The measurement postulates of quantum mechanics are operationally redundant

Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for assigning outcome probabilities (Born's rule) and the post-measurement state-update rule, can be deduced from the other quantum postulates, often referred to as "unitary quantum mechanics", and the assumption that ensembles on finite-dimensional Hilbert spaces are characterised by finitely many parameters. This is achieved by taking an operational approach to physical theories, and using the fact that the manner in which a physical system is partitioned into subsystems is a subjective choice of the observer, and hence should not affect the predictions of the theory. In contrast to other approaches, our result does not assume that measurements are related to operators or bases, it does not rely on the universality of quantum mechanics, and it is independent of the interpretation of probability.Comment: This is a post-peer-review, pre-copyedit version of an article published in Nature Communications. The final authenticated version is available online at: http://dx.doi.org/10.1038/s41467-019-09348-

Universally-composable privacy amplification from causality constraints

We consider schemes for secret key distribution which use as a resource correlations that violate Bell inequalities. We provide the first security proof for such schemes, according to the strongest notion of security, the so called universally-composable security. Our security proof does not rely on the validity of quantum mechanics, it solely relies on the impossibility of arbitrarily-fast signaling between separate physical systems. This allows for secret communication in situations where the participants distrust their quantum devices.Comment: 4 page

Useful entanglement can be extracted from all nonseparable states

We consider entanglement distillation from a single-copy of a multipartite state, and instead of rates we analyze the "quality" of the distilled entanglement. This "quality" is quantified by the fidelity with the GHZ-state. We show that each not fully-separable state $\sigma$ can increase the "quality" of the entanglement distilled from other states, no matter how weakly entangled is $\sigma$. We also generalize this to the case where the goal is distilling states different than the GHZ. These results provide new insights on the geometry of the set of separable states and its dual (the set of entanglement witnesses).Comment: 7 page

Interconversion of Nonlocal Correlations

In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these extreme correlations are interconvertible. This suggests that the simplest extremal nonlocal distribution (called a PR box) might be the basic unit of nonlocality. We also show that this unit of nonlocality is sufficient to simulate all quantum states when measured with two outcome measurements.Comment: 7 pages + appendix, single colum

Response to "The measurement postulates of quantum mechanics are not redundant"

Adrian Kent has recently presented a critique [arXiv:2307.06191] of our paper [Nat. Comms. 10, 1361 (2019)] in which he claims to refute our main result: the measurement postulates of quantum mechanics can be derived from the rest of postulates, once we assume that the set of mixed states of a finite-dimensional Hilbert space is finite-dimensional. To construct his argument, Kent considers theories resulting from supplementing quantum mechanics with hypothetical "post-quantum" measurement devices. We prove that each of these theories contains pure states (i.e. states of maximal knowledge) which are not rays of the Hilbert space, in contradiction with the "pure state postulate" of quantum mechanics. We also prove that these alternatives violate the finite-dimensionality of mixed states. Each of these two facts separately invalidates the refutation. In this note we also clarify the assumptions used in the above-cited paper and discuss the notions of pure state, physical system, and the sensitivity of the structure of the state space under modifications of the measurements or the dynamics.Comment: 7 page

Atmospheric Carbon Dioxide variability at Aigüestortes, Central Pyrenees, Spain

Unidad de excelencia María de Maeztu MdM-2015-0552In order to improve the understanding of the carbon cycle in the Pyrenean region, two atmospheric monitoring mountain stations were set up within the Long-Term Ecological Research node of Aigüestortes i Estany de Sant Maurici at Central Pyrenees, Spain. The atmospheric concentration of carbon dioxide (CO2) was measured over 2008-2014 and 2010-2014 at Estany Llong (ELL) site and Centre de Recerca d'Alta Muntanya (CRAM), respectively. Measurements were carried out fortnightly off-line with high precision instrumentation at ELL and every minute online with a lower precision sensor at CRAM in conjunction with meteorological variables. The two datasets were analyzed in this study, quantifying whenever possible annual growth rates (AGR), seasonal variability, and diurnal amplitudes. Results were also compared with the NOAA Marine Boundary Layer (MBL) reference product and CO2 data from other background monitoring stations. Four-harmonics adjusted CO2 data from ELL showed a high correlation with the NOAA MBL reference product for the same latitude (Spearman's rho ρ = 0.96). In addition, AGRs of CO2 at ELL correlated well with those observed at Mace Head (MHD) station (ρ = 0.94), suggesting that ELL can be considered a background station. Winter CRAM CO2 data was not statistically different from ELL data, while in summer, it was 5.5 ppm lower on average, suggesting a higher photosynthesis uptake. The amplitude of the CO2 diurnal cycle at CRAM was found to be exponentially related to the local mean daily temperature and dependent on forthcoming wind sector (N-NW or E-SE-S-SW). An increase in CRAM CO2 concentrations was observed under N-NW winds during daytime, which could be related to traffic emissions. This study demonstrates that the use of CO2 sensors with low precision but continuously corrected and periodically calibrated can be used for the study of local and regional CO2 sources and sinks

The complexity of energy eigenstates as a mechanism for equilibration

Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and the complexity of their eigenvectors, provided that a conjecture about the incompressibility of quantum circuits holds. We quantify the complexity by the size of the smallest quantum circuit mapping the local basis onto the energy eigenbasis. Specifically, we consider the set of all Hamiltonians having complexity C, and show that almost all such Hamiltonians equilibrate if C is super-quadratic with the system size, which includes the fully random Hamiltonian case in the limit C to infinity, and do not equilibrate if C is sub-linear. We also provide a simple formula for the equilibration time-scale in terms of the Fourier transform of the level density. Our results are statistical and, therefore, do not apply to specific Hamiltonians. Yet, they establish a fundamental link between equilibration and complexity theory.Comment: improved version (6 pages + appendix

Convertibility between two-qubit states using stochastic local quantum operations assisted by classical communication

In this paper we classify the four-qubit states that commute with UUVV, where U and V are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39