203 citations · 362 across the 11 of their papers we have counts for
11 papers
The -Divisor Graph on is Planar and 3-Colorable
Michael D. Walton, Zachary D. Walton
We prove that a divisor graph on an interval of integers is a planar graph whenever the interval satisfies , and that 7 is the greatest such real number for which…
Quantum Mechanics as Naturalized Time
Zachary D. Walton, Bernard S. McNamara, Tommaso Toffoli
We bring together two topics (quantum mechanics and time passage) with the goal of clarifying questions about each. Specifically, we claim that the formalism of quantum mechanics p…
Generating Polarization-Entangled Photon Pairs with Arbitrary Joint Spectrum
Zachary D. Walton, Alexander V. Sergienko, Bahaa E. A. Saleh +1
We present a scheme for generating polarization-entangled photons pairs with arbitrary joint spectrum. Specifically, we describe a technique for spontaneous parametric down-convers…
Symmetric Autocompensating Quantum Key Distribution
Zachary D. Walton, Alexander V. Sergienko, Lev B. Levitin +2
We present quantum key distribution schemes which are autocompensating (require no alignment) and symmetric (Alice and Bob receive photons from a central source) for both polarizat…
Decoherence-Free Subspaces in Quantum Key Distribution
Zachary D. Walton, Ayman F. Abouraddy, Alexander V. Sergienko +2
We demonstrate that two recent innovations in the field of practical quantum key distribution (one-way autocompensation and passive detection) are closely related to the methods de…
Maximum speed of quantum gate operation
Lev B. Levitin, Tommaso Toffoli, Zachary Walton
We consider a quantum gate, driven by a general time-dependent Hamiltonian, that complements the state of a qubit and then adds to it an arbitrary phase shift. It is shown that the…