This is a course on Relativistic Quantum Information (RQI), whose goal is to explore quantum information beyond the confines of its non-relativistic orgins. (see course announcemnt In this course we will explore such topics as the role of Lorentz transformations on qubits used for quantum information processing (QIP), how accelerated frames and gravity effect qubits - including the Unruh and Hawking effect, the role of gravity on decoherence, entanglement in the presense of horizons and black holes and its relation to the generalized second law of black hole dynamics, can qubits be used to transfer information about reference frames, and the self consistency of quantum mechanics and quantum information in the presence of closed timelike loops.

This course will be graded completely upon class participation. We will explore the articles listed in RQI articles (which will continually expanded and added to). Students will be asked to give presentations (chalk board, power point, etc...) on articles and topics that they find interesting. If there is holes in our understanding of certain topics, students and/or I will present short background lectures to bring the class up to speed. The goal here is to expand your event horizons and think about quantum information in a broader setting - and have fun at the same time. There are a lot of interesting ideas out there, (many of which have come about in the last 5-10 years) about the the merging of quantum mechanics and gravity, and we want to explore how quantum information might possibly shed some light, or produce new insights into these areas.

Reading Assignments

Other articles and books of interest.

Transformation of states in Special Relativity; Bell Inequalities/Lorentz transformations.

(by date; see lecture 3 notes: end pages P1 and P2 for description)
1. Quantum entropy and special relativity  Peres, Scudo and Terno, PRL 88, p230402 (2002).
2. Lorentz invariance of entanglement   Alsing, Milburn quant-ph/0203051; Quant. Inf. Comput 2, p487 (2002).
3. Quantum entanglement of moving bodies  Gingrich and Adami, PRL 89, p270402 (2002).
4. Entangled light in moving frames  Gingrich, Bergou and Adami, PRA 68, p042102 (2003).
5. EPR correlation seen from moving observers  Terashima and Ueda, quant-ph/0204138 v4 (4 Nov 2002), Quantum Inf.Comput. 3, 224-228 (2003). Relativistic EPR correlationa nd Bell's inequality   quant-ph/0211177, (longer version of the above paper, more details)
6. Lorentz-invariant Bell Inequalities  Kim and Son, quant-ph/0408127.
7. Photon polarization and Wigner's little group  Caban and Rembielinski, PRA 68, 042107 (2003).
8. Relativistically invariant quantum information  PRA 71, p012302 (2005).
9. Dynamics of momentum entanglement in lowest order QED  PRA 73, p012335 (2006).

   Acceleration, Unruh/Hawking effect

   1. Vacuum noise and stress induced by uniform acceleration: Hawking-Unruh effect in Rindler Manifold in arbitrary dimensions,   S. Takagi, Progress in Theoretical Physics Supplement vol. {88, pp. 1-142 (1986); Chapter 2, "Thermalization Theorem."
   2. A secret tunnel through the horizon   parikh, hep-th/0405160
      Hawking radiation as tunneling   parikh and wilczek, hep-th/9907001
   3. Rindler observers, correlated states, boundary conditions and the meaning of the thermal spectrum   pringle, PRD39, p2178 (1989)
   4. Minkowski Bessel modes  Gerlach, gr-qc/9910097

   Quantum Information and Black Holes/Entropy/Area/Generalized 2nd Law of Thermodynamics

   1. Generalized second law of black hole thermodynamics and quantum information theory,   Hosoya, Carlini and Shinomura, PRD 63, p104008 (2001).
      Quantum Entropy bound by information in black hole spacetime  Hosoya and Carlini, quant-ph/0203085.
   2. Locking Information in Black Hole   Smolin and Oppenheim PRL 96, p081302 (2006).
   3. The Holographic Entropy Bound and Local QFT   Yurtsever, PRL91 p 041302 (2003)
   4. Entanglement, entropy, black holes and hologrpahy   Buniy and Hsu, hep-th/0510021
      Physical limits on quantum information processing   Buniy and Hsu, hep-th/0607082
   5. Quantum source of entropy for black holes  Bombelli et al., PRD34, p373 (1986)
      Entropy and area  Srednicki, PRL71, p666 (1993)
      Entropy, entanglement, and area: analytical results for harmonic lattice systems   Plenio et al., PRL94 p060503 (2005)
   6. Almost certain escape from black hole in final state projection models   Lloyd, PRL 96, p061302 (2006)
      Comment on "The black hole final state"   Gottesman and Preskill, hep-th/0311269
      Signaling, entanglement and quantum evolution beyond Cauchy horizons   Yurtsever and Hockney, gr-qc/0409112

   Quantum Mechanics/Information and Closed Timelike Curves

   Quantum mechanics near closed timelike lines   Deutsch, PRD44, p3197 (1991)
   Quantum computational complexity in the presence of closed timelike curves   Bacon, PRA70, p 032309 (2004)
   Time displace entanglement and non-linear quantum evolution  Ralph, quant-ph/0510038
   

   Class Date	Topic(s)	Presenter(s)
   22 Aug	Class Organization: BriefOverview of RQI articles	Paul Alsing
   29 Aug	Review of Special Relativity; Intro to QFT	Paul Alsing   lecture notes :  Reivew of SR and Intro to QFT
   5 Sep	Introduction to Entanglement	Paul Alsing   lecture notes:   Introduction to Entanglement
   12 Sep	Missed Class	Need to Schedule Makeup Date
   19 Sep	Bell inequalities; Representation and transformation of staes in QFT Wigner rotations	Patrick Kilian Presentation:   Bell Inequalities; Paul Alsing   lecture notes:   Representations and Transformation of States in QFT
   26 Sep	Representation and transformation of staes in QFT Wigner rotations (cont.)	Paul Alsing   article:   On Quantum Entropy and Special Relativity A. Peres, P.F. Scudo and D.R. Terno, PRL88, 230402 (2002), On Quantum Entanglement of Moving Bodies R.M. Gingrich and C. Adami, PRL89, p270402 (2002), On Entanglement and Lorentz Transformation P.M. Alsing and G.J. Milburn, quant-ph/0203051, On Relativistic EPR correlation and Bell's inequality H. Terashima and M. Ueda, quant-ph/0211177
   3 Oct	Finish up lectures on transformation of states in QFT under Poincare Group	Paul Alsing   Representations and Transformation of States in QFT
   10 Oct	Class presentations on selected papers	Wigner angle for massive particles Paul   Wigner angle for massless particles Pieter and David   Bell Inequality for massive particles: Terashima and Ueda paper Patrick   Covariant Bell Inequalities: Kim and Son paper Iris   Invariant Quantum Info: Bartlett and Terno paper
   19 Oct (Thurs)	GR in a Nutshell	Iris   Invariant Quantum Info: Bartlett and Terno paper Paul   GR in a Nutshell; Wigner rotation in a gravitational field lecture notes article   Terashima and Ueda, PRA 69, p032113 (2004)
   24 Oct (Thurs)	QFT in Curved Spacetime	Paul   QFT in Curved Spacetime lecture notes
   26 Oct (Thurs)	QFT in Curved Spacetime	Paul   QFT in Curved Spacetime lecture notes
   31 Oct	The Unruh-Hawking Effect	Paul   The Unruh-Hawking Effect and analogies lecture notes (Download Notes: on PC: right-click to use "Save Target As"; on Mac: control-click to use "Save Link Target As") Brief survey of the Unruh effect lecture notes
   2 Nov	Acceleration in Special Relativity and Teleportation	Alsing and Milburn  Teleportation with a uniformly accelerated partner; quant-ph/0302179 Teleportation with a uniformly accelerated partner, PRL 91, p180404 (2003).
   7 Nov	Quantum Information and Black Holes	lecture notes Kerr Metric and Black Hole Thermodynamics
   14 Nov	Generalized Law of BH Thermodynamics and Quantum Information	Seth: Entropy, entanglement, and area: analytical results for harmonic lattice systems   Plenio et al., PRL94 p060503 (2005) Notes on Plenio paper  Generalized second law of black hole thermodynamics and quantum information theory Hosoya, Carlini and Shimomura, PRD63, p104008 (2001). see also Quantum Entropy bound by information in black hole spacetime  Hosoya and Carlini, quant-ph/0203085. Paul: lecture notes on Generalized second law of black hole thermodynamics and quantum information theory
   21 Nov	Discussion of various papers	Quantum mechanics near closed timelike lines D. Deutsch PRD44, p3197 (1991). Quantum computational complexity in the presence of closed timelike curves Bacon, PRA 70, p032309 (2004). David Notes on Bacon paper: nonlinear QM calculation  Patrick Notes on Bacon paper: complexity  Aaron: Parikh papers: A secret tunnel through the horizon Parikh hep-th/0405160 Hawking Radiation as Tunneling Parikh and Wilczek hep-th/9907001
   28 Nov
   5 Dec No Class

   
   Last updated/modified: 20 Jan 04