Quantum physics is full of counterintuitive twists, but a proposed concept in quantum information theory could help to relieve some of the perplexities.
He has nearly solved the riddle, but now Bob is at his wits’ end. Alice (who else?) would have the missing bits, he is sure, and so Bob picks up the phone. But how much information will she have to send? How great is his ignorance? How much is there to know?
Classical information theory has well-established answers to such questions: quantum communication, where information is contained in qubits rather than bits, does not. In this week’s issue of Nature, however, Michal Horodecki and colleagues1 present a fresh approach to understanding quantum phenomena that cannot be grasped simply by considering their classical counterparts.
When a quantum state is distributed over two parties, the question arises of how much (quantum) information is required to transfer the full state to one of them. In other words, what is the smallest number of qubits that Alice can send to Bob, and still have the option of sending classical bits at zero cost? Surely, the number of qubits needed — a measure of Bob’s ignorance — is larger than zero? Wrong. Horodecki et al. argue that his ignorance can be negative, when the full quantum state can be transferred by purely classical communication. In this instance, Alice and Bob can have more than just a cheap classical chat: they can also gain an advantage for future exchange, when they will be able to transfer quantum information at no further cost.
The quantum equivalents of key concepts in classical information theory — such as quantum conditional entropy — have not been firmly positioned until now. With their fresh interpretation, the authors are not only likely to impact the field of quantum information, but could also help make better sense of the often bizarre beauty of quantum theory.
Horodecki, M., Oppenheim, J. & Winter, A. Partial quantum information. Nature 436, 673–676 doi:10.1038/nature03909 (2005)
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Trabesinger, A. What do you know!. Nature Phys (2005). https://doi.org/10.1038/nphys104