Resource Marginal Problems

Chung-Yun Hsieh; Gelo Noel M. Tabia; Yu-Chun Yin; Yeong-Cherng Liang

doi:10.22331/q-2024-05-22-1353

Resource Marginal Problems

Chung-Yun Hsieh^1,2, Gelo Noel M. Tabia^3,4,5,6, Yu-Chun Yin^7,4, and Yeong-Cherng Liang^4,5

¹H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK
²ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain
³Foxconn Quantum Computing Research Center, Taipei 114, Taiwan
⁴Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan
⁵Physics Division, National Center for Theoretical Sciences, Taipei 106319, Taiwan
⁶Center for Quantum Technology, National Tsing Hua University, Hsinchu 300, Taiwan
⁷Institute of Communications Engineering, National Yang Ming Chiao Tung University, Hsinchu 300093, Taiwan

Published:	2024-05-22, volume 8, page 1353
Eprint:	arXiv:2202.03523v3
Doi:	https://doi.org/10.22331/q-2024-05-22-1353
Citation:	Quantum 8, 1353 (2024).

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Abstract

We introduce the $\textit{resource marginal problems}$, which concern the possibility of having a resource-free target subsystem compatible with a $given$ collection of marginal density matrices. By identifying an appropriate choice of resource R and target subsystem T, our problems reduce, respectively, to the well-known $\textit{marginal problems}$ for quantum states and the problem of determining if a given quantum system is a resource. More generally, we say that a set of marginal states is $\textit{resource-free incompatible}$ with a target subsystem T if all global states compatible with this set must result in a resourceful state in T of type R. We show that this incompatibility $induces$ a resource theory that can be quantified by a monotone and obtain necessary and sufficient conditions for this monotone to be computable as a conic program with finite optimum. We further show, via the corresponding witnesses, that (1) resource-free incompatibility is equivalent to an operational advantage in some channel-discrimination tasks, and (2) some specific cases of such tasks fully characterize the convertibility between marginal density matrices exhibiting resource-free incompatibility. Through our framework, one sees a clear connection between any marginal problem – which implicitly involves some notion of incompatibility – for quantum states and a resource theory for quantum states. We also establish a close connection between the physical relevance of resource marginal problems and the ground state properties of certain many-body Hamiltonians. In terms of application, the universality of our framework leads, for example, to a further quantitative understanding of the incompatibility associated with the recently-proposed entanglement marginal problems and entanglement transitivity problems.

► BibTeX data

@article{Hsieh2024resourcemarginal,
  doi = {10.22331/q-2024-05-22-1353},
  url = {https://doi.org/10.22331/q-2024-05-22-1353},
  title = {Resource {M}arginal {P}roblems},
  author = {Hsieh, Chung-Yun and Tabia, Gelo Noel M. and Yin, Yu-Chun and Liang, Yeong-Cherng},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1353},
  month = may,
  year = {2024}
}

► References

[1] A. Higuchi, A. Sudbery, and J. Szulc, One-qubit reduced states of a pure many-qubit state: polygon inequalities, Phys. Rev. Lett. 90, 107902 (2003).
https://doi.org/10.1103/PhysRevLett.90.107902

[2] S. Bravyi, Requirements for compatibility between local and multipartite quantum states, Quantum Inf. Comput. 4, 012 (2004).
https://doi.org/10.48550/arXiv.quant-ph/0301014
arXiv:quant-ph/0301014

[3] A. Klyachko, Quantum marginal problem and N-representability, J. Phys. Conf. Ser. 36, 014 (2006).
https://doi.org/10.1088/1742-6596/36/1/014

[4] C. Schilling, Quantum Marginal Problem and Its Physical Relevance, Ph.D. thesis, ETH Zurich, 2014.
https://doi.org/10.3929/ethz-a-010139282

[5] R. M. Erdahl and B. Jin, On Calculating Approximate and Exact Density Matrices, book chapter (2000), in Many-Electron Densities and Density Matrices, edited by J. Cioslowski (Kluwer, Boston, 2000).
https://doi.org/10.1007/978-1-4615-4211-7_4

[6] M. Navascues, F. Baccari, and A. Acín, Entanglement marginal problems, Quantum 5, 589 (2021).
https://doi.org/10.22331/q-2021-11-25-589

[7] G.Tóth, C.Knapp, O.Gühne, and H. J. Briegel, Optimal spin squeezing inequalities detect bound entanglement in spin models, Phys. Rev. Lett. 99, 250405 (2007).
https://doi.org/10.1103/PhysRevLett.99.250405

[8] Z. Wang, S. Singh, and M. Navascués, Entanglement and nonlocality in infinite 1D systems, Phys. Rev. Lett. 118, 230401 (2017).
https://doi.org/10.1103/PhysRevLett.118.230401

[9] R. Horodecki, P. Horodecki, M.Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
https://doi.org/10.1103/RevModPhys.81.865

[10] E. Chitambar and G. Gour, Quantum resource theories, Rev. Mod. Phys. 91, 025001 (2019).
https://doi.org/10.1103/RevModPhys.91.025001

[11] A. Streltsov, G. Adesso, and M. B. Plenio, Colloquium: quantum coherence as a resource, Rev. Mod. Phys. 89, 041003 (2017).
https://doi.org/10.1103/RevModPhys.89.041003

[12] F. G. S. L. Brand$\tilde{\rm a}$o, M. Horodecki, J. Oppenheim, J. M. Renes, and R. W. Spekkens, Resource theory of quantum states out of thermal equilibrium, Phys. Rev. Lett. 111, 250404 (2013).
https://doi.org/10.1103/PhysRevLett.111.250404

[13] G. Gour and R. W. Spekkens, The resource theory of quantum reference frames: manipulations and monotones, New J. Phys. 10, 033023 (2008).
https://doi.org/10.1088/1367-2630/10/3/033023

[14] J. I. de Vicente, On nonlocality as a resource theory and nonlocality measures, J. Phys. A: Math. Theor. 47, 424017 (2014).
https://doi.org/10.1088/1751-8113/47/42/424017

[15] R. Gallego and L. Aolita, Resource theory of steering, Phys. Rev. X 5, 041008 (2015).
https://doi.org/10.1103/PhysRevX.5.041008

[16] M. Lostaglio, An introductory review of the resource theory approach to thermodynamics, Rep. Prog. Phys. 82, 114001 (2019).
https://doi.org/10.1088/1361-6633/ab46e5

[17] E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, Quantifying Bell: the resource theory of nonclassicality of common-cause boxes. Quantum 4, 280 (2020).
https://doi.org/10.22331/q-2020-06-08-280

[18] V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Quantifying entanglement, Phys. Rev. Lett. 78, 2275 (1997).
https://doi.org/10.1103/PhysRevLett.78.2275

[19] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Quantifying Einstein-Podolsky-Rosen steering, Phys. Rev. Lett. 112, 180404 (2014).
https://doi.org/10.1103/PhysRevLett.112.180404

[20] T. Baumgratz, M. Cramer, and M. B. Plenio, Quantifying coherence, Phys. Rev. Lett. 113, 140401 (2014).
https://doi.org/10.1103/PhysRevLett.113.140401

[21] D. Chruściński and F. A. Wudarski, Non-Markovianity degree for random unitary evolution, Phys. Rev. A 91, 012104 (2014).
https://doi.org/10.1103/PhysRevA.91.012104

[22] F. J. Curchod, N. Gisin, and Y.-C. Liang, Quantifying multipartite nonlocality via the size of the resource, Phys. Rev. A 91, 012121 (2015).
https://doi.org/10.1103/PhysRevA.91.012121

[23] I. Marvian and R. W. Spekkens, How to quantify coherence: distinguishing speakable and unspeakable notions, Phys. Rev. A 94, 052324 (2016).
https://doi.org/10.1103/PhysRevA.94.052324

[24] I. Marvian and R. Spekkens, The theory of manipulations of pure state asymmetry: I. basic tools, equivalence classes and single copy transformations, New. J. Phys. 15, 033001 (2013).
https://doi.org/10.1088/1367-2630/15/3/033001

[25] F. G. S. L. Brand$\tilde{\rm a}$o, M. Horodecki, N. Ng, J. Oppenheim, and S. Wehner, The second laws of quantum thermodynamics, Proc. Natl. Acad. Sci. U.S.A. 112, 3275 (2015).
https://doi.org/10.1073/pnas.1411728112

[26] M. Horodecki and J. Oppenheim, Fundamental limitations for quantum and nanoscale thermodynamics, Nat. Commun. 4, 2059 (2013).
https://doi.org/10.1038/ncomms3059

[27] V. Narasimhachar, S. Assad, F. C. Binder, J. Thompson, B. Yadin, and M. Gu, Thermodynamic resources in continuous-variable quantum systems, npj Quantum Inf. 7, 9 (2021).
https://doi.org/10.1038/s41534-020-00342-6

[28] A. Serafini, M. Lostaglio, S. Longden, U. Shackerley-Bennett, C.-Y. Hsieh, and G. Adesso, Gaussian thermal operations and the limits of algorithmic cooling, Phys. Rev. Lett. 124, 010602 (2020).
https://doi.org/10.1103/PhysRevLett.124.010602

[29] S. Bartlett, T. Rudolph, and R. Spekkens, Reference frames, superselection rules, and quantum information, Rev. Mod. Phys. 79, 55 (2007).
https://doi.org/10.1103/RevModPhys.79.555

[30] I. Marvian, Symmetry, Asymmetry and Quantum Information, Ph.D. thesis, UWSpace, 2012.
http://hdl.handle.net/10012/7088

[31] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell nonlocality, Rev. Mod. Phys. 86, 419 (2014).
https://doi.org/10.1103/RevModPhys.86.419

[32] R. Uola, A. C. S. Costa, H. C. Nguyen, and O. G$\ddot{\rm u}$hne, Quantum steering, Rev. Mod. Phys. 92, 015001 (2020).
https://doi.org/10.1103/RevModPhys.92.015001

[33] D. Cavalcanti and P. Skrzypczyk, Quantum steering: a review with focus on semidefinite programming, Rep. Prog. Phys. 80, 024001 (2017).
https://doi.org/10.1088/1361-6633/80/2/024001

[34] B. Regula, Convex geometry of quantum resource quantification, J. Phys. A: Math. Theor. 51, 045303 (2018).
https://doi.org/10.1088/1751-8121/aa9100

[35] Z.-W. Liu, X. Hu, and S. Lloyd, Resource destroying maps, Phys. Rev. Lett. 118, 060502 (2017).
https://doi.org/10.1103/PhysRevLett.118.060502

[36] A. Anshu, M.-H. Hsieh, and R. Jain, Quantifying resources in general resource theory with catalysts, Phys. Rev. Lett. 121, 190504 (2018).
https://doi.org/10.1103/PhysRevLett.121.190504

[37] Z.-W. Liu, K. Bu, and R. Takagi, One-shot operational quantum resource theory, Phys. Rev. Lett. 123, 020401 (2019).
https://doi.org/10.1103/PhysRevLett.123.020401

[38] K. Fang and Z.-W. Liu, No-go theorems for quantum resource purification, Phys. Rev. Lett. 125, 060405 (2020).
https://doi.org/10.1103/PhysRevLett.125.060405

[39] R. Takagi and B. Regula, General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks, Phys. Rev. X 9, 031053 (2019).
https://doi.org/10.1103/PhysRevX.9.031053

[40] R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Operational advantage of quantum resources in subchannel discrimination, Phys. Rev. Lett. 122, 140402 (2019).
https://doi.org/10.1103/PhysRevLett.122.140402

[41] B.Regula, K. Bu, R. Takagi, and Z.-W. Liu, Benchmarking one-shot distillation in general quantum resource theories, Phys. Rev. A 101, 062315 (2020).
https://doi.org/10.1103/PhysRevA.101.062315

[42] C. Sparaciari, L. del Rio, C. M. Scandolo, P. Faist, and J. Oppenheim, The first law of general quantum resource theories, Quantum 4, 259 (2020).
https://doi.org/10.22331/q-2020-04-30-259

[43] R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. G$\ddot{\rm u}$hne, Quantifying quantum resources with conic programming, Phys. Rev. Lett. 122, 130404 (2019).
https://doi.org/10.1103/PhysRevLett.122.130404

[44] M. Walter, B. Doran, D. Gross, and M. Christandl, Entanglement polytopes: multiparticle entanglement from single-particle information, Science 340, 1205 -1208 (2013).
https://doi.org/10.1126/science.1232957

[45] J. Tura, R. Augusiak, A. B. Sainz, T. Vértesi, M. Lewenstein, and A. Ací n, Detecting nonlocality in many-body quantum states. Science 344, 1256 (2014).
https://doi.org/10.1126/science.1247715

[46] G. N. M. Tabia, K.-S. Chen, C.-Y. Hsieh, Y.-C. Yin, and Y.-C. Liang, Entanglement transitivity problems, npj Quantum Inf 8, 98 (2022).
https://doi.org/10.1038/s41534-022-00616-1

[47] J.-D. Bancal, S. Pironio, A. Acín, Y.-C. Liang, V. Scarani, and N. Gisin, Quantum non-locality based on finite-speed causal influences leads to superluminal signalling, Nat. Phys. 8, 864 (2012).
https://doi.org/10.1038/nphys2460

[48] T. J. Barnea, J.-D. Bancal, Y.-C. Liang, and N. Gisin, Tripartite quantum state violating the hidden-influence constraints. Phys. Rev. A. 88, 022123 (2013).
https://doi.org/10.1103/PhysRevA.88.022123

[49] S. Coretti, E. Hänggi, and S. Wolf, Nonlocality is transitive, Phys. Rev. Lett. 107, 100402 (2011).
https://doi.org/10.1103/PhysRevLett.107.100402

[50] W. D$\ddot{\rm u}$r, G. Vidal, and J. I. Cirac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000).
https://doi.org/10.1103/PhysRevA.62.062314

[51] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, 70, 1895 (2022).
https://doi.org/10.1103/PhysRevLett.70.1895

[52] P. Skrzypczyk and N. Linden, Robustness of measurement, discrimination games, and accessible information, Phys. Rev. Lett. 122, 140403 (2019).
https://doi.org/10.1103/PhysRevLett.122.140403

[53] N. Linden and P. Skrzypczyk, How to use arbitrary measuring devices to perform almost perfect measurements, arXiv:2203.02593.
https://doi.org/10.48550/arXiv.2203.02593
arXiv:2203.02593

[54] D. Rosset, F. Buscemi, and Y.-C. Liang, A resource theory of quantum memories and their faithful verification with minimal assumptions, Phys. Rev. X 8, 021033 (2018).
https://doi.org/10.1103/PhysRevX.8.021033

[55] S. B$\ddot{\rm a}$uml, S. Das, X. Wang, and M. M. Wilde, Resource theory of entanglement for bipartite quantum channels. arXiv:1907.04181.
arXiv:1907.04181

[56] Z.-W. Liu and A. Winter, Resource theories of quantum channels and the universal role of resource erasure, arXiv:1904.04201.
arXiv:1904.04201

[57] Y. Liu and X. Yuan, Operational resource theory of quantum channels, Phys. Rev. Res. 2, 012035(R) (2020).
https://doi.org/10.1103/PhysRevResearch.2.012035

[58] L. Li, K. Bu, and Z.-W. Liu, Quantifying the resource content of quantum channels: an operational approach, Phys. Rev. A 101, 022335 (2020).
https://doi.org/10.1103/PhysRevA.101.022335

[59] H.-Y. Ku, J. Kadlec, A. $\check{\rm C}$ernoch, M. T. Quintino, W. Zhou, K. Lemr, N. Lambert, A. Miranowicz, S.-L. Chen, F. Nori, and Y.-N. Chen, Quantifying Quantumness of Channels Without Entanglement, PRX Quantum 3, 020338 (2022).
https://doi.org/10.1103/PRXQuantum.3.020338

[60] L. B. Vieira, H.-Y. Ku, C. Budroni, Entanglement-breaking channels are a quantum memory resource, arXiv:2402.16789.
https://doi.org/10.48550/arXiv.2402.16789
arXiv:2402.16789

[61] B. Stratton, C.-Y. Hsieh, and P. Skrzypczyk, Dynamical Resource Theory of Informational Nonequilibrium Preservability, Phys. Rev. Lett. 132, 110202 (2024).
https://doi.org/10.1103/PhysRevLett.132.110202

[62] C.-Y. Hsieh, Y.-C. Liang, and R.-K. Lee, Quantum steerability: characterization, quantification, superactivation, and unbounded amplification, Phys. Rev. A 94, 062120 (2016).
https://doi.org/10.1103/PhysRevA.94.062120

[63] M. T. Quintino, M. Huber, and N. Brunner, Superactivation of quantum steering, Phys. Rev. A 94, 062123 (2016).
https://doi.org/10.1103/PhysRevA.94.062123

[64] H.-Y. Ku, C.-Y. Hsieh, S.-L. Chen, Y.-N. Chen, and C. Budroni, Complete classification of steerability under local filters and its relation with measurement incompatibility, Nat. Commun. 13, 4973 (2022).
https://doi.org/10.1038/s41467-022-32466-y

[65] H.-Y. Ku, C.-Y. Hsieh, and C. Budroni, Measurement incompatibility cannot be stochastically distilled, arXiv:2308.02252.
https://doi.org/10.48550/arXiv.2308.02252
arXiv:2308.02252

[66] C.-Y. Hsieh, H.-Y. Ku, and C. Budroni, Characterisation and fundamental limitations of irreversible stochastic steering distillation, arXiv:2309.06191.
https://doi.org/10.48550/arXiv.2309.06191
arXiv:2309.06191

[67] C.-Y. Hsieh, S.-L. Chen, A thermodynamic approach to quantifying incompatible instruments, arXiv:2402.13080.
https://doi.org/10.48550/arXiv.2402.13080
arXiv:2402.13080

[68] C.-Y. Hsieh, M. Gessner, General quantum resources provide advantages in work extraction tasks, arXiv:2403.18753.
https://doi.org/10.48550/arXiv.2403.18753
arXiv:2403.18753

[69] P. Skrzypczyk, I. $\check{\rm S}$upić, and D. Cavalcanti All sets of incompatible measurements give an advantage in quantum state discrimination, Phys. Rev. Lett. 122, 130403 (2019).
https://doi.org/10.1103/PhysRevLett.122.130403

[70] F. Buscemi, E. Chitambar, and W. Zhou, Complete resource theory of quantum incompatibility as quantum programmability, Phys. Rev. Lett. 124, 120401 (2020).
https://doi.org/10.1103/PhysRevLett.124.120401

[71] F. Buscemi, K. Kobayashi, S. Minagawa, P. Perinotti, and A. Tosini, Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication, Quantum 7, 1035 (2023).
https://doi.org/10.22331/q-2023-06-07-1035

[72] N. Linden, S. Popescu, and W. K. Wootters, Almost Every Pure State of Three Qubits Is Completely Determined by Its Two-Particle Reduced Density Matrices, Phys. Rev. Lett. 89, 207901 (2002).
https://doi.org/10.1103/PhysRevLett.89.207901

[73] N. Linden and W. K. Wootters, The Parts Determine the Whole in a Generic Pure Quantum State, Phys. Rev. Lett. 89, 277906 (2002).
https://doi.org/10.1103/PhysRevLett.89.277906

[74] X.-D. Yu, T. Simnacher, N. Wyderka, H. C. Nguyen, and O. Gühne, A complete hierarchy for the pure state marginal problem in quantum mechanics, Nat. Commun. 12, 1012 (2021).
https://doi.org/10.1038/s41467-020-20799-5

[75] C.-Y. Hsieh, M. Lostaglio, and A. Acín, Quantum channel marginal problem, Phys. Rev. Res. 4, 013249 (2022).
https://doi.org/10.1103/PhysRevResearch.4.013249

[76] S. Boyd and L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004).

[77] R. Uola, T. Kraft, and A. A. Abbott, Quantification of quantum dynamics with input-output games, Phys. Rev. A 101, 052306 (2020).
https://doi.org/10.1103/PhysRevA.101.052306

[78] B. G$\ddot{\rm a}$rtner and J. Matou$\check{\rm s}$ek, Approximation Algorithms and Semidefinite Programming (Springer-Verlag, Berlin, Heidelberg, 2012).

[79] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).

[80] D. Beckman, D. Gottesman, M. A. Nielsen, and J. Preskill, Causal and localizable quantum operations, Phys. Rev. A 64, 052309 (2001).
https://doi.org/10.1103/PhysRevA.64.052309

[81] M. Piani, M. Horodecki, P. Horodecki, and R. Horodecki, On quantum non-signalling boxes, Phys. Rev. A 74, 012305 (2006).
https://doi.org/10.1103/PhysRevA.74.012305

[82] T. Eggeling, D. Schlingemann, and R. F. Werner, Semicausal operations are semilocalizable, EPL 57, 782 (2002).
https://doi.org/10.1209/epl/i2002-00579-4

[83] R. Duan and A. Winter, No-signalling-assisted zero-error capacity of quantum channels and an information theoretic interpretation of the Lovász number, IEEE Trans. Inf. Theory 62, 891 (2016).
https://doi.org/10.1109/TIT.2015.2507979

[84] N. Datta, Min- and max-relative entropies and a new entanglement monotone, IEEE Trans. Inf. Theory 55, 2816 (2009).
https://doi.org/10.1109/TIT.2009.2018325

[85] W. Hall, Compatibility of subsystem states and convex geometry, Phys. Rev. A 75, 032102 (2007).
https://doi.org/10.1103/PhysRevA.75.032102

[86] K.-S. Chen, C.-Y. Hsieh, G. N. M. Tabia, and Y.-C. Yin, and Y.-C. Liang, Nonlocality transitivity for quantum states, in preparation.

[87] C.-Y. Hsieh, G. N. M. Tabia, and Y.-C. Liang, Resource transitivity, in preparation.

[88] X. Wu, G.-J. Tian, W. Huang, Q.-Y. Wen, S.-J. Qin, and F. Gao, Determination of $W$ states equivalent under stochastic local operations and classical communication by their bipartite reduced density matrices with tree form, Phys. Rev. A 90, 012317 (2014).
https://doi.org/10.1103/PhysRevA.90.012317

[89] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi, Fundamental limits of repeaterless quantum communications, Nat. Commun. 8, 15043 (2017).
https://doi.org/10.1038/ncomms15043

[90] J.-H. Hsieh, S.-H. Chen, and C.-M. Li, Quantifying quantum-mechanical processes, Sci. Rep. 7, 13588 (2017).
https://doi.org/10.1038/s41598-017-13604-9

[91] M. G. Díaz, K. Fang, X. Wang, M. Rosati, M. Skotiniotis, J. Calsamiglia, and A. Winter, Using and reusing coherence to realize quantum processes, Quantum 2, 100 (2018).
https://doi.org/10.22331/q-2018-10-19-100

[92] M. M. Wilde, Entanglement cost and quantum channel simulation, Phys. Rev. A 98, 042338 (2018).
https://doi.org/10.1103/PhysRevA.98.042338

[93] J. R. Seddon and E. Campbell, Quantifying magic for multi-qubit operations, Proc. R. Soc. A 475, 20190251 (2019).
https://doi.org/10.1098/rspa.2019.0251

[94] G. Gour, Comparison of quantum channels by superchannels, IEEE Trans. Inf. Theory 65, 5880 (2019).
https://doi.org/10.1109/TIT.2019.2907989

[95] G. Gour and A. Winter, How to quantify a dynamical resource? Phys. Rev. Lett. 123, 150401 (2019).
https://doi.org/10.1103/PhysRevLett.123.150401

[96] G. Gour and C. M. Scandolo, The entanglement of a bipartite channel. Phys. Rev. A 103, 062422 (2021).
https://doi.org/10.1103/PhysRevA.103.062422

[97] G. Gour and C. M. Scandolo, Dynamical entanglement, Phys. Rev. Lett. 125, 180505 (2020).
https://doi.org/10.1103/PhysRevLett.125.180505

[98] R. Takagi, K. Wang, and M. Hayashi, Application of the resource theory of channels to communication scenarios, Phys. Rev. Lett. 124, 120502 (2020).
https://doi.org/10.1103/PhysRevLett.124.120502

[99] T. Theurer, D. Egloff, L. Zhang, and M. B. Plenio, Quantifying operations with an application to coherence, Phys. Rev. Lett. 122, 190405 (2019).
https://doi.org/10.1103/PhysRevLett.122.190405

[100] G. Saxena, E. Chitambar, and G. Gour, Dynamical resource theory of quantum coherence, Phys. Rev. Res. 2, 023298 (2020).
https://doi.org/10.1103/PhysRevResearch.2.023298

[101] C.-Y. Hsieh, Resource preservability, Quantum 4, 244 (2020).
https://doi.org/10.22331/q-2020-03-19-244

[102] C.-Y. Hsieh, Communication, dynamical resource theory, and thermodynamics, PRX Quantum 2, 020318 (2021).
https://doi.org/10.1103/PRXQuantum.2.020318

[103] C.-Y. Hsieh, Quantifying classical information transmission by thermodynamics, arXiv:2201.12110.
arXiv:2201.12110

[104] C.-Y. Hsieh, G. N. M. Tabia, and Y.-C. Liang, Dynamical resource marginal problems, in preparation.

[105] E. Haapasalo, T. Kraft, N. Miklin, and R. Uola, Quantum marginal problem and incompatibility, Quantum 5, 476 (2021).
https://doi.org/10.22331/q-2021-06-15-476

[106] C.-Y. Hsieh, R. Uola, and P. Skrzypczyk, Quantum complementarity: A novel resource for unambiguous exclusion and encryption, arXiv:2309.11968.
https://doi.org/10.48550/arXiv.2309.11968
arXiv:2309.11968

[107] A. F. Ducuara and P. Skrzypczyk, Characterization of quantum betting tasks in terms of Arimoto mutual information, PRX Quantum 3, 020366 (2022).
https://doi.org/10.1103/PRXQuantum.3.020366

[108] A. F. Ducuara, P. Skrzypczyk, F. Buscemi, P. Sidajaya, and V. Scarani, Maxwell’s Demon Walks into Wall Street: Stochastic Thermodynamics Meets Expected Utility Theory, Phys. Rev. Lett. 131, 197103 (2023).
https://doi.org/10.1103/PhysRevLett.131.197103

[109] A. F. Ducuara and P. Skrzypczyk, Fundamental connections between utility theories of wealth and information theory, arXiv:2306.07975.
https://doi.org/10.48550/arXiv.2306.07975
arXiv:2306.07975

[110] C.-Y. Hsieh, G. N. M. Tabia, Y.-C. Yin, and Y.-C. Liang, Resource Marginal Problems, arXiv:2202.03523v1 (2022).
arXiv:2202.03523

[111] D. P. Bertsekas, Lecture Slides on Convex Analysis And Optimization, https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-253-convex-analysis-and-optimization-spring-2012/lecture-notes/.
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-253-convex-analysis-and-optimization-spring-2012/lecture-notes/

[112] D. P. Bertsekas, Convex Optimization Theory (Athena Scientific Belmont, 2009).

[113] C.-Y. Hsieh, Study on Nonlocality, Steering, Teleportation, and Their Superactivation, Master thesis, National Tsing Hua University, 2016.
https://hdl.handle.net/11296/pajsp5

[114] T. M. Apostol, Mathematical Analysis: A Modern Approach To Advanced Calculus (2nd edition, Pearson press, 1973).

[115] J. R. Munkres, Topology (2nd edition, Prentice Hall press, 2000).

[116] S. L. Braunstein, A. Mann, and M. Revzen, Maximal violation of Bell inequalities for mixed states, Phys. Rev. Lett. 68, 3259 (1992).
https://doi.org/10.1103/PhysRevLett.68.3259

[117] B. Baumgartner, An inequality for the trace of matrix products, using absolute values, arXiv:1106.6189.
arXiv:1106.6189

[118] J. Watrous, The Theory of Quantum Information (Cambridge University Press, 2018).
https://doi.org/10.1017/9781316848142

Cited by

[1] Huan-Yu Ku, Chung-Yun Hsieh, and Costantino Budroni, "Measurement incompatibility cannot be stochastically distilled", arXiv:2308.02252, (2023).

[2] Chung-Yun Hsieh, Huan-Yu Ku, and Costantino Budroni, "Characterisation and fundamental limitations of irreversible stochastic steering distillation", arXiv:2309.06191, (2023).

[3] Chung-Yun Hsieh, Matteo Lostaglio, and Antonio Acín, "Quantum channel marginal problem", Physical Review Research 4 1, 013249 (2022).

[4] Chung-Yun Hsieh and Shin-Liang Chen, "A thermodynamic approach to quantifying incompatible instruments", arXiv:2402.13080, (2024).

[5] Chung-Yun Hsieh and Manuel Gessner, "General quantum resources provide advantages in work extraction tasks", arXiv:2403.18753, (2024).

[6] Gelo Noel M. Tabia, Kai-Siang Chen, Chung-Yun Hsieh, Yu-Chun Yin, and Yeong-Cherng Liang, "Entanglement transitivity problems", npj Quantum Information 8, 98 (2022).

The above citations are from SAO/NASA ADS (last updated successfully 2024-06-15 15:56:43). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2024-06-15 15:56:42).

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