242 research outputs found
Factorization and Entanglement in Quantum Systems
We discuss the question of entanglement versus separability of pure quantum
states in direct product Hilbert spaces and the relevance of this issue to
physics. Different types of separability may be possible, depending on the
particular factorization or split of the Hilbert space. A given orthonormal
basis set for a Hilbert space is defined to be of type (p,q) if p elements of
the basis are entangled and q are separable, relative to a given bi-partite
factorization of that space. We conjecture that not all basis types exist for a
given Hilbert space.Comment: 11 page
Basic Logic and Quantum Entanglement
As it is well known, quantum entanglement is one of the most important
features of quantum computing, as it leads to massive quantum parallelism,
hence to exponential computational speed-up. In a sense, quantum entanglement
is considered as an implicit property of quantum computation itself. But...can
it be made explicit? In other words, is it possible to find the connective
"entanglement" in a logical sequent calculus for the machine language? And
also, is it possible to "teach" the quantum computer to "mimic" the EPR
"paradox"? The answer is in the affirmative, if the logical sequent calculus is
that of the weakest possible logic, namely Basic logic. A weak logic has few
structural rules. But in logic, a weak structure leaves more room for
connectives (for example the connective "entanglement"). Furthermore, the
absence in Basic logic of the two structural rules of contraction and weakening
corresponds to the validity of the no-cloning and no-erase theorems,
respectively, in quantum computing.Comment: 10 pages, 1 figure,LaTeX. Shorter version for proceedings
requirements. Contributed paper at DICE2006, Piombino, Ital
Quantum Computation toward Quantum Gravity
The aim of this paper is to enlight the emerging relevance of Quantum
Information Theory in the field of Quantum Gravity. As it was suggested by J.
A. Wheeler, information theory must play a relevant role in understanding the
foundations of Quantum Mechanics (the "It from bit" proposal). Here we suggest
that quantum information must play a relevant role in Quantum Gravity (the "It
from qubit" proposal). The conjecture is that Quantum Gravity, the theory which
will reconcile Quantum Mechanics with General Relativity, can be formulated in
terms of quantum bits of information (qubits) stored in space at the Planck
scale. This conjecture is based on the following arguments: a) The holographic
principle, b) The loop quantum gravity approach and spin networks, c) Quantum
geometry and black hole entropy. Here we present the quantum version of the
holographic principle by considering each pixel of area of an event horizon as
a qubit. This is possible if the horizon is pierced by spin networks' edges of
spin 1\2, in the superposed state of spin "up" and spin "down".Comment: 11 pages. Contributed to XIII International Congress on Mathematical
Physics (ICMP 2000), London, England, 17-22 Jul 2000. Typos corrected.
Accepted for publication in General Relativity and Gravitatio
Holography, Quantum Geometry and Quantum Information Theory
We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labeled by the spin-1/2 representation of SU(2), which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, which leads to a quantum-computing picture of the early inflationary universe. A discrete micro-causality emerges, where the time parameter is given in terms of the discrete increase of entropy. Then, the model is analysed in the framework of the theory of presheaves (varying sets on a causal set) and we get a quantum history. A (bosonic) Fock space of the whole history is considered. The Fock space wavefunction, which resembles a Bose-Einstein condensate, undergoes decoherence at the end of inflation. This fact seems to be responsible for the rather low entropy of our universe
Computational capacity of the universe
Merely by existing, all physical systems register information. And by
evolving dynamically in time, they transform and process that information. The
laws of physics determine the amount of information that a physical system can
register (number of bits) and the number of elementary logic operations that a
system can perform (number of ops). The universe is a physical system. This
paper quantifies the amount of information that the universe can register and
the number of elementary operations that it can have performed over its
history. The universe can have performed no more than ops on
bits.Comment: 17 pages, TeX. submitted to Natur
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