivalence transformation allows us to measure correlations in a quantum gravity space with the stable, well-defined mathematical background and apparatus of the causally-biased functions of quantum Shannon theory.

Mar 8, 20160 citations

Quantum estimation for gravitation and quantum information with acceleration

T. G. Downes

In this thesis we shall apply techniques from quantum information theory to the problem of measuring the structure of spacetime or equivalently measuring the gravitational field. In turn we will also look at how acceleration may effect quantum information techniques for processing and transmitting information. Measuring the structure of spacetime is a slight abuse of terminology as spacetime structure is not directly observable. We will be investigating the estimation of spacetime structure by making measurements on quantum systems which depend on the spacetime background. The structure of spacetime and the gravitational field will be treated in accordance with Einstein's general theory of relativity. This is currently the most accurately tested classical theory for gravity. It is widely believed that fundamentally, gravity should be treated within the framework of quantum mechanics, just like the other forces of nature. This is yet to be seen experimentally and a theory capable of falsifiable predictions is yet to be found. In this thesis we shall focus on the effects of gravity at the classical level, however we shall treat matter and non-gravitational energy using quantum mechanics. When looking at how gravity effects quantum information we will specifically be focusing on the simple case of acceleration, yet we shall treat it in this relativistic spacetime context. Knowing the structure of spacetime in general relativity amounts to knowing an object called the metric tensor. This object contains all the information about a spacetime. This may include local curvature, for instance around a star or black hole, gravitational radiation coming from a binary pulsar and even the large scale structure of the universe such as the rate of expansion. By performing local experiments one may attempt to extract this information. Fundamentally these experiments will be governed by quantum mechanics, hence the accuracy of the estimation will be fundamentally limited by the statistical nature of quantum theory. In this thesis we shall develop an equation which states just what accuracy one can ultimately achieve when attempting to measure the structure of spacetime. This equation will be shown to be a generalisation of known results for the accuracy to which one can ultimately measure position and momentum as well as time and energy. The result will be applied to a range of relativistic phenomena including acceleration in flat spacetime, the local curvature around a black hole, the amplitude of a gravitational wave and the expansion of the universe in a cosmological model. Following the use of quantum information theory to investigate gravity we shall look at how acceleration can effect quantum information. Firstly we shall see how quantum entanglement can be created and stored between two optical cavities when one is uniformly accelerating. This is in contrast to a number of results which predict that entanglement will be lost in the presence of acceleration. This loss of entanglement is predicted due to an as yet unobserved phenomena known as the Unruh effect. The Unruh effect states that an observer uniformly accelerating will see a thermal distribution of particles even if an inertial observer will see no particles at all. We will show how the use of optical cavities can prevent this effect from causing problems both for the storage and creation of entanglement. Finally we shall look at how a particular quantum detection scheme can be employed in the presence of acceleration. Our technique will emphasis the importance of locality, that is the localisation of physics in spacetime. We will also show how some commonly used approximations used to study the Unruh effect, can be avoided with our new formulation.

Jan 1, 20112 citations

Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure

Lucien Hardy

General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper, we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. We adopt an operational methodology for the purposes of theory construction (though without committing to operationalism as a fundamental philosophy). The key idea in the construction is physical compression . A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for a composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. The third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate everything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.

arXiv:gr-qc/0608043Journal of Physics A Mathematical and TheoreticalMar 7, 2007213 citations

Towards Quantum Gravity: A Framework for Probabilistic Theories with Non-Fixed Causal Structure

Lucién Hardy

General relativity is a deterministic theory with non-fixed causal structure. Quantum theory is a probabilistic theory with fixed causal structure. In this paper we build a framework for probabilistic theories with non-fixed causal structure. This combines the radical elements of general relativity and quantum theory. The key idea in the construction is physical compression. A physical theory relates quantities. Thus, if we specify a sufficiently large set of quantities (this is the compressed set), we can calculate all the others. We apply three levels of physical compression. First, we apply it locally to quantities (actually probabilities) that might be measured in a particular region of spacetime. Then we consider composite regions. We find that there is a second level of physical compression for the composite region over and above the first level physical compression for the component regions. Each application of first and second level physical compression is quantified by a matrix. We find that these matrices themselves are related by the physical theory and can therefore be subject to compression. This is the third level of physical compression. This third level of physical compression gives rise to a new mathematical object which we call the causaloid. From the causaloid for a particular physical theory we can calculate verything the physical theory can calculate. This approach allows us to set up a framework for calculating probabilistic correlations in data without imposing a fixed causal structure (such as a background time). We show how to put quantum theory in this framework (thus providing a new formulation of this theory). We indicate how general relativity might be put into this framework and how the framework might be used to construct a theory of quantum gravity.

Aug 9, 2006124 citations