Quantum Tasks in Minkowski Space
Adrian Kent University of Cambridge
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Entanglement Generation in Relativistic Quantum Fields
PIRSA:12060068
On the Preparation of States in Nonlinear Quantum Mechanics
Nicolas Menicucci Royal Melbourne Institute of Technology University (RMIT)
Photon Location in Rindler Coordinates
PIRSA:12060066
Quantum Communication Between Localized, Non-Inertial Observers
Tim Ralph University of Queensland
PIRSA:12060065
Future-past Correlations in Relativistic Quantum Information
Jorma Louko University of Nottingham
PIRSA:12060064
Uncertainty Relations on a Planck Lattice and Black Hole Temperature
Fabio Scardigli Politecnico Milano
PIRSA:12060063
Quantum Limits to the Measurement of Spacetime Geometry
Seth Lloyd Massachusetts Institute of Technology (MIT) - Center for Extreme Quantum Information Theory (xQIT)
PIRSA:12060061
A Fully-Relativistic Bandlimit on Quantum Fields' Two-Point Correlation Functions
Aidan Chatwin-Davies University of Rhode Island
PIRSA:12060041
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Quantum Tasks in Minkowski Space
Adrian Kent University of Cambridge
The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics. In this talk I describe a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography. -
Entanglement Generation in Relativistic Quantum Fields
PIRSA:12060068We present a general, analytic recipe to compute the entanglement that is generated between arbitrary, discrete modes of bosonic quantum fields by Bogoliubov transformations. Our setup allows the complete characterization of the quantum correlations in all Gaussian field states. Additionally, it holds for all Bogoliubov transformations. These are commonly applied in quantum optics for the description of squeezing operations, relate the modedecompositions of observers in different regions of curved spacetimes, and describe observers moving along non-stationary trajectories. We focus on a quantum optical example in a cavity quantum electrodynamics setting: an uncharged scalar field within a cavity provides a model for an optical resonator, in which entanglement is created by non-uniform acceleration.We show that the amount of generated entanglement can be magnified by initialsingle-mode squeezing, for which we provide an explicit formula.Applications to quantum fields in curved spacetimes, such as an expanding universe, are discussed. -
On the Preparation of States in Nonlinear Quantum Mechanics
Nicolas Menicucci Royal Melbourne Institute of Technology University (RMIT)
Recent analysis of closed timelike curves from an information-theoretic perspective has led to contradictory conclusions about their information-processing power. One thing is generally agreed upon, however, which is that if such curves exist, the quantum-like evolution they imply would be nonlinear, but the physical interpretation of such theories is still unclear. It is known that any operationally verifiable instance of a nonlinear, deterministic evolution on some set of pure states makes the density matrix inadequate for representing mixtures of those pure states. We re-cast the problem in the language of operational quantum mechanics, building on previous work to show that the no-signalling requirement leads to a splitting of the equivalence classes of preparation procedures. This leads to the conclusion that any non-linear theory satisfying certain minimal conditions must be regarded as inconsistent unless it contains distinct representations for the two different kinds of mixtures, and incomplete unless it contains a rule for determining the physical preparations associated with each type. We refer to this as the `preparation problem' for nonlinear theories. -
Photon Location in Rindler Coordinates
PIRSA:12060066Bases of orthonormal localized states are constructed in Rindler coordinates and applied to an Unruh detector with good time resolution and an accelerated rod-like array detector. 
Any Quantum State Can be Cloned in the Presence of a Closed Timelike Curve
PIRSA:12060075Using the Deutsch approach, we show that the no-cloning theorem can be circumvented in the presence of closed timelike curves, allowing the perfect cloning of a quantum state chosen randomly from a finite alphabet of states. Further, we show that a universal cloner can be constructed that when acting on a completely arbitrary qubit state, exceeds the no-cloning bound on fidelity. Since the “no cloning theorem” has played a central role in the development of quantum information science, it is clear that the existence of closed timelike curves would radically change the rules for quantum information technology.-
Quantum Communication Between Localized, Non-Inertial Observers
Tim Ralph University of Queensland
PIRSA:12060065An unsolved problem in relativistic quantum information research is how to model efficient, directional quantum communication between localised parties in a fully quantum field theoretical framework. We propose a tractable approach to this problem based on calculating expectation values of localized field observables in the Heisenberg Picture. We illustrate our approach by analysing, and obtaining approximate analytical solutions to, the problem of communicating quantum states between an inertial sender, Alice and an accelerated homodyne receiver, Rob. We discuss the effect on quantum protocols carried out over such a communication channel. -
Future-past Correlations in Relativistic Quantum Information
Jorma Louko University of Nottingham
PIRSA:12060064In the Unruh effect, long-distance correlations in a pure quantum state cause accelerated observers to experience the state as a thermal bath. We discuss a similar phenomenon for quantum states that contain correlations between the distant future and the distant past. Examples include Minkowski half-space with a static mirror and an eternal black hole with an unusual global structure behind the horizon. The question of utilising the future-past correlations in quantum information tasks is raised. -
Uncertainty Relations on a Planck Lattice and Black Hole Temperature
Fabio Scardigli Politecnico Milano
PIRSA:12060063After an introduction to generalized uncertainty principle(s), we study uncertainty relations as formulated in a crystal-like universe, whose lattice spacing is of order of Planck length. For Planckian energies, the uncertainty relation for position and momenta has a lower bound equal to zero. Connections of this result with 't Hooft's deterministic quantization proposal, and with double special relativity are briefly presented. We then apply our formulae to (micro) black holes, we derive a new mass-temperature relation for Schwarzschild black holes, and we discuss the new thermodynamic entropy and heat capacity. In contrast to standard results based on Heisenberg and stringy uncertainty relations, we obtain both a finite Hawking's temperature and a zero rest-mass remnant at the end of the (micro) black hole evaporation. [Ref.Paper: PRD 81, 084030 (2010). arXiv:0912.2253] -
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Quantum Limits to the Measurement of Spacetime Geometry
Seth Lloyd Massachusetts Institute of Technology (MIT) - Center for Extreme Quantum Information Theory (xQIT)
PIRSA:12060061This talk analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the fundamental physical bounds to measurement accuracy ensembles of clocks and signals, as in the global positioning system, I present a covariant version of the quantum geometric limit, which states that the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius R and temporal extent is less than or equal to RT divided by the Planck length times the Planck time. The quantum geometric bound limits the number of events or `ops' that can take place in a four-volume of spacetime and is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a three-volume of spacetime. -
A Fully-Relativistic Bandlimit on Quantum Fields' Two-Point Correlation Functions
Aidan Chatwin-Davies University of Rhode Island
PIRSA:12060041The bridge between continuous information and discrete information is provided by sampling theory. In this talk, I will discuss an application of covariant sampling theory to cosmology (see the previous talk by Dr. R. Martin). In cosmology, the two-point correlation function of a quantum field is of central importance because it is a measure of the size of the fluctuations of the quantum field and of the entanglement of the vacuum in a given spacetime. Furthermore, the two-point function is experimentally accessible through the cosmic microwave background. Using covariant sampling theory, I will show how an information-theoretic bandlimit imposed at the Planck scale manifests itself in the two-point function. We will examine this bandlimit in Minkowski space and in de Sitter space. 
A Fully Covariant Information Theoretic Ultraviolet Cutoff for Fields on Expanding FRW Spacetimes
PIRSA:12060060A covariant ultra-violet cutoff on the modes of physical fields on a given space-time can be achieved by cutting off the spectrum of the D'Alembertian of the manifold. This cutoff is a natural generalization of the naive ultra-violet cutoff inEuclidean space which is obtained by simply projecting out frequencies greater in magnitude than a given maximum frequency. Here it is shown that for flat spacetime and expanding FRW spacetimes thiscutoff manifests itself as a decrease in temporal degrees of freedom for large spatial modes. In a large class of expanding FRW spacetimes where the proper time co-ordinate ends at a finite value, it is shown how the numberof temporal degrees of freedom of a fixed spatial mode depends on the magnitude of the spatial mode. We further indicate how the effects of this ultra-violet cutoff on the dynamics of field theories can be studied, and how the resulting modifications to inflationary predictions of the CMB spectrum could be calculated. This talk is based on ongoing joint work with Prof. Achim Kempf (University of Waterloo) and Aidan Chatwin-Davies (UW).