Building one-time memories from isolated qubits

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One-time memories (OTM's) are simple tamper-resistant cryptographic devices,\nwhich can be used to implement one-time programs, a very general form of\nsoftware protection and program obfuscation. Here we investigate the\npossibility of building OTM's using quantum mechanical devices. It is known\nthat OTM's cannot exist in a fully-quantum world or in a fully-classical world.\nInstead, we propose a new model based on "isolated qubits" -- qubits that can\nonly be accessed using local operations and classical communication (LOCC).\nThis model combines a quantum resource (single-qubit measurements) with a\nclassical restriction (on communication between qubits), and can be implemented\nusing current technologies, such as nitrogen vacancy centers in diamond. In\nthis model, we construct OTM's that are information-theoretically secure\nagainst one-pass LOCC adversaries that use 2-outcome measurements.\n Our construction resembles Wiesner's old idea of quantum conjugate coding,\nimplemented using random error-correcting codes; our proof of security uses\nentropy chaining to bound the supremum of a suitable empirical process. In\naddition, we conjecture that our random codes can be replaced by some class of\nefficiently-decodable codes, to get computationally-efficient OTM's that are\nsecure against computationally-bounded LOCC adversaries.\n In addition, we construct data-hiding states, which allow an LOCC sender to\nencode an (n-O(1))-bit messsage into n qubits, such that at most half of the\nmessage can be extracted by a one-pass LOCC receiver, but the whole message can\nbe extracted by a general quantum receiver.\n