![]() ![]() To construct examples of this effect, we take a classical message and encode it into a two-part quantum message: a cyphertext, which is roughly as large as the message, and a much smaller key. In particular, this violation occurs when one defines the information contained in a quantum system as the amount of classical information that can be extracted by the best possible measurement. While this is true for most information measures, in quantum mechanics, there exist natural ways of measuring information that violate this principle by a wide margin. For example, if one receives 10 physical bits, then one's information, regardless of what that information is ‘about’, should not increase by more than 10 bits. ![]() One of the most basic and intuitive properties of most information measures is that the amount of information carried by a physical system must be bounded by its size. Finally, we exhibit a quantum key distribution protocol that is ‘secure’ in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others. We find that classical information is strongly locked almost until it can be completely decoded. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. As such, the effect might be relevant to statistical mechanics or black hole physics. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. ![]() It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. ![]()
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