Trade-off relations and divergences in quantum information theory  Page description

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Details of project

  
Identifier
124152
Type K
Principal investigator Mosonyi, Milán
Title in Hungarian "Trade-off" relációk és divergenciák a kvantum-információelméletben
Title in English Trade-off relations and divergences in quantum information theory
Keywords in Hungarian Kvantum-információelmélet, Rényi divergenciák, hipotézsivizsgálat, csatornakapacitások, hibaexponensek
Keywords in English Quantum information theory, Rényi divergences, hypothesis testing, channel capacities, error exponents
Discipline
Mathematics (Council of Physical Sciences)100 %
Ortelius classification: Mathematics
Panel Mathematics and Computing Science
Department or equivalent Department of Mathematical Analysis (Budapest University of Technology and Economics)
Participants Andai, Attila
Frenkel, Peter
Lovas, Attila
Pitrik, József
Virosztek, Dániel
Vrana, Péter
Weiner, Mihály
Zimborás, Zoltán
Starting date 2017-09-01
Closing date 2022-08-31
Funding (in million HUF) 7.840
FTE (full time equivalent) 9.57
state running project





 

Final report

  
Results in Hungarian
Számos új eredményt értünk el a kvantum-információelmélet területén, többek közt: - Gauge-invariáns fermionikus állapotokat használva megmutattuk, hogy a független azonos eloszlású esettől eltérően a korrelált állapotok megkülönböztetésében elérhető a minta méretében szuper-exponenciális csökkenése a hibavalószínűségeknek. - Megmutattuk, hogy a klasszikus esettel szemben a kompozit kvantum állapotmegkülönböztetés direkt exponenseire általában szigorú felső korlátot ad a két hipotézist leíró halmazokba eső állapotok legrosszabb páronkénti hibaexponense. - Meghatároztuk két végtelendimenziós kvantum állapot aszimptotikus megkülönböztetési exponensét, valamint ugyanezt általánosabban nukleáris C*-algebrák állapotpárjaira. - Új megkülönböztethetőségi mértékeit konstruáltuk kvantum állapotoknak (relatív entrópiákat és Rényi-divergenciákat), amelyek kedvező matematikai tulajdonságokkal bírnak, mint a kvantum operációk alatti monotonitás és az additivitás. Új mértékeit konstruáltuk a többkomponensű összefonódottságnak. - Az algebrai bonyolultságelméletből származó eszközökkel meghatároztuk többkomponensű összefonódott állapotok egymásba képezhetőségének optimális rátáját, illetve a hibaexponens és a ráta közöti összefüggést munkával segített Gibbs-állapot őrző leképezésekre a kvantum termodinamikában.
Results in English
We have obtained new results in quantum information theory, in particular: - We have used gauge-invariant fermionic states to show that, unlike in the i.i.d. case, a super-exponential decrease of error probabilities in the sample size is attainable for the discrimination of correlated quantum states. - We have shown that in the case of binary composite quantum state discrimination, the optimal error exponents are generally strictly bounded from above by the optimal pairwise exponents of discriminating single elements of the sets describing the two hypotheses, in contrast with the classical case. - We have determined the strong converse exponent of the asymptotic discrimination of two infinite-dimensional quantum states, and, more generally, of two states of nuclear C*-algebras. - We have constructed new distinguishability measures of quantum states (relative entropies and Rényi divergences) with good mathematical properties, like monotonicity under data processing and additivity. We have also constructed new measures to quantify multi-partite entanglement. - We have applied techniques from algebraic complexity theory to finding optimal rates of multi-party entanglement conversion, and to giving the trade-off between the error exponent and the rate for work-assisted Gibbs-preserving operations in quantum thermodynamics.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=124152
Decision
Yes





 

List of publications

  
D. Virosztek: Characterizations of centrality by local convexity of certain functions on C^* - algebras, In: A. Böttcher, D. Potts, P. Stollmann, D. Wenzel (eds), The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, vol 268. 487-, 2018
D. Virosztek: Jointly convex quantum Jensen divergences, Linear Algebra Appl. 576, pp. 67-78, 2019, 2018
P. Vrana, M. Christandl: Distillation of Greenberger-Horne-Zeilinger states by combinatorial methods, IEEE Transactions on information theory 65, 5945-5958, 2019
Asger Kjærulff Jensen, Péter Vrana: The asymptotic spectrum of LOCC transformations, IEEE Transactions on Information theory, 2019, 2019
Róbert Juhász, Johannes M. Oberreuter, Zoltán Zimborás: Entanglement Entropy of Disordered Quantum Wire Junctions, Journal of Statistical Mechanics, 123106, 2018
G. P. Geher, T. Titkos, D. Virosztek:: On isometric embeddings of Wasserstein spaces --- the discrete case, J. Math. Anal. Appl. 480, 123435, 2019
J. Pitrik, D. Virosztek: Quantum Hellinger distances revisited, https://arxiv.org/abs/1903.10455, 2019
G. P. Geher, T. Titkos, D. Virosztek: Isometric study of Wasserstein spaces --- the real line, submitted, 2019
G. P. Geher, T. Titkos, D. Virosztek: Dirac masses and isometric rigidity, RIMS Kokyuroku (Kyoto Univ.), to appear, 2019
Norbert Barankai, Zoltán Zimborás: Generalized quantum Zeno dynamics and ergodic means, arXiv:1811.02509, 2018
Balázs E. Szigeti, Gábor Homa, Zoltán Zimborás, Norbert Barankai: Short time behavior of continuous time quantum walks on graphs, arXiv:1905.03914, 2019
Filiberto Ares, José G Esteve, Fernando Falceto, Zoltán Zimborás: Sublogarithmic behaviour of the entanglement entropy in fermionic chains, Journal of Statistical Mechanics, to appear, 2019
Péter Vrana, Máté Farkas: Homological codes and abelian anyons, Reviews in Mathematical Physics Vol. 31, No. 10, 1950038, 2019
Matthias Christandl, Angelo Lucia, Péter Vrana, Albert H Werner: Tensor network representations from the geometry of entangled states, arXiv:1809.08185, 2018
Matthias Christandl, Péter Vrana, Jeroen Zuiddam: Barriers for fast matrix multiplication from irreversibility, arXiv:1812.06952, 2018
Péter Vrana: Probabilistic refinement of the asymptotic spectrum of graphs, arXiv:1903.01857, 2019
Srinivasan Arunachalam, Péter Vrana, Jeroen Zuiddam: The asymptotic induced matching number of hypergraphs: balanced binary strings, arXiv:1905.03148, 2019
Attila Lovas, Attila Andai: On the notation of quantum copulas, arXiv:1902.08460, 2019
Milán Mosonyi, Tomohiro Ogawa: Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions, arXiv:1811.10599, 2018
J. Pitrik, D. Virosztek: Quantum Hellinger distances revisited, Lett. Math. Phys. 110, 2039–2052, 2020
G. P. Geher, T. Titkos, D. Virosztek: Isometric study of Wasserstein spaces --- the real line, Trans. Amer. Math. Soc. 373, 5855–5883, 2020
G. P. Geher, T. Titkos, D. Virosztek: Dirac masses and isometric rigidity, RIMS Kokyuroku, 2125, 34-41, 2019
Balázs E. Szigeti, Gábor Homa, Zoltán Zimborás, Norbert Barankai: Short time behavior of continuous time quantum walks on graphs, Physical Review A, 100, 062320, 2019, 2019
Srinivasan Arunachalam, Péter Vrana, Jeroen Zuiddam: The asymptotic induced matching number of hypergraphs: balanced binary strings, The Electronic Journal of Combinatorics 27 P3.12, 2020
G. P. Geher, T. Titkos, D. Virosztek: Isometric study of Wasserstein spaces — Hilbert spaces, manuscript, submitted, 2020
J. Pitrik, D. Virosztek: A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means, Linear Algebra Appl. 609, 203–217, 2021
D. Virosztek: The metric property of the quantum Jensen-Shannon divergence, Under minor revision in Adv. Math., 2019
G Roósz, Z Zimborás, R Juhász: Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations, Physical Review B 102, 064204, 2020
FB Maciejewski, Z Zimborás, M Oszmaniec: Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography, Quantum 4, 257, 2020
A Berezutskii, M Beketov, D Yudin, Z Zimborás, JD Biamonte: Probing criticality in quantum spin chains with neural networks, Journal of Physics: Complexity 1, 03LT01, 2020
MES Morales, JD Biamonte, Z Zimborás: On the universality of the quantum approximate optimization algorithm, Quantum Information Processing 19, 1-26, 2020
D Jakab, Z Zimborás: Quantum phases of collective SU (3) spin systems with bipartite symmetry, arXiv:2001.08310, 2020
Zimborás Z, Farrelly T, Farkas S, Masanes L: Does causal dynamics imply local interactions?, arXiv:2006.10707, 2020
S Szalay, Z Zimborás, M Máté, G Barcza, C Schilling, Ö Legeza: Fermionic systems for quantum information people, arXiv:2006.03087, 2020
Zs. Szilágyi, S. Nietert and M. Weiner: Rigidity and a common framework for mutually unbiased bases and k-nets, Journal of Combinatorial Designs, accepted, 2020
Péter Vrana: A generalization of Strassen’s spectral theorem, arXiv:2003.14176, 2020
Christopher Perry, Péter Vrana, Albert H. Werner: The semiring of dichotomies and asymptotic relative submajorization, arXiv:2004.10587, 2020
Alonso Botero, Matthias Christandl, Péter Vrana: Large deviation principle for moment map estimation, arXiv:2004.14504, 2020
Gergely Bunth, Péter Vrana: Asymptotic relative submajorization of multiple-state boxes, arXiv:2007.11258, 2020
Péter Vrana: A family of multipartite entanglement measures, arXiv:2008.11108, 2020
G. P. Geher, T. Titkos, D. Virosztek: Isometric study of Wasserstein spaces --- the real line, Trans. Amer. Math. Soc. 373, 5855–5883, 2020
Matthias Christandl, Angelo Lucia, Péter Vrana, Albert H Werner: Tensor network representations from the geometry of entangled states, SciPost Phys., 9(3):42, 2020
Matthias Christandl, Péter Vrana, Jeroen Zuiddam: Barriers for fast matrix multiplication from irreversibility, Leibniz International Proceedings in Informatics (LIPIcs), 137(26):1–17, 2019
Péter Vrana: Probabilistic refinement of the asymptotic spectrum of graphs, Combinatorica, 2021
Attila Lovas, Attila Andai: On the notion of quantum copulas, arXiv:1902.08460, 2019
Milán Mosonyi, Tomohiro Ogawa: Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions, IEEE Transactions on Information Theory, 67(3):1668-1698, 2021
G. P. Geher, T. Titkos, D. Virosztek: The isometry group of Wasserstein spaces: the Hilbertian case, arXiv:2102.02037, 2021
D. Virosztek: The metric property of the quantum Jensen-Shannon divergence, Adv. Math. 380 (2021), 107595., 2021
D Jakab, Z Zimborás: Quantum phases of collective SU (3) spin systems with bipartite symmetry, Phys. Rev. B 103, 214448, 2021
S Szalay, Z Zimborás, M Máté, G Barcza, C Schilling, Ö Legeza: Fermionic systems for quantum information people, Journal of Physics A: Mathematical and Theoretical, 2021
Péter Vrana: A Generalization of Strassen’s Theorem on Preordered Semirings, Order, 2021
Christopher Perry, Péter Vrana, Albert H. Werner: The semiring of dichotomies and asymptotic relative submajorization, IEEE Transactions on Information Theory, to appear, 2021
Alonso Botero, Matthias Christandl, Péter Vrana: Large deviation principle for moment map estimation, Electronic J. Probab., 26:1-23, 2021
Gergely Bunth, Péter Vrana: Asymptotic relative submajorization of multiple-state boxes, Letters in Mathematical Physics, 111(4), 2021
Péter Vrana: Asymptotic continuity of additive entanglement measures, arXiv:2107.08537, 2021
Gergely Bunth, Péter Vrana: Equivariant relative submajorization, arXiv:2108.13217, 2021
P.E. Frenkel: Classical simulations of communication channels, arXiv:2101.10985, 2021
P.E. Frenkel, M. Weiner: On entanglement assistance to a noiseless classical channel, larXiv:2103.08567, 2021
Milán Mosonyi: The strong converse exponent of discriminating infinite-dimensional quantum states, arXiv:2107.08036, 2021
Milán Mosonyi, Mihály Weiner, Zsombor Szilágyi: On the error exponents of binary quantum state discrimination with composite hypotheses, arXiv:2011.04645, 2020
Filip B Maciejewski, Flavio Baccari, Zoltán Zimborás, Michał Oszmaniec: Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm, Quantum, 5:464, 2021
A. Glos, A. Krawiec, Z. Zimborás: Space-efficient binary optimization for variational computing, arXiv:2009.07309, 2020
M. Oszmaniec, N. Dangniam, M.E. Morales, Z. Zimborás: Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states, arXiv:2012.15825, 2020
B Maciejewski, F. Baccari, Z. Zimborás: Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm, Quantum, 5:464, 2021
L. Botelho, A. Glos, A. Kundu, J.A. Miszczak, Ö. Salehi, Z. Zimborás: Error mitigation for variational quantum algorithms through mid-circuit measurements, arXiv:2108.10927, 2021
D. Nagy, Z. Tabi, P. Hága, Z. Kallus, Z. Zimborás: Photonic Quantum Policy Learning in OpenAI Gym, arXiv:2108.12926, 2021
Á. Kaposi, Z. Kolarovszki, T. Kozsik, Z. Zimborás, P. Rakyta: Polynomial speedup in Torontonian calculation by a scalable recursive algorithm, arXiv:2109.04528, 2021
P. Rakyta, Z. Zimborás: Approaching the theoretical limit in quantum gate decomposition, arXiv:2109.06770, 2021
P. Vrana, M. Christandl: Distillation of Greenberger-Horne-Zeilinger states by combinatorial methods, IEEE Transactions on Information Theory 65, 5945-5958, 2019
Asger Kjærulff Jensen, Péter Vrana: The asymptotic spectrum of LOCC transformations, IEEE Transactions on Information theory, vol. 66, no. 1, pp. 155-166, 2019
M. Matolcsi, M. Weiner: Character tables and the problem of existence of finite projective planes, Journal of Combinatorial Designs 26(11):540-546, 2018
Balázs E. Szigeti, Gábor Homa, Zoltán Zimborás, Norbert Barankai: Short time behavior of continuous time quantum walks on graphs, Physical Review A, 100, 062320, 2019
Filiberto Ares, José G Esteve, Fernando Falceto, Zoltán Zimborás: Sublogarithmic behaviour of the entanglement entropy in fermionic chains, Journal of Statistical Mechanics, 093105, 2019
Péter Vrana: Probabilistic refinement of the asymptotic spectrum of graphs, Combinatorica vol. 41, pp. 873–904, 2021
G. P. Geher, T. Titkos, D. Virosztek: The isometry group of Wasserstein spaces: the Hilbertian case, Journal of the London Mathematical Society, 2022
Zimborás Z, Farrelly T, Farkas S, Masanes L: Does causal dynamics imply local interactions?, Quantum 6, 748 (2022), 2022
S Szalay, Z Zimborás, M Máté, G Barcza, C Schilling, Ö Legeza: Fermionic systems for quantum information people, Journal of Physics A: Mathematical and Theoretical, vol. 54, no. 39, 393001, 2021
Zs. Szilágyi, S. Nietert and M. Weiner: Rigidity and a common framework for mutually unbiased bases and k-nets, Journal of Combinatorial Designs, Volume 28, Issue 12 , Pages 869-892, 2020
Péter Vrana: A Generalization of Strassen’s Theorem on Preordered Semirings, Order, vol. 39, pp. 209–228, 2022
Christopher Perry, Péter Vrana, Albert H. Werner: The semiring of dichotomies and asymptotic relative submajorization, IEEE Transactions on Information Theory 68(1):311–321, 2022
Gergely Bunth, Péter Vrana: Asymptotic relative submajorization of multiple-state boxes, Letters in Mathematical Physics, 111(4), 2021
Péter Vrana: A family of multipartite entanglement measures, arXiv:2008.11108, 2020
Péter Vrana: Asymptotic continuity of additive entanglement measures, IEEE Transactions on Information Theory, vol. 68, no. 5, pp. 3208-3217, 2022
Gergely Bunth, Péter Vrana: Equivariant relative submajorization, IEEE Transactions on Information Theory, to appear, 2022
P.E. Frenkel: Classical simulations of communication channels, Quantum 6, 751, (2022), 2022
P.E. Frenkel, M. Weiner: On entanglement assistance to a noiseless classical channel, Quantum, 6:662, 2022
Milán Mosonyi, Mihály Weiner, Zsombor Szilágyi: On the error exponents of binary quantum state discrimination with composite hypotheses, IEEE Transactions on Information Theory, 68(2):1032-1067, 2022
A. Glos, A. Krawiec, Z. Zimborás: Space-efficient binary optimization for variational computing, npj Quantum Information, 8(1):1–8, 2022
M. Oszmaniec, N. Dangniam, M.E. Morales, Z. Zimborás: Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states, PRX Quantum, 3(2):020328, 2022
L. Botelho, A. Glos, A. Kundu, J.A. Miszczak, Ö. Salehi, Z. Zimborás: Error mitigation for variational quantum algorithms through mid-circuit measurements, Physical Review A, 105(2):022441, 2022
D. Nagy, Z. Tabi, P. Hága, Z. Kallus, Z. Zimborás: Photonic Quantum Policy Learning in OpenAI Gym, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE), pp. 123-129, 2021
P. Rakyta, Z. Zimborás: Approaching the theoretical limit in quantum gate decomposition, Quantum, 6:710, 2022
Attila Lovas, Attila Andai: Volume of the space of qubit-qubit channels and state transformations under random quantum channels, Reviews in Mathematical Physics, Vol. 30, No. 10, 1850019, 2018
Fumio Hiai, Milán Mosonyi: Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras, arXiv:2110.07320, 2021
Máté Matolcsi, Mihály Weiner: A rigidity property of complete systems of mutually unbiased bases, Open Systems & Information Dynamics, 28:2150012, 2021
Milán Mosonyi, Fumio Hiai: Test-measured Rényi divergences, IEEE Transactions on Information Theory, 2022
György Pál Gehér, Tamás Titkos, Dániel Virosztek: Isometric rigidity of Wasserstein tori and spheres, arXiv:2203.04054, 2022
Gergely Bunth, Gábor Maróti, Milán Mosonyi, Zoltán Zimborás: Super-exponential distinguishability of correlated quantum states, arXiv:2203.16511, 2022
György Pál Gehér, Tamás Titkos, József Pitrik, Dániel Virosztek: Quantum Wasserstein isometries on the qubit state space, arXiv:2204.14134, 2022
Tamás Tasnádi, Péter Vrana: Asymptotic equipartition property for a Markov source having ambiguous alphabet, arXiv:2207.13789, 2022
Péter Vrana: Noncommutative extensions of parameters in the asymptotic spectrum of graphs, arXiv:2207.10483, 2022
Milán Mosonyi, Gergely Bunth, Péter Vrana: Geometric relative entropies and barycentric Rényi divergences, arXiv:2207.14282, 2022
Dávid Jakab, Adrián Solymos, Zoltán Zimborás: Extendibility of Werner States, arXiv:2208.13743, 2022
Péter E. Frenkel: Integral formula for quantum relative entropy implies data processing inequality, arXiv:2208.12194, 2022
Dávid Bugár, Péter Vrana: Interpolating between Rényi entanglement entropies for arbitrary bipartitions via operator geometric means, arXiv:2208.14438, 2022
József Pitrik, Géza Tóth: Quantum Wasserstein distance based on an optimization over separable states, arXiv:2209.09925, 2022
Milán Mosonyi: Some continuity properties of quantum Rényi divergences, arXiv:2209.00646, 2022
György Pál Gehér, Tamás Titkos, Dániel Virosztek: On isometries of Wasserstein spaces, RIMS Kôkyûroku Bessatsu, to appear, 2022
D. Virosztek: Characterizations of centrality by local convexity of certain functions on C^* - algebras, In: A. Böttcher, D. Potts, P. Stollmann, D. Wenzel (eds), The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, vol 268. pp. 48, 2018
D. Virosztek: Jointly convex quantum Jensen divergences, Linear Algebra Appl., 2018
D. Virosztek: Maps on probability measures preserving certain distances — a survey and some new results, Acta Sci. Math. (Szeged) 84:1-2, pp. 65-80, 2018
P. Vrana, M. Christandl: Distillation of Greenberger-Horne-Zeilinger states by combinatorial methods, arXiv:1805.09096, 2018
Asger Kjærulff Jensen, Péter Vrana: The asymptotic spectrum of LOCC transformations, arXiv:1807.05130, 2018
M. Matolcsi, M. Weiner: Finite projective planes and the Delsarte LP-bound, Analysis Mathematica 44, pp. 89-98, 2018
M. Matolcsi, M. Weiner: Character tables and the problem of existence of finite projective planes, Journal of Combinatorial Designs, 2018
Christian Krumnow, Zoltán Zimborás, Jens Eisert: A fermionic de Finetti theorem, J. Math. Phys. 58, 122204, 2017
Michał Oszmaniec , Zoltán Zimborás: Universal extensions of restricted classes of quantum operations, Phys. Rev. Lett. 119, 220502, 2017
Iagoba Apellaniz, Inigo Urizar-Lanz, Zoltán Zimborás, Philipp Hyllus, Géza Tóth: Precision bounds for gradient magnetometry with atomic ensembles, Phys. Rev. A 97, 053603, 2018
Jens Eisert, Viktor Eisler, Zoltán Zimborás,: Entanglement negativity bounds for fermionic Gaussian states, Phys. Rev. B 97, 165123, 2018
Dávid Jakab, Gergely Szirmai, and Zoltán Zimborás: The bilinear-biquadratic model on the complete graph, J. Phys. A: Math. Theor. 51, 105201, 2018
Cédric Bény, Zoltán Zimborás, Fernando Pastawski: Approximate recovery with locality and symmetry constraints, arXiv:1806.10324, 2018
Róbert Juhász, Johannes M. Oberreuter, Zoltán Zimborás: Entanglement Entropy of Disordered Quantum Wire Junctions, arXiv:1808.02576, 2018




 

Events of the project

  
2018-09-18 15:23:58
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