In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of $any$ type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of $any$ type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.
 C. J. Wood and R. W. Spekkens, New J. Phys. 17, 033002 (2015).
 F. Costa and S. Shrapnel, New Journal of Physics 18, 063032 (2016).
 N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014a).
 J. Watrous, The theory of quantum information (Cambridge University Press, 2018).
 D. Cavalcanti and P. Skrzypczyk, Reports on Progress in Physics 80, 024001 (2017).
 D. Cavalcanti, P. Skrzypczyk, and I. Šupić, Phys. Rev. Lett. 119, 110501 (2017).
 F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012a).
 D. Schmid, T. C. Fraser, R. Kunjwal, A. B. Sainz, E. Wolfe, and R. W. Spekkens, ``Why standard entanglement theory is inappropriate for the study of bell scenarios,'' (2019a), arXiv:2004.09194 [quant-ph].
 J. I. de Vicente, J. Phys. A 47, 424017 (2014).
 R. Gallego and L. Aolita, Phys. Rev. A 95 (2017).
 E. Wolfe, D. Schmid, A. B. Sainz, R. Kunjwal, and R. W. Spekkens, ``Quantifying Bell: the resource theory of nonclassicality of common-cause boxes,'' (2019), arXiv:1903.06311 [quant-ph].
 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy (Cambridge University Press, 2004).
 G. Pütz, D. Rosset, T. J. Barnea, Y.-C. Liang, and N. Gisin, Physical Review Letters 113, 190402 (2014).
 S. Pironio, V. Scarani, and T. Vidick, New Journal of Physics 18, 100202 (2016).
 C. Branciard, D. Rosset, Y.-C. Liang, and N. Gisin, Physical Review Letters 110, 060405 (2013).
 D. Rosset, C. Branciard, N. Gisin, and Y.-C. Liang, New Journal of Physics 15, 053025 (2013).
 F. Shahandeh, M. J. W. Hall, and T. C. Ralph, Physical Review Letters 118, 150505 (2017).
 N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014b).
 D. Chruściński and G. Sarbicki, Journal of Physics A: Mathematical and Theoretical 47, 483001 (2014).
 J. I. de Vicente, Journal of Physics A: Mathematical and Theoretical 47, 424017 (2014).
 P. Skrzypczyk, M. Navascués, and D. Cavalcanti, Physical Review Letters 112, 180404 (2014).
 M. Piani and J. Watrous, Physical Review Letters 114, 060404 (2015).
 G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. A 80, 022339 (2009).
 P. Lipka-Bartosik and P. Skrzypczyk, ``The operational advantages provided by non-classical teleportation,'' (2019), arXiv:1908.05107 [quant-ph].
 W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000).
 D. Schmid, H. Du, M. Mudassar, G. Coulter-de Wit, D. Rosset, and M. J. Hoban, ``Postquantum common-cause channels: the resource theory of local operations and shared entanglement,'' (2020), arXiv:2004.06133 [quant-ph].
 D. Mayers and A. Yao, Quantum Information & Computation 4, 273 (2004).
 J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
 I. Šupić and M. J. Hoban, New Journal of Physics 18, 075006 (2016), arXiv:1601.01552.
 A. Gheorghiu, E. Kashefi, and P. Wallden, New Journal of Physics 17, 083040 (2015).
 J.-D. Bancal, N. Sangouard, and P. Sekatski, Physical Review Letters 121, 250506 (2018).
 M. O. Renou, J. Kaniewski, and N. Brunner, Physical Review Letters 121, 250507 (2018), arXiv:1807.04956.
 P. Sekatski, J.-D. Bancal, S. Wagner, and N. Sangouard, Physical Review Letters 121, 180505 (2018).
 J. Sperling and W. Vogel, Physica Scripta 83, 045002 (2011).
 F. Buscemi, Phys. Rev. Lett. 108, 200401 (2012b).
 P. Skrzypczyk and N. Linden, Phys. Rev. Lett. 122, 140403 (2019).
 P. Skrzypczyk, I. Supic, and D. Cavalcanti, Phys. Rev. Lett. 122, 130403 (2019).
 R. Takagi, B. Regula, K. Bu, Z.-W. Liu, and G. Adesso, Phys. Rev. Lett. 122, 140402 (2019).
 R. Uola, T. Kraft, J. Shang, X.-D. Yu, and O. Gühne, Phys. Rev. Lett. 122, 130404 (2019b).
 Elie Wolfe, David Schmid, Ana Belén Sainz, Ravi Kunjwal, and Robert W. Spekkens, "Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes", arXiv:1903.06311.
 Denis Rosset, David Schmid, and Francesco Buscemi, "Characterizing nonclassicality of arbitrary distributed devices", arXiv:1911.12462.
 Miguel Navascues, Elie Wolfe, Denis Rosset, and Alejandro Pozas-Kerstjens, "Genuine Network Multipartite Entanglement", arXiv:2002.02773.
 Ana Belén Sainz, Matty J. Hoban, Paul Skrzypczyk, and Leandro Aolita, "Bipartite post-quantum steering in generalised scenarios", arXiv:1907.03705.
 David Schmid, Thomas C. Fraser, Ravi Kunjwal, Ana Belen Sainz, Elie Wolfe, and Robert W. Spekkens, "Why standard entanglement theory is inappropriate for the study of Bell scenarios", arXiv:2004.09194.
 David Schmid, Haoxing Du, Maryam Mudassar, Ghi Coulter-de Wit, Denis Rosset, and Matty J. Hoban, "Postquantum common-cause channels: the resource theory of local operations and shared entanglement", arXiv:2004.06133.
 Denis Rosset, Ämin Baumeler, Jean-Daniel Bancal, Nicolas Gisin, Anthony Martin, Marc-Olivier Renou, and Elie Wolfe, "Algebraic and geometric properties of local transformations", arXiv:2004.09405.
 John H. Selby and Ciarán M. Lee, "Compositional resource theories of coherence", arXiv:1911.04513.
 Patricia Contreras-Tejada, Carlos Palazuelos, and Julio I. de Vicente, "Genuine multipartite nonlocality is intrinsic to quantum networks", arXiv:2004.01722.
 Andrés F. Ducuara, Patryk Lipka-Bartosik, and Paul Skrzypczyk, "Multi-object operational tasks for convex quantum resource theories", arXiv:2004.12898.
 Yi-Zheng Zhen, Yingqiu Mao, Kai Chen, Francesco Buscemi, and Oscar Dahlsten, "Unified Approach to Witness Nonentanglement-Breaking Quantum Channels", arXiv:1912.10605.
The above citations are from Crossref's cited-by service (last updated successfully 2020-06-02 06:30:57) and SAO/NASA ADS (last updated successfully 2020-06-02 06:30:58). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.