# Focus: Quantum Info Defies Logic

Published July 16, 1999  |  Phys. Rev. Focus 4, 3 (1999)  |  DOI: 10.1103/PhysRevFocus.4.3

#### Spin Flips and Quantum Information for Antiparallel Spins

N. Gisin and S. Popescu

Published July 12, 1999

Quantum computers promise to perform calculations much faster than silicon-based computers by manipulating the strange rules of quantum mechanics. Since an atom can inhabit many quantum states at once, it can perform many operations simultaneously. But the best ways of storing and transmitting data are sometimes surprising in the quantum realm. In the 12 July PRL a team shows that storing a direction in space with two oppositely directed (antiparallel) spins is more efficient than using two parallel spins, even though in the classical world there is no difference. The finding is an example of the enigmatic behavior researchers will have to understand as they try to develop quantum computers.

If Alice wants to tell Bob which direction to look for her, she can align the spin of an electron in that direction and count on Bob’s spin analyzer to decode the information. The uncertainty principle always limits Bob’s accuracy, but his guess at the direction will be closer if Alice sends a second identically prepared electron. In 1995 Serge Massar of the Free University of Brussels and Sandu Popescu of the University of Cambridge and Hewlett-Packard Laboratories in Bristol, United Kingdom, showed that Bob’s accuracy is maximized if he measures the spins in a way that quantum mechanically “entangles” them–so that they no longer have separate identities–rather than measuring them individually. Now Popescu and Nicolas Gisin of the University of Geneva in Switzerland show that the direction Bob determines would be even more accurate if the pair of spins were antiparallel, rather than parallel.

Popescu explains that the effect is purely quantum mechanical and defies classical intuition. If Alice used a single spin aligned antiparallel to the direction she wanted to communicate, Bob could simply turn his spin analyzer upside down, or just switch the labels on the “spin up” and “spin down” indicator lights. So with one spin, parallel and antiparallel spins provide the same information. But if Alice sends a pair of spins, and Bob uses the optimal measurement technique, the spins must become entangled and measured as a single entity. There is no separate part of Bob’s analyzer devoted to each spin individually, no way for him to reverse the output for one spin and not for the other. Popescu and Gisin show that the “fidelity” of Bob’s measurement is 0.75 for parallel spins and about 0.79 for antiparallel spins, which means that the antiparallel pair contains a bit more information.

Researchers have only recently begun to scrutinize the information content of quantum states, says Popescu, and as they do, “we run into all kinds of paradoxical behaviors like this.” By investigating them he and his colleagues hope to better understand quantum information and provide insights to those developing quantum computation, encryption, and other applications.

“It’s remarkable how many new insights into quantum mechanics one gets” by applying information theory to the quantum world, says William Wootters of Williams College in Williamstown, Massachusetts. He adds that the field has developed mainly in the past few years, even though some of the results, such as those of Gisin and Popescu, could have been discovered many decades ago if anyone had asked the right questions.