Topic: "Why Does Nature Like the Square Root of Negative One?" (Video)
Abstract: Abstract:This talk will not answer the question posed in the title. Instead, the question motivates an investigation into the differences between standard quantum theory, based on the complex numbers, and a closely analogous theory based on the real numbers. I focus particularly on three information-theoretic questions: (i) Is information transferred optimally from preparation to measurement? (ii) Is a quantum state locally accessible? (iii) Is entanglement “monogamous”? It turns out that the two theories give opposite answers to all three questions. Though the answers don’t tell us why nature prefers the complex theory, they do tell us that the choice between real and complex numbers has significant information-theoretic consequences.