When Amazon.com Inc was developing its most advanced tablet to date, it asked a little-known company to solve a tricky problem with the screen: how to produce rich colors without draining battery life. With the help of Milpitas, California-based Nanosys Inc, the Kindle Fire HDX 7 became one of Amazon’s best-selling tablets, winning critical acclaim for its vibrant display. Quantum dots, which are semiconductor crystals 10,000 times finer than a human hair. “If you put a regular LCD display next to a quantum-dot LCD display, your grandmother can tell the difference,” said Jason Carlson, chief executive officer of QD Vision Inc, which makes quantum dots for Sony Corp’s Triluminos TV.