scholarly journals Duality of privacy amplification against quantum adversaries and data compression with quantum side information

2010 ◽  
Vol 467 (2130) ◽  
pp. 1604-1623 ◽  
Author(s):  
Joseph M. Renes
Keyword(s):  
Information Processing ◽  
Data Compression ◽  
Uncertainty Principle ◽  
Quantum Information Processing ◽  
Side Information ◽  
Quantum Error Correction ◽  
Privacy Amplification ◽  
Classical Information ◽  
Quantum Error ◽  
Quantum Side Information

Information processing protocols are typically built out of simpler parts, called primitives, and two of the most important such primitives are privacy amplification (PA) and data compression. The former extracts the truly secret part of some classical data, while the latter squeezes it into the smallest possible form. We show these tasks are dual in the setting of quantum information processing. Specifically, the tasks of PA of classical information against quantum adversaries and classical data compression with quantum side information are dual in the sense that the ability to perform one implies the ability to perform the other. The duality arises because the two protocols are connected by complementarity and the uncertainty principle in the quantum setting. Applications include a new uncertainty principle formulated in terms of smooth min- and max-entropies, which are useful in the study of one-shot protocols, as well as new conditions for approximate quantum error correction.

scholarly journals Non-Asymptotic Classical Data Compression with Quantum Side Information

2020 ◽  
pp. 1-1
Author(s):  
Hao-Chung Cheng ◽  
Eric P. Hanson ◽  
Nilanjana Datta ◽  
Min-Hsiu Hsieh
Keyword(s):  
Data Compression ◽  
Side Information ◽  
Quantum Side Information

scholarly journals Encryption with weakly random keys using quantum ciphertext

2012 ◽  
Vol 12 (5&6) ◽  
pp. 395-403
Author(s):  
Jan Bouda ◽  
Matej Pivoluska ◽  
Martin Plesch
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Single Case ◽  
Full Information ◽  
Classical Information ◽  
Random Source ◽  
Random Keys

The lack of perfect randomness can cause significant problems in securing communication between two parties. McInnes and Pinkas \cite{McInnesPinkas-ImpossibilityofPrivate-1991} proved that unconditionally secure encryption is impossible when the key is sampled from a weak random source. The adversary can always gain some information about the plaintext, regardless of the cryptosystem design. Most notably, the adversary can obtain full information about the plaintext if he has access to just two bits of information about the source (irrespective on length of the key). In this paper we show that for every weak random source there is a cryptosystem with a classical plaintext, a classical key, and a quantum ciphertext that bounds the adversary's probability $p$ to guess correctly the plaintext strictly under the McInnes-Pinkas bound, except for a single case, where it coincides with the bound. In addition, regardless of the source of randomness, the adversary's probability $p$ is strictly smaller than $1$ as long as there is some uncertainty in the key (Shannon/min-entropy is non-zero). These results are another demonstration that quantum information processing can solve cryptographic tasks with strictly higher security than classical information processing.

scholarly journals Neutron Interferometry at the National Institute of Standards and Technology

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
D. A. Pushin ◽  
M. G. Huber ◽  
M. Arif ◽  
C. B. Shahi ◽  
J. Nsofini ◽  
...  
Keyword(s):  
Quantum Information Processing ◽  
Energy Difference ◽  
Quantum Error Correction ◽  
Quantum Mechanical ◽  
Material Research ◽  
Neutron Interferometry ◽  
Neutron Interferometer ◽  
Quantum Error ◽  
New Facility ◽  
Vibrational Noise

Neutron interferometry has proved to be a very precise technique for measuring the quantum mechanical phase of a neutron caused by a potential energy difference between two spatially separated neutron paths inside interferometer. The path length inside the interferometer can be many centimeters (and many centimeters apart) making it very practical to study a variety of samples, fields, potentials, and other macroscopic medium and quantum effects. The precision of neutron interferometry comes at a cost; neutron interferometers are very susceptible to environmental noise that is typically mitigated with large, active isolated enclosures. With recent advances in quantum information processing especially quantum error correction (QEC) codes we were able to demonstrate a neutron interferometer that is insensitive to vibrational noise. A facility at NIST’s Center for Neutron Research (NCNR) has just been commissioned with higher neutron flux than the NCNR’s older interferometer setup. This new facility is based on QEC neutron interferometer, thus improving the accessibility of neutron interferometry to the greater scientific community and expanding its applications to quantum computing, gravity, and material research.

scholarly journals Cost-optimal single-qubit gate synthesis in the Clifford hierarchy

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 396
Author(s):  
Gary J. Mooney ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Error Correction ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Quantum Error Correction ◽  
Practical Implementation ◽  
Error Correction Code ◽  
Universal Quantum ◽  
Arbitrary Precision ◽  
Qubit Gate ◽  
Quantum Error

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary operators built from logical gates within the quantum error correction code. A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision by assembling sequences of logical gates chosen from a small set of universal gates that are fault-tolerantly performable while encoded in a quantum error-correction code. However, current procedures do not yet support individual assignment of base gate costs and many do not support extended sets of universal base gates. We analysed cost-optimal sequences using an exhaustive search based on Dijkstra’s pathfinding algorithm for the canonical Clifford+T set of base gates and compared them to when additionally including Z-rotations from higher orders of the Clifford hierarchy. Two approaches of assigning base gate costs were used. First, costs were reduced to T-counts by recursively applying a Z-rotation catalyst circuit. Second, costs were assigned as the average numbers of raw (i.e. physical level) magic states required to directly distil and implement the gates fault-tolerantly. We found that the average sequence cost decreases by up to 54±3% when using the Z-rotation catalyst circuit approach and by up to 33±2% when using the magic state distillation approach. In addition, we investigated observed limitations of certain assignments of base gate costs by developing an analytic model to estimate the proportion of sets of Z-rotation gates from higher orders of the Clifford hierarchy that are found within sequences approximating random target gates.

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