A paramount topic in quantum foundations, rooted in the study of the EPR paradox and Bell inequalities, is that of characterizing quantum theory in terms of the space-like correlations it allows. Here we show that to focus only on space-like correlations is not enough: we explicitly construct a toy model theory that, while not contradicting classical and quantum theories at the level of space-like correlations, still displays an anomalous behavior in its time-like correlations. We call this anomaly, quantified in terms of a specific communication game, the "hypersignaling" phenomena. We hence conclude that the "principle of quantumness," if it exists, cannot be found in space-like correlations alone: nontrivial constraints need to be imposed also on time-like correlations, in order to exclude hypersignaling theories.One of the main tenets in modern physics is that if two space-like separated events are correlated, then such correlations must not carry any information [1]. This assumption, constituting the so-called no-signaling principle, was the starting point used by Bell [2] to quantify and compare space-like correlations of different theories on even grounds-an idea of vital importance for his argument about the EPR paradox [3] and the derivation of his famous inequality. Subsequently, due to seminal works by Tsirelson (Cirel'son) [4] and Popescu and Rohrlich [5], it became clear that the no-signaling principle alone is not enough to characterize "physical" space-like correlations: non-signaling space-like correlations allowed by quantum theory form a strict subset within the set of all non-signaling correlations [6].A natural question is then to try to identify additional principles that, together with the no-signaling principle, may be able to rule out all super-quantum non-signaling correlations at once. Various ideas have been proposed, ranging from complexity theory, e.g. the collapse of the complexity tower [7] to information theory, e.g. the information causality principle [8]. However, none of these has been able to characterize the quantum/superquantum boundary in full. In particular, an outstanding open question is whether quantum theory can be characterized in terms of the space-like correlations it allows [6].In this paper, we show that this cannot be done: any approach to characterize quantum theory based only on space-like correlations is necessarily incomplete unless it also takes into account time-like correlations as well. Our approach, which is completely unrelated to the study of temporal correlationsà la Leggett-Garg [9-12], considers the elementary resource of noiseless commu- * cqtmda@nus.edu.sg † sbrandse@caltech.edu ‡ alessandro.tosini@unipv.it § buscemi@is.nagoya-u.ac.jp ¶ phyvv@nus.edu.sg nication and the input/output correlations that can be so established. By analogy with the no-signaling principle, we operationally introduce what we call the "nohypersignaling principle," which roughly states that any input/output correlation that can be obtained by transmitting a composite system...

We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input-output correlations. Formally, the problem consists of characterizing the set of input-output correlations compatible with any arbitrary given quantum channel. For binary (i.e. two input symbols, two output symbols) correlations, we show that extremal correlations are always achieved by orthogonal encodings and measurements, irrespective of whether or not the channel preserves commutativity. We further provide a full, closed-form characterization of the sets of binary correlations in the case of: (i) any dihedrally covariant qubit channel (such as any Pauli and amplitude-damping channels) and (ii) any universally-covariant commutativity-preserving channel in an arbitrary dimension (such as any erasure, depolarizing, universal cloning and universal transposition channels).

Clean two-dimensional electron systems in GaAs/AlGaAs heterostructures exhibit anisotropic collective phases, the quantum Hall nematics, at high Landau level occupancy and low temperatures.An as yet unknown native symmetry-breaking potential consistently orients these phases relative to the crystalline axes of the host material. Here we report an extensive set of measurements examining the role of the structural symmetries of the heterostructure in determining the orientation of the nematics. In single quantum well samples we find that neither the local symmetry of the confinement potential nor the distance between the electron system and the sample surface dictates the orientation of the nematic. In remarkable contrast, for two-dimensional electrons confined at a single heterointerface between GaAs and AlGaAs, the nematic orientation depends on the depth of the two-dimensional electron system beneath the sample surface.