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Capability of local operations and classical communication to distinguish bipartite unitary operations

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Physical Review A 2017年第5期96卷 052327-052327页

作者： Lvzhou Li Shenggen Zheng Haozhen Situ Daowen Qiu Institute of Computer Science Theory School of Data and Computer Science Sun Yat-Sen University Guangzhou 510006 China The Key Laboratory of Machine Intelligence and Advanced Computing (Sun Yat-Sen University) Ministry of Education Guangzhou 510006 China College of Mathematics and Informatics South China Agricultural University Guangzhou 510642 China

The problem studied in this paper is, if the number of queries to unitary operations is fixed, say k, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of k=1, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain the following: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfectly distinguishable by LOCC also, and (ii) if they are not perfectly distinguishable by global operations, then LOCC can achieve the same optimal discrimination probability as the global operations.

关键词： quantum gates Resource theories

Structure of correlated worldline theories of quantum gravity

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Physical Review D 2018年第8期98卷 084052-084052页

作者： A. O. Barvinsky D. Carney P. C. E. Stamp Theory Department Lebedev Physics Institute Leninsky Prospect 53 Moscow 119991 Russia Pacific Institute of Theoretical Physics University of British Columbia 6224 Agricultural Road Vancouver British Columbia V6T 1Z1 Canada Joint Center for Quantum Information and Computer Science 3100 Atlantic Building University of Maryland College Park Maryland 20742 USA Joint Quantum Institute National Institute of Standards and Technology 100 Bureau Drive Gaithersburg Maryland 20899 USA Department of Physics and Astronomy University of British Columbia 6224 Agricultural Road Vancouver British Columbia V6T 1Z1 Canada School of Mathematics and Statistics Victoria University of Wellington P.O. Box 600 Wellington 6140 New Zealand

We consider the general form of correlated worldline (CWL) theories of quantum gravity. We show that one can have two different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to two-point and four-point functions, again for each version of the theory, up to second order in the gravitational coupling.

关键词： Alternative gravity theories General relativity Open quantum systems & decoherence quantum gravity quantum-to-classical transition

Cr doping induced negative transverse magnetoresistance in Cd3As2 thin films

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Physical Review B 2018年第8期97卷 085303-085303页

作者： Yanwen Liu Rajarshi Tiwari Awadhesh Narayan Zhao Jin Xiang Yuan Cheng Zhang Feng Chen Liang Li Zhengcai Xia Stefano Sanvito Peng Zhou Faxian Xiu State Key Laboratory of Surface Physics and Department of Physics Fudan University Shanghai 200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200433 China School of Physics AMBER and CRANN Institute Trinity College Dublin 2 Ireland Department of Physics University of Illinois at Urbana-Champaign Champaign Illinois USA 61801 Materials Theory ETH Zurich Wolfgang-Pauli-Strasse 27 CH 8093 Zurich Switzerland Wuhan National High Magnetic Field Center Huazhong University of Science and Technology Wuhan 430074 China State Key Laboratory of ASIC and System Department of Microelectronics Fudan University Shanghai 200433 China Collaborative Innovation Center of Advanced Microstructures Nanjing 210093 China

The magnetoresistance of a material conveys various dynamic information about charge and spin carriers, inspiring both fundamental studies in physics and practical applications such as magnetic sensors, data storage, and spintronic devices. Magnetic impurities play a crucial role in the magnetoresistance as they induce exotic states of matter such as the quantum anomalous Hall effect in topological insulators and tunable ferromagnetic phases in dilute magnetic semiconductors. However, magnetically doped topological Dirac semimetals are hitherto lacking. Here, we report a systematic study of Cr-doped Cd3As2 thin films grown by molecular-beam epitaxy. With the Cr doping, Cd3As2 thin films exhibit unexpected negative transverse magnetoresistance and strong quantum oscillations, bearing a trivial Berry's phase and an enhanced effective mass. More importantly, with ionic gating the magnetoresistance of Cr-doped Cd3As2 thin films can be drastically tuned from negative to positive, demonstrating the strong correlation between electrons and the localized spins of the Cr impurities, which we interpret through the formation of magnetic polarons. Such a negative magnetoresistance under perpendicular magnetic field and its gate tunability have not been observed previously in the Dirac semimetal Cd3As2. The Cr-induced topological phase transition and the formation of magnetic polarons in Cd3As2 provide insights into the magnetic interaction in Dirac semimetals as well as their potential applications in spintronics.

关键词： Growth Magnetoresistance Dirac semimetal Density functional theory Shubnikov-de Haas effect

Active classification with comparison queries

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arXiv 2017年

作者： Kane, Daniel M. Lovetty, Shachar Moran, Shay Zhang, Jiapeng Department of Computer Science and Engineering Department of Mathematics University of California San Diego Department of Computer Science and Engineering University of California San Diego United States Simons Institute for the Theory of Computing Berkeley United States Max Planck Institute for Informatics Saarbrucken Germany

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a speci Copyright © 2017, The Authors. All rights reserved.

关键词： Learning algorithms

Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation

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Physical Review A 2018年第1期97卷 012116-012116页

作者： N. Pradeep Kumar Radhakrishnan Balu Raymond Laflamme C. M. Chandrashekar The Institute of Mathematical Sciences C. I. T Campus Taramani Chennai 600113 India U.S. Army Research Laboratory Computational and Information Sciences Directorate Adelphi Maryland 20783 USA Computer Science and Electrical Engineering University of Maryland Baltimore County 1000 Hilltop Circle Baltimore Maryland 21250 USA Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo N2L 3G1 Ontario Canada Perimeter Institute for Theoretical Physics Waterloo N2L 2Y5 Ontario Canada Homi Bhabha National Institute Training School Complex Anushakti Nagar Mumbai 400094 India

We study the dynamics of discrete-time quantum walk using quantum coin operations, Ĉ(θ1) and Ĉ(θ2), in time-dependent periodic sequence. For the two-period quantum walk with the parameters θ1 and θ2 in the coin operations we show that the standard deviation [σθ1,θ2(t)] is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations θ1 or θ2, σθ1,θ2(t)=min{σθ1(t),σθ2(t)}. Our numerical result is analytically corroborated using the dispersion relation obtained from the continuum limit of the dynamics. Using the dispersion relation for one- and two-period quantum walks, we present the bounds on the dynamics of three- and higher-period quantum walks. We also show that the bounds for the two-period quantum walk will hold good for the split-step quantum walk which is also defined using two coin operators using θ1 and θ2. Unlike the previous known connection of discrete-time quantum walks with the massless Dirac equation where coin parameter θ=0, here we show the recovery of the massless Dirac equation with nonzero θ parameters contributing to the intriguing interference in the dynamics in a totally nonrelativistic situation. We also present the effect of periodic sequence on the entanglement between coin and position space.

关键词： quantum algorithms quantum entanglement quantum simulation quantum walks

Drinfeld modules with complex multiplication, Hasse invariants and factoring polynomials over finite fields

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arXiv 2017年

作者： Doliskani, Javad Narayanan, Anand Kumar Schost, Éric Institute for Quantum Computing University of Waterloo Laboratoire d'Informatique de Paris 6 Pierre et Marie Curie University Cheriton School of Computer Science University of Waterloo

We present a novel randomized algorithm to factor polynomials over a finite field Fqof odd characteristic using rank 2 Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial f ∈ Fq[x] to be factored) with respect to a random Drinfeld module φ with complex multiplication. Factors of f supported on prime ideals with supersingular reduction at φ have vanishing Hasse invariant and can be separated from the rest. Incorporating a Drinfeld module analogue of Deligne's congruence, we devise an algorithm to compute the Hasse invariant lift, which turns out to be the crux of our algorithm. The resulting expected runtime of n3/2+ϵ(log q)1+o(1)+ n1+ϵ(log q)2+o(1)to factor polynomials of degree n over Fqmatches the fastest previously known algorithm, the Kedlaya-Umans implementation of the Kaltofen-Shoup algorithm.11G09, 11Y16, 12Y05 Copyright © 2017, The Authors. All rights reserved.

关键词： Polynomials

Online learning via the differential privacy lens

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arXiv 2017年

作者： Abernethy, Jacob Jung, Young Hun Lee, Chansoo McMillan, Audra Tewari, Ambuj College of Computing Georgia Institute of Technology Department of Statistics University of Michigan Google Brain Simons Inst. for the Theory of Computing Department of Computer Science Boston University Khoury College of Computer Sciences Northeastern University Department of Statistics Department of EECS University of Michigan

In this paper, we use differential privacy as a lens to examine online learning in both full and partial information settings. The differential privacy framework is, at heart, less about privacy and more about algorithmic stability, and thus has found application in domains well beyond those where information security is central. Here we develop an algorithmic property called one-step differential stability which facilitates a more refined regret analysis for online learning methods. We show that tools from the differential privacy literature can yield regret bounds for many interesting online learning problems including online convex optimization and online linear optimization. Our stability notion is particularly well-suited for deriving first-order regret bounds for follow-the-perturbed-leader algorithms, something that all previous analyses have struggled to achieve. We also generalize the standard max-divergence to obtain a broader class called Tsallis max-divergences. These define stronger notions of stability that are useful in deriving bounds in partial information settings such as multi-armed bandits and bandits with experts. Copyright © 2017, The Authors. All rights reserved.

关键词： Stability

quantum-classical correspondence in the vicinity of periodic orbits

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arXiv 2018年

作者： Kumari, Meenu Ghose, Shohini Institute for Quantum Computing University of Waterloo N2L 3G1 Canada Department of Physics and Astronomy University of Waterloo N2L 3G1 Canada Department of Physics and Computer Science Wilfrid Laurier University WaterlooN2L 3C5 Canada Perimeter Institute for Theoretical Physics 31 Caroline St N WaterlooONN2L 2Y5 Canada

quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr’s correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems. Copyright © 2018, The Authors. All rights reserved.

关键词： quantum theory

A quantum-Proof Non-Malleable Extractor With Application to Privacy Amplification against Active quantum Adversaries

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arXiv 2017年

作者： Aggarwal, Divesh Chung, Kai-Min Lin, Han-Hsuan Vidick, Thomas Center of Quantum Technologies and Department of Computer Science NUS Singapore Singapore Institute of Information Science Academia Sinica Taipei11529 Taiwan SPMS Nanyang Technological University and Centre for Quantum Technologies Singapore Singapore Department of Computing and Mathematical Sciences California Institute of Technology Pasadena United States

In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret X in order to establish a shared private key K by exchanging messages over an insecure communi-cation channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor;choosing a quantum-proof extractor allows one to establish security against quantum adversaries. In the case that the channel is not authenticated, Dodis and Wichs (STOC-09) showed that the problem can be solved in two rounds of communication using a non-malleable extractor, a stronger pseudo-random construction than a strong extractor. We give the first construction of a non-malleable extractor that is secure against quantum adversaries. The extractor is based on a construction by Li (FOCS-12), and is able to extract from source of min-entropy rates larger than 1/2. Combining this construction with a quantum-proof variant of the reduction of Dodis and Wichs, shown by Cohen and Vidick (unpublished), we obtain the first privacy amplification protocol secure against active quantum adversaries. Copyright © 2017, The Authors. All rights reserved.

关键词： quantum cryptography