We describe the main classes of non-signalling bipartite correlations in terms of states on operator system tensor products. This leads to the introduction of another new class of games, called reflexive games, which are characterised as the hardest non-local games that can be won using a given set of strategies. We provide a characterisation of their perfect strategies in terms of operator system quotients. We introduce a new class of non-local games, called imitation games, in which the players display linked behaviour, and which contain as subclasses the classes of variable assignment games, binary constraint system games, synchronous games, many games based on graphs, and unique games. We associate a C*-algebra C∗(G)\$C\^{*}($\backslash$mathcal {G})\$ to any imitation game G\$$\backslash$mathcal {G}\$, and show that the existence of perfect quantum commuting (resp. quantum, local) strategies of G\$$\backslash$mathcal {G}\$ can be characterised in terms of properties of this C*-algebra. We single out a subclass of imitation games, which we call mirror games, and provide a characterisation of their quantum commuting strategies that has an algebraic flavour, showing in addition that their approximately quantum perfect strategies arise from amenable traces on the encoding C*-algebra.

1 aLupini, M.1 aMančinska, L.1 aPaulsen, V., I.1 aRoberson, D., E.1 aScarpa, G.1 aSeverini, S.1 aTodorov, I., G.1 aWinter, A uhttps://doi.org/10.1007/s11040-020-9331-700532nas a2200157 4500008003900000022001400039245007500053210006900128260001600197300001100213490000700224100001500231700001400246700001300260856010100273 2019 d a0022-248800aEvery entangled state provides an advantage in classical communication0 aEvery entangled state provides an advantage in classical communi cJan-07-2019 a0722010 v601 aBäuml, S.1 aWinter, A1 aYang, D. uhttp://aip.scitation.org/doi/10.1063/1.5091856http://aip.scitation.org/doi/pdf/10.1063/1.509185601506nas a2200181 4500008003900000022002500039245007300064210006900137260000800206300001400214490000700228520096300235100001901198700001601217700001401233700001301247856006401260 2016 d a0032-9460, 1608-325300aClassical capacities of quantum channels with environment assistance0 aClassical capacities of quantum channels with environment assist cjul a214–2380 v523 aA quantum channel physically is a unitary interaction between an information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [1], we consider a benevolent third party, i.e., a helper, controlling the environment state, and show how the helper’s presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.1 aKarumanchi, S.1 aMancini, S.1 aWinter, A1 aYang, D. uhttps://link.springer.com/article/10.1134/S003294601603002900724nas a2200181 4500008003900000022001400039245005600053210005600109260001600165490000800181100001800189700001800207700001300225700001300238700001400251700001800265856025900283 2016 d a0031-900700aEntanglement and Coherence in Quantum State Merging0 aEntanglement and Coherence in Quantum State Merging cJan-06-20160 v1161 aStreltsov, A.1 aChitambar, E.1 aRana, S.1 aBera, N.1 aWinter, A1 aLewenstein, M uhttp://link.aps.org/doi/10.1103/PhysRevLett.116.240405http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.116.240405/fulltexthttp://link.aps.org/accepted/10.1103/PhysRevLett.116.240405http://link.aps.org/article/10.1103/PhysRevLett.116.240405