401 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
Theoretical Setting of Inner Reversible Quantum Measurements
We show that any unitary transformation performed on the quantum state of a
closed quantum system, describes an inner, reversible, generalized quantum
measurement. We also show that under some specific conditions it is possible to
perform a unitary transformation on the state of the closed quantum system by
means of a collection of generalized measurement operators. In particular,
given a complete set of orthogonal projectors, it is possible to implement a
reversible quantum measurement that preserves the probabilities. In this
context, we introduce the concept of "Truth-Observable", which is the physical
counterpart of an inner logical truth.Comment: 11 pages. More concise, shortened version for submission to journal.
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