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 ${\Bbb Z}_2^{\otimes (N-1)} \otimes S_N$. 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 $N$ state quantum particle is encoded as five $N$ 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