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International Conference on Symmetry (Symmetry)

Quantum Metrology and Relativistic Symmetries

Marc-Thierry Jaekel, Serge Reynaud

Published Jan 3, 2018• 0 citations
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Abstract

first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Quantum Metrology and Relativistic Symmetries † by Marc-Thierry Jaekel 1 and Serge Reynaud 2,* 1 Laboratoire de Physique Théorique CNRS, ENS-PSL, UPMC-SU, F-75231 Paris, France 2 Laboratoire Kastler Brossel CNRS, ENS-PSL, UPMC-SU, Collège de France, F-75252 Paris, France * Author to whom correspondence should be addressed. † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 41; https://doi.org/10.3390/proceedings2010041 Published: 3 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Modern metrology is based on quantum and relativistic physics. The second is defined as a fixed integer number of periods of atomic caesium clocks while the meter is derived from the exact value fixed for the speed of light in vacuum c. Clock synchronization, distance measurement (ranging) or localization in space-time (GNSS localization) are built on the remote distribution of electromagnetic field phases. In 2018, the Planck constant h and elementary charge e should be defined to have exact values, replacing the old definitions of the kilogram and Ampere units.However, the quantum status of time, space and mass observables and its compatibility with relativistic symmetries remain open questions. We address this problem in a quantum algebraic approach where observable positions in space and time are defined so that they obey relativistic and quantum requirements [1]. A mass observable is defined which is no longer a constant as expected from its dimension with respect to dilatation.The commutators of quantum positions involve spin, and frame transformations to accelerated frames differ from their classical counterparts [2]. Relativistic symmetries nevertheless allow one to extend the covariance rules of general relativity to the quantum algebraic framework [3]. It leads to a quantum version of the Einstein equivalence principle identified to the transformation of the mass observable. ReferencesJaekel, M.-T.; Reynaud, S. Quantum Observables associated with Einstein Localisation. arXiv 1998, arXiv:quant-ph/9810027. [Google Scholar]Jaekel, M.-T.; Reynaud, S. Quantum algebraic representation of localization and motion of a Dirac electron. arXiv 2001, arXiv:quant-ph/0101121. [Google Scholar]Jaekel, M.-T.; Reynaud, S. Mass, inertia and gravitation. arXiv 2011, arXiv:0812.3936. [Google Scholar]Publisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Jaekel, M.-T.; Reynaud, S. Quantum Metrology and Relativistic Symmetries. Proceedings 2018, 2, 41. https://doi.org/10.3390/proceedings2010041 AMA Style Jaekel M-T, Reynaud S. Quantum Metrology and Relativistic Symmetries. Proceedings. 2018; 2(1):41. https://doi.org/10.3390/proceedings2010041 Chicago/Turabian Style Jaekel, Marc-Thierry, and Serge Reynaud. 2018. "Quantum Metrology and Relativistic Symmetries" Proceedings 2, no. 1: 41. https://doi.org/10.3390/proceedings2010041 Find Other Styles Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here. Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.

DOI
10.3390/proceedings2010041

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The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of their commutation relations including the energy-time relation. These commutators also describe the relativistic shifts undergone under frame transformations, not only for inertial frames but also for uniformly accelerated frames. The quantum redshift laws differ from their classical counterparts while still obeying universal metric properties. The paper presents this approach in terms closely connected to the seminal Einstein conception of localisation in space-time and refers to already published papers for more technical developments.

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first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Quantum Metrology and Relativistic Symmetries † by Marc-Thierry Jaekel 1 and Serge Reynaud 2,* 1 Laboratoire de Physique Théorique CNRS, ENS-PSL, UPMC-SU, F-75231 Paris, France 2 Laboratoire Kastler Brossel CNRS, ENS-PSL, UPMC-SU, Collège de France, F-75252 Paris, France * Author to whom correspondence should be addressed. † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 41; https://doi.org/10.3390/proceedings2010041 Published: 3 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Modern metrology is based on quantum and relativistic physics. The second is defined as a fixed integer number of periods of atomic caesium clocks while the meter is derived from the exact value fixed for the speed of light in vacuum c. Clock synchronization, distance measurement (ranging) or localization in space-time (GNSS localization) are built on the remote distribution of electromagnetic field phases. In 2018, the Planck constant h and elementary charge e should be defined to have exact values, replacing the old definitions of the kilogram and Ampere units.However, the quantum status of time, space and mass observables and its compatibility with relativistic symmetries remain open questions. We address this problem in a quantum algebraic approach where observable positions in space and time are defined so that they obey relativistic and quantum requirements [1]. A mass observable is defined which is no longer a constant as expected from its dimension with respect to dilatation.The commutators of quantum positions involve spin, and frame transformations to accelerated frames differ from their classical counterparts [2]. Relativistic symmetries nevertheless allow one to extend the covariance rules of general relativity to the quantum algebraic framework [3]. It leads to a quantum version of the Einstein equivalence principle identified to the transformation of the mass observable. ReferencesJaekel, M.-T.; Reynaud, S. Quantum Observables associated with Einstein Localisation. arXiv 1998, arXiv:quant-ph/9810027. [Google Scholar]Jaekel, M.-T.; Reynaud, S. Quantum algebraic representation of localization and motion of a Dirac electron. arXiv 2001, arXiv:quant-ph/0101121. [Google Scholar]Jaekel, M.-T.; Reynaud, S. Mass, inertia and gravitation. arXiv 2011, arXiv:0812.3936. [Google Scholar]Publisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Jaekel, M.-T.; Reynaud, S. Quantum Metrology and Relativistic Symmetries. Proceedings 2018, 2, 41. https://doi.org/10.3390/proceedings2010041 AMA Style Jaekel M-T, Reynaud S. Quantum Metrology and Relativistic Symmetries. Proceedings. 2018; 2(1):41. https://doi.org/10.3390/proceedings2010041 Chicago/Turabian Style Jaekel, Marc-Thierry, and Serge Reynaud. 2018. "Quantum Metrology and Relativistic Symmetries" Proceedings 2, no. 1: 41. https://doi.org/10.3390/proceedings2010041 Find Other Styles Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here. Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.
The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of their commutation relations including the energy-time relation. These commutators also describe the relativistic shifts undergone under frame transformations, not only for inertial frames but also for uniformly accelerated frames. The quantum redshift laws differ from their classical counterparts while still obeying universal metric properties. The paper presents this approach in terms closely connected to the seminal Einstein conception of localisation in space-time and refers to already published papers for more technical developments.
first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Physics in the Complex Domain † by Carl M. Bender Physics Department, Washington University, St. Louis, MO 63130, USA † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 47; https://doi.org/10.3390/proceedings2010047 Published: 3 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods, one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments. © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Bender, C.M. Physics in the Complex Domain. Proceedings 2018, 2, 47. https://doi.org/10.3390/proceedings2010047 AMA Style Bender CM. Physics in the Complex Domain. Proceedings. 2018; 2(1):47. https://doi.org/10.3390/proceedings2010047 Chicago/Turabian Style Bender, Carl M. 2018. "Physics in the Complex Domain" Proceedings 2, no. 1: 47. https://doi.org/10.3390/proceedings2010047 Find Other Styles Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here. Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.
first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Irreversibility and Quantum Information Flow under Global & Local Gauge Symmetries † by Cristina Cirstoiu 1,* and David Jennings 2 1 Department of Physics, Imperial College London, London SW7 2AZ, UK 2 Department of Physics, Oxford University, Oxford OX1 2JD, UK * Author to whom correspondence should be addressed. † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 4; https://doi.org/10.3390/proceedings2010004 Published: 5 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we develop an information-theoretic framework to address these questions and show that every symmetric quantum process on a system has an essentially unique decomposition in terms of the flow of symmetry-breaking degrees of freedom between each subsystem and its environment. The decomposition has a natural causal structure that can be represented diagrammatically and makes explicit gauge degrees of freedom between subsystems. Our framework also provides a novel quantum information perspective on lattice gauge theories and a method to gauge general quantum processes beyond Lagrangian formulations. This procedure admits a simple resource-theoretic interpretation, and thus offers a natural context in which features such as information flow and entanglement in gauge theories could be studied. The framework also provides a flexible toolkit with which to analyse the structure of general quantum processes. As an application, we make use of a 'polar decomposition' for quantum processes to discuss incompatibility in the use of quantum resources and to provide a novel perspective in terms of the geometry induced on the orbit of a local process under a symmetry action. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Cirstoiu, C.; Jennings, D. Irreversibility and Quantum Information Flow under Global & Local Gauge Symmetries. Proceedings 2018, 2, 4. https://doi.org/10.3390/proceedings2010004 AMA Style Cirstoiu C, Jennings D. Irreversibility and Quantum Information Flow under Global & Local Gauge Symmetries. Proceedings. 2018; 2(1):4. https://doi.org/10.3390/proceedings2010004 Chicago/Turabian Style Cirstoiu, Cristina, and David Jennings. 2018. "Irreversibility and Quantum Information Flow under Global & Local Gauge Symmetries" Proceedings 2, no. 1: 4. https://doi.org/10.3390/proceedings2010004 Find Other Styles Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here. Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.
We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.
Abstract Quantum mechanics and relativity are two of the most successful theoretical frameworks in modern physics, yet their conceptual foundations remain difficult to reconcile at the deepest level. Quantum theory describes physical systems through states, observables, probabilities, measurement contexts, superposition, entanglement, and nonclassical correlations. Relativity describes physical processes through space-time structure, causal order, invariant physical law, observer-dependent decomposition of time and space, and constraints on signal propagation. This article examines the conceptual relationship between quantum measurement, relativistic causality, and space-time description. The purpose is not to present a mathematical unification but to analyze how the two frameworks organize physical explanation differently and where their interpretive tensions arise. Special attention is given to the measurement problem, the status of quantum states, the role of observers and reference frames, the meaning of locality, the distinction between correlation and causal influence, and the challenge of describing quantum processes without privileging a single global time. The article argues that many apparent conflicts between quantum theory and relativity result from importing classical intuitions into domains where they no longer apply. Quantum entanglement does not permit controllable faster-than-light communication, yet it challenges classical separability. Relativity forbids superluminal signaling, yet it does not require that all physically meaningful correlations be reducible to local classical properties. Measurement introduces another difficulty because standard quantum theory often describes state update in a way that appears instantaneous, while relativistic space-time does not provide a universal present. The discussion develops a conceptual framework in which quantum measurement is treated as a physical interaction, relativistic causality as a constraint on operational influence, and space-time description as an organizing structure for events rather than a simple background stage. This analysis is relevant for quantum field theory, quantum information, relativistic quantum foundations, and future approaches to quantum gravity.
first_page settings Order Article Reprints Font Type: Arial Georgia Verdana Font Size: Aa Aa Aa Line Spacing:    Column Width:    Background: Open AccessAbstract Quantum Simulation of SU(4) Symmetric Spin Lattice Models † by Bruno Uchoa Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA † Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017. Proceedings 2018, 2(1), 39; https://doi.org/10.3390/proceedings2010039 Published: 8 January 2018 (This article belongs to the Proceedings of The First International Conference on Symmetry) Download Download PDF Download PDF with Cover Download XML Versions Notes Quantum spin-orbital liquids are strongly correlated states that emerge from quantum frustration between spin and orbital degrees of freedom. Those states are highly entangled, have non-local excitations but do not break any symmetries. A promising route towards observing those elusive states is the creation of artificial Mott insulators, where antiferromagnetic correlations between spins and orbitals can be designed. I will show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models in the Mott regime. The antiferromagnetic correlations follow from super-exchange interactions between Coulomb impurity bound states at quarter filling, with spin and valley degeneracies. I propose that quantum spin-orbital liquids can be engineered in artificially designed solid-state systems at vastly higher temperatures than achievable in optical lattices with cold atoms. © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Share and Cite MDPI and ACS Style Uchoa, B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings 2018, 2, 39. https://doi.org/10.3390/proceedings2010039 AMA Style Uchoa B. Quantum Simulation of SU(4) Symmetric Spin Lattice Models. Proceedings. 2018; 2(1):39. https://doi.org/10.3390/proceedings2010039 Chicago/Turabian Style Uchoa, Bruno. 2018. "Quantum Simulation of SU(4) Symmetric Spin Lattice Models" Proceedings 2, no. 1: 39. https://doi.org/10.3390/proceedings2010039 Find Other Styles Article Metrics No No Article Access Statistics Multiple requests from the same IP address are counted as one view.