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Foiling quantum cheats
Quantum cryptography — one of the most promising applications in the rapidly developing field of quantum information processing — allows two friendly parties, prosaically known as Alice and Bob, to communicate with each other securely without anyone listening in. But what if Alice and Bob find themselves in a messy divorce, and want to decide how to divide their belongings without having to meet face to face? How might they do this in an atmosphere of mutual distrust? Writing in Physical Review Letters this week, Robert Spekkens and Terry Rudolph describe a quantum protocol that could help to resolve Alice and Bob's dilemma. It allows them to divide their property on the flip of a coin while minimizing the amount of cheating that each can get away with. Consider a situation in which Alice and Bob wish to decide who will keep the pet budgerigar. To decide the matter, they agree that one of them will toss a coin and the other will pick heads or tails. Classically, there is no way to call the result down a telephone line without the possibility of outright cheating. But using quantum cryptography, cheating can be minimized. For example, after flipping a coin, Alice prepares two copies of the quantum system in a state that reflects the outcome, and sends one copy to Bob. Once Bob receives his copy, he makes a prediction of heads or tails without making a measurement, and then Alice tells him whether he won or not. If Bob loses, he can check Alice's honesty by measuring the system sent to him. If Alice loses, Bob returns the system (without making any measurement) so that she can check his honesty by comparing it to her copy. Because any measurement made by Bob will affect the state of the copy sent to him, comparing the returned system with that retained by Alice will let her know whether Bob's guess was genuine. Although cheat-sensitive quantum protocols such as this are far better than classical approaches, which cannot guard against any level of cheating, they are not perfect. For example, although there is no way for Bob to ensure he wins without being caught, he can increase his chances by carrying out an imperfect measurement of the system sent to him that only subtly affects its state, thereby reducing his chance of being caught when Alice subsequently tests this state. To investigate the cheat-sensitivity and limits to which the outcome of such quantum coin flipping protocols can be influenced, Spekkens and Rudolph present a variation of the above protocol. In their protocol, if both parties are honest, the probability of either party winning is exactly 1/2 — just as in a classical coin toss. But assuming that either Alice or Bob cannot be trusted, the exact nature of the protocol can be altered. At the extremes, this protocol can be designed so that it is impossible for one party to cheat without being caught, but it allows the other to increase their chances of winning up to a maximum of 1/√2 without detection. In between, although it is not possible to achieve a situation where neither party can cheat without being caught, it is possible to make a trade-off where the maximum probability of winning for both parties is smaller than this 1/√2 limit. Quantum protocol for cheat-sensitive weak coin
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