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Privacy Amplification in the Isolated Qubits Model

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 Added by Yi-Kai Liu
 Publication date 2014
  fields Physics
and research's language is English
 Authors Yi-Kai Liu




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Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTMs). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTMs which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting.



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243 - Yi-Kai Liu 2014
One-time memories (OTMs) are simple, tamper-resistant cryptographic devices, which can be used to implement sophisticated functionalities such as one-time programs. Can one construct OTMs whose security follows from some physical principle? This is not possible in a fully-classical world, or in a fully-quantum world, but there is evidence that OTMs can be built using isolated qubits -- qubits that cannot be entangled, but can be accessed using adaptive sequences of single-qubit measurements. Here we present new constructions for OTMs using isolated qubits, which improve on previous work in several respects: they achieve a stronger single-shot security guarantee, which is stated in terms of the (smoothed) min-entropy; they are proven secure against adversaries who can perform arbitrary local operations and classical communication (LOCC); and they are efficiently implementable. These results use Wiesners idea of conjugate coding, combined with error-correcting codes that approach the capacity of the q-ary symmetric channel, and a high-order entropic uncertainty relation, which was originally developed for cryptography in the bounded quantum storage model.
We demonstrate heralded qubit amplification for Time-Bin and Fock-state qubits in an all-fibre, telecom-wavelength, scheme that highlights the simplicity, the stability and potential for fully integrated photonic solutions. Exploiting high-efficiency superconducting detectors, the gain, the fidelity and the performance of the amplifier are studied as a function of loss. We also demonstrate the first heralded Fock-state qubit amplifier without post-selection. This provides a significant advance towards demonstrating Device-Independent Quantum Key Distribution as well as fundamental tests of quantum mechanics over extended distances.
69 - Frederic Dupuis 2021
We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched Renyi entropy of order $alpha in (1,2]$; this extends previous results which worked for $alpha=2$. The fact that this proof works for $alpha$ close to 1 means that we can bypass the smooth min-entropy in the many applications where the bound comes from the fully quantum AEP or entropy accumulation, and carry out the whole proof using the Renyi entropy, thereby easily obtaining an error exponent for the final task. This effectively replaces smoothing, which is a difficult high-dimensional optimization problem, by an optimization problem over a single real parameter $alpha$.
119 - Wei Li , Shengmei Zhao 2021
Privacy amplification is an indispensable step in the post-processing of quantum key distribution, which can be used to compress the redundancy of shared key and improve the security level of the key. The commonly used privacy amplification is based on the random selection of universal hash functions, which needs the help of an additional random source, while it does not exist in general. In this paper, we propose a privacy amplification scheme based on composite coding, which is an extension of quantum CSS codes to classical linear codes. Compared with the universal hashing function, the proposed scheme does not need other random sources, and the randomness can be completely provided by the qubit string. Furthermore, the information-theoretic bound for the extraction of the key is obvious in composite coding.
177 - Yi-Kai Liu 2013
One-time memories (OTMs) are simple tamper-resistant cryptographic devices, which can be used to implement one-time programs, a very general form of software protection and program obfuscation. Here we investigate the possibility of building OTMs using quantum mechanical devices. It is known that OTMs cannot exist in a fully-quantum world or in a fully-classical world. Instead, we propose a new model based on isolated qubits -- qubits that can only be accessed using local operations and classical communication (LOCC). This model combines a quantum resource (single-qubit measurements) with a classical restriction (on communication between qubits), and can be implemented using current technologies, such as nitrogen vacancy centers in diamond. In this model, we construct OTMs that are information-theoretically secure against one-pass LOCC adversaries that use 2-outcome measurements. Our construction resembles Wiesners old idea of quantum conjugate coding, implemented using random error-correcting codes; our proof of security uses entropy chaining to bound the supremum of a suitable empirical process. In addition, we conjecture that our random codes can be replaced by some class of efficiently-decodable codes, to get computationally-efficient OTMs that are secure against computationally-bounded LOCC adversaries. In addition, we construct data-hiding states, which allow an LOCC sender to encode an (n-O(1))-bit messsage into n qubits, such that at most half of the message can be extracted by a one-pass LOCC receiver, but the whole message can be extracted by a general quantum receiver.
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