Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

1 aNakata, Yoshifumi1 aHirche, Christoph1 aKoashi, Masato1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/85301748nas a2200133 4500008003900000020002200039245007000061210006900131300001400200520131300214100001901527700002001546856004801566 2017 d a978-1-5386-2913-000aInformation Theoretic Principles of Universal Discrete Denoising0 aInformation Theoretic Principles of Universal Discrete Denoising a205–2103 aSocial media platforms make tremendous amounts of data available. Often times, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, one may assume such a distorted image to be corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA).

1 aNoetzel, Janis1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/85601912nas a2200157 4500008003900000022001400039245006200053210005900115490000700174520144300181100002201624700002201646700001801668700002001686856004801706 2017 d a0022-248800aUnitary 2-designs from random X- and Z-diagonal unitaries0 aUnitary 2designs from random X and Zdiagonal unitaries0 v583 aUnitary 2-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and practical quantum information protocols and also have been used to model the dynamics in complex quantum many-body systems. Here, we show that unitary 2-designs can be approximately implemented by alternately repeating random unitaries diagonal in the Pauli-Z basis and Pauli-X basis. We also provide a converse about the number of repetitions needed to achieve unitary 2-designs. These results imply that the process after l repetitions achieves a Theta(d(-l))-approximate unitary 2-design. Based on the construction, we further provide quantum circuits that efficiently implement approximate unitary 2-designs. Although a more efficient implementation of unitary 2-designs is known, our quantum circuit has its own merit that it is divided into a constant number of commuting parts, which enables us to apply all commuting gates simultaneously and leads to a possible reduction of an actual execution time. We finally interpret the result in terms of the dynamics generated by time-dependent Hamiltonians and provide for the first time a random disordered time-dependent Hamiltonian that generates a unitary 2-design after switching interactions only a few times. Published by AIP Publishing.

1 aNakata, Yoshifumi1 aHirche, Christoph1 aMorgan, Ciara1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/85000384nas a2200121 4500008003900000245005300039210005200092100002200144700002200166700001800188700002000206856003600226 2015 d00aDecoupling with random diagonal-unitary matrices0 aDecoupling with random diagonalunitary matrices1 aNakata, Yoshifumi1 aHirche, Christoph1 aMorgan, Ciara1 aWinter, Andreas uhttp://arxiv.org/abs/1509.0515500422nas a2200121 4500008003900000245007400039210006900113100002200182700002200204700001800226700002000244856003600264 2015 d00aImplementing unitary 2-designs using random diagonal-unitary matrices0 aImplementing unitary 2designs using random diagonalunitary matri1 aNakata, Yoshifumi1 aHirche, Christoph1 aMorgan, Ciara1 aWinter, Andreas uhttp://arxiv.org/abs/1502.0751400525nas a2200145 4500008004100000022001400041245008200055210006900137300001100206490000700217100001300224700002100237700002200258856009900280 2014 eng d a1367-263000aQuantumness of correlations, quantumness of ensembles and quantum data hiding0 aQuantumness of correlations quantumness of ensembles and quantum a1130010 v161 aPiani, M1 aNarasimhachar, V1 aCalsamiglia, John uhttp://stacks.iop.org/1367-2630/16/i=11/a=113001?key=crossref.9f5154f8c85e7f9471e2931d9a02df8800737nas a2200205 4500008004100000245008200041210006900123260001200192300001600204490000700220653002300227653002300250653002500273653002500298100002200323700001800345700002000363700001800383856013000401 2008 eng d00aMultipartite continuous-variable solution for the Byzantine agreement problem0 aMultipartite continuousvariable solution for the Byzantine agree c06/2008 a062307–110 v7710aGaussian processes10ahomodyne detection10aquantum cryptography10aquantum entanglement1 aNeigovzen, Rodion1 aRodó, Carles1 aAdesso, Gerardo1 aSanpera, Anna uhttp://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PLRAAN000077000006062307000001&idtype=cvips&prog=normal00335nas a2200097 4500008004100000245005700041210005700098100002200155700001800177856004200195 2005 eng d00aContinuous Variable Solution for Byzantine Agreement0 aContinuous Variable Solution for Byzantine Agreement1 aNeigovzen, Rodion1 aSanpera, Anna uhttp://arxiv.org/abs/quant-ph/050724901086nas a2200205 4500008004100000022001400041245007300055210006900128260003900197300001100236490000700247520045700254100001800711700001100729700002200740700002300762700001800785700001900803856005800822 2005 eng d a0031-900700aQuantum Key Distillation from Gaussian States by Gaussian Operations0 aQuantum Key Distillation from Gaussian States by Gaussian Operat bAmerican Physical Societyc01/2005 a0105020 v943 aWe study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process.1 aNavascués, M1 aBae, J1 aCirac, Ignacio, J1 aLewenstein, Maciej1 aSanpera, Anna1 aAcín, Antonio uhttp://link.aps.org/doi/10.1103/PhysRevLett.94.01050201507nas a2200169 4500008003700000020002400037245009600061210006900157260006000226300001600286520090900302100001801211700002101229700001901250700002001269856004801289 0 d a{978-1-5386-4781-3}00a{Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy}0 aFully Quantum Arbitrarily Varying Channels Random Coding Capacit b{IEEE; IEEE Informat Theory Soc; NSF; Huawei; Qualcomm} a{2012-2016}3 a{We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, via a quantum version of the ``elimination of of correlation{''} using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.}1 aBoche, Holger1 aDeppe, Christian1 aNoetzel, Janis1 aWinter, Andreas uhttps://grupsderecerca.uab.cat/giq/node/924