arXiv subjects
Publications and source records attributed to Samuel L. Braunstein.
We propose an error correction coding algorithm for continuous quantum variables. We use this algorithm to construct a highly efficient 5-wavepacket code which can correct arbitrary single wavepacket errors. We show that this class of continuous variable codes is robust against imprecision in the error syndromes. A potential implemetation of the scheme is presented.
We present a toy model for growing wormholes as a model of effective low-energy topology changes. We study the propagation of quantum fields on a $1+1$ spacetime analogous to the trouser-leg topology change. A low-energy effective topology change is produced by a physical model which corresponds to a barrier smoothly changing the tunneling probability between two spatial regions.
An efficient coding circuit is given for the perfect quantum error correction of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The circuit presented employs a double `classical' code, i.e., one for bit flips and one for phase shifts. An implementation of this coding circuit on an ion-trap quantum computer is described that requires 26 laser pulses. A further circuit is presented requiring only 24 laser pulses, making it an efficient protection scheme against arbitrary 1-qubit errors. In addition, the performance of two error correction schemes, one based on the quantum Zeno effect and the other using standard methods, is compared. The quantum Zeno error correction scheme is found to fail completely for a model of noise based on phase-diffusion.
This paper is withdrawn as it is equivalent to the paper quant-ph/9605035 by Gilles Brassard.
We show how to perform error correction of single qubit dephasing by encoding a single qubit into a minimum of three. This may be performed in a manner closely analogous to classical error correction schemes. Further, the resulting quantum error correction schemes are trivially generalized to the minimal encoding of arbitrarily many qubits so as to allow for multiqubit dephasing correction under the sole condition that the environment acts independently on each qubit.
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter---e.g., elapsed time---may be determined via arbitrary data analysis of arbitrary measurements on $N$ identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter---e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincaré group.