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This was too long for a comment. There are two papers that have a nice characterization of positivity in terms of the Bloch vector: quant-ph/0301152 and quant-ph/0302024. You might be able to use dynamic programming to speed up a check of positivity by using the conditions in these papers. Basically, they reduce the positivity constraint to a constraint on ...

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You are right that there's not much you can do with a single qubit. However it doesn't take many before you can do things that can't be done with classical bits. Here are a few illustrative examples. Communication Imagine I make this offer to you and a friend of yours: I will give you each a classical bit, and then you will each give me a classical bit. If ...

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Because the very act of viewing the code changes it. Maybe not uncrackable but any sniffing will be evident because it will be changed. From RSA Laboratories: Quantum cryptography has a special defense against eavesdropping: If an enemy measures the photons during transmission, he will use the wrong basis half the time, and thus will change some of the ...

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Such statements emerge when trying to capture quantum physics in classical physics terms. In other words, statements like "P or not P is not a valid proposition in a quantum world" are typically made by philosophers who don't really understand quantum physics and stubbornly attempt to map the quantum onto their classical intuition. A much more insightful ...

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