7,934 research outputs found
Inverse Avalanches On Abelian Sandpiles
A simple and computationally efficient way of finding inverse avalanches for
Abelian sandpiles, called the inverse particle addition operator, is presented.
In addition, the method is shown to be optimal in the sense that it requires
the minimum amount of computation among methods of the same kind. The method is
also conceptually nice because avalanche and inverse avalanche are placed in
the same footing.Comment: 5 pages with no figure IASSNS-HEP-94/7
Correcting Quantum Errors In Higher Spin Systems
I consider the theory of quantum error correcting code (QECC) where each
quantum particle has more than two possible eigenstates. In this higher spin
system, I report an explicit QECC that is related to the symmetry group . This QECC, which generalizes Shor's simple
majority vote code, is able to correct errors arising from exactly one quantum
particle. I also provide a simple encoding algorithm.Comment: In REVTEX 3.0, requires AMS fonts. Typos corrected. To appear in PRA
(Rapid Comm.
Quantum Speed Limit With Forbidden Speed Intervals
Quantum mechanics imposes fundamental constraints known as quantum speed
limits (QSLs) on the information processing speed of all quantum systems. Every
QSL known to date comes from the restriction imposed on the evolution time
between two quantum states through the value of a single system observable such
as the mean energy relative to its ground state. So far these restrictions only
place upper bounds on the information processing speed of a quantum system.
Here I report QSLs each with permissible information processing speeds
separated by forbidden speed intervals. They are found by a systematic and
efficient procedure that takes the values of several compatible system
observables into account simultaneously. This procedure generalizes almost all
existing QSL proofs; and the new QSLs show a novel first order phase transition
in the minimum evolution time.Comment: revised with clarification, 7 pages, to appear in PR
Reply To "Comment on 'Quantum Convolutional Error-Correcting Codes' "
In their comment, de Almedia and Palazzo \cite{comment} discovered an error
in my earlier paper concerning the construction of quantum convolutional codes
(quant-ph/9712029). This error can be repaired by modifying the method of code
construction.Comment: 1 page, to appear in PR
Metrics On Unitary Matrices And Their Application To Quantifying The Degree Of Non-Commutativity Between Unitary Matrices
By studying the minimum resources required to perform a unitary
transformation, families of metrics and pseudo-metrics on unitary matrices that
are closely related to a recently reported quantum speed limit by the author
are found. Interestingly, this family of metrics can be naturally converted
into useful indicators of the degree of non-commutativity between two unitary
matrices.Comment: 13 pages in RevTex 4.1, 2 figures, to appear in QIC. This replacement
concentrates only on the more physics and quantum information aspects of the
results reported in the original manuscript with a more detailed proof. The
mathematical results involving the discovery of several matrix inequalities
reported in the original version will be strengthened and rewritten in a
separate postin
Five Quantum Register Error Correction Code For Higher Spin Systems
I construct a quantum error correction code (QECC) in higher spin systems
using the idea of multiplicative group character. Each state quantum
particle is encoded as five state quantum registers. By doing so, this code
can correct any quantum error arising from any one of the five quantum
registers. This code generalizes the well-known five qubit perfect code in
spin-1/2 systems and is shown to be optimal for higher spin systems. I also
report a simple algorithm for encoding. The importance of multiplicative group
character in constructing QECCs will be addressed.Comment: Revised version, to appear in Phys.Rev.A (Rapid Communications). 4
pages in Revtex 3.1, using amssymb.st
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