Williams College

Theory of games and economic behavior

This is the classic work upon which modern-day game theory is based. What began more than sixty years ago as a modest proposal that a mathematician and an economist write a shor...

Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels

An unknown quantum state \ensuremath{\Vert}\ensuremath{\varphi}〉 can be disassembled into, then later reconstructed from, purely classical information and purely nonclassical Ei...

Entanglement of Formation of an Arbitrary State of Two Qubits

The entanglement of a pure state of a pair of quantum systems is defined as\nthe entropy of either member of the pair. The entanglement of formation of a\nmixed state is defined...

Mixed-state entanglement and quantum error correction

Entanglement purification protocols (EPP) and quantum error-correcting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EP...

Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states (e.g., singlets shared through a noisy channel), can prepare a smaller numbe...

Entanglement of a Pair of Quantum Bits

The ``entanglement of formation'' of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no furthe...

Scientists' warning on invasive alien species

ABSTRACT Biological invasions are a global consequence of an increasingly connected world and the rise in human population size. The numbers of invasive alien species – the subs...

Marine20—The Marine Radiocarbon Age Calibration Curve (0–55,000 cal BP)

ABSTRACT The concentration of radiocarbon ( 14 C) differs between ocean and atmosphere. Radiocarbon determinations from samples which obtained their 14 C in the marine environme...

Methods of Applied Mathematics

First Page

A complete classification of quantum ensembles having a given density matrix