1,491 research outputs found
Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
Quantum gravity is studied nonperturbatively in the case in which space has a
boundary with finite area. A natural set of boundary conditions is studied in
the Euclidean signature theory, in which the pullback of the curvature to the
boundary is self-dual (with a cosmological constant). A Hilbert space which
describes all the information accessible by measuring the metric and connection
induced in the boundary is constructed and is found to be the direct sum of the
state spaces of all Chern-Simon theories defined by all choices of
punctures and representations on the spatial boundary . The integer
level of Chern-Simons theory is found to be given by , where is the cosmological constant and is a
breaking phase. Using these results, expectation values of observables which
are functions of fields on the boundary may be evaluated in closed form. The
Beckenstein bound and 't Hooft-Susskind holographic hypothesis are confirmed,
(in the limit of large area and small cosmological constant) in the sense that
once the two metric of the boundary has been measured, the subspace of the
physical state space that describes the further information that the observer
on the boundary may obtain about the interior has finite dimension equal to the
exponent of the area of the boundary, in Planck units, times a fixed constant.
Finally,the construction of the state space for quantum gravity in a region
from that of all Chern-Simon theories defined on its boundary confirms the
categorical-theoretic ``ladder of dimensions picture" of Crane.Comment: TEX File, Minor Changes Made, 59 page
The quantization of unimodular gravity and the cosmological constant problem
A quantization of unimodular gravity is described, which results in a quantum
effective action which is also unimodular, ie a function of a metric with fixed
determinant. A consequence is that contributions to the energy momentum tensor
of the form of the metric times a spacetime constant, whether classical or
quantum, are not sources of curvature in the equations of motion derived from
the quantum effective action. This solves the first cosmological constant
problem, which is suppressing the enormous contributions to the cosmological
constant coming from quantum corrections. We discuss several forms of uniodular
gravity and put two of them, including one proposed by Henneaux and Teitelboim,
in constrained Hamiltonian form. The path integral is constructed from the
latter. Furthermore, the second cosmological constant problem, which is why the
measured value is so small, is also addressed by this theory. We argue that a
mechanism first proposed by Ng and van Dam for suppressing the cosmological
constant by quantum effects obtains at the semiclassical level.Comment: 22 pages, no figure
How to efficiently select an arbitrary Clifford group element
We give an algorithm which produces a unique element of the Clifford group
C_n on n qubits from an integer 0\le i < |C_n| (the number of elements in the
group). The algorithm involves O(n^3) operations. It is a variant of the
subgroup algorithm by Diaconis and Shahshahani which is commonly applied to
compact Lie groups. We provide an adaption for the symplectic group Sp(2n,F_2)
which provides, in addition to a canonical mapping from the integers to group
elements g, a factorization of g into a sequence of at most 4n symplectic
transvections. The algorithm can be used to efficiently select randomelements
of C_n which is often useful in quantum information theory and quantum
computation. We also give an algorithm for the inverse map, indexing a group
element in time O(n^3).Comment: 7 pages plus 4 1/2 pages of python cod
Additive Extensions of a Quantum Channel
We study extensions of a quantum channel whose one-way capacities are
described by a single-letter formula. This provides a simple technique for
generating powerful upper bounds on the capacities of a general quantum
channel. We apply this technique to two qubit channels of particular
interest--the depolarizing channel and the channel with independent phase and
amplitude noise. Our study of the latter demonstrates that the key rate of BB84
with one-way post-processing and quantum bit error rate q cannot exceed
H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur
Unimodular loop quantum gravity and the problems of time
We develop the quantization of unimodular gravity in the Plebanski and
Ashtekar formulations and show that the quantum effective action defined by a
formal path integral is unimodular. This means that the effective quantum
geometry does not couple to terms in the expectation value of the
energy-momentum tensor proportional to the metric tensor. The path integral
takes the same form as is used to define spin foam models, with the additional
constraint that the determinant of the four metric is constrained to be a
constant by a gauge fixing term. We also review the proposal of Unruh, Wald and
Sorkin- that the hamiltonian quantization yields quantum evolution in a
physical time variable equal to elapsed four volume-and discuss how this may be
carried out in loop quantum gravity. This then extends the results of
arXiv:0904.4841 to the context of loop quantum gravity.Comment: 14 pages lagex, no figure
Classical signature of quantum annealing
A pair of recent articles concluded that the D-Wave One machine actually
operates in the quantum regime, rather than performing some classical
evolution. Here we give a classical model that leads to the same behaviors used
in those works to infer quantum effects. Thus, the evidence presented does not
demonstrate the presence of quantum effects.Comment: 8 pages, 3 pdf figure
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