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Register a new userSelf-testing using only marginal information
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The partial states of a multipartite quantum state may carry a lot of information: in some cases, they determine the global state uniquely. This result is known for tomographic information, that is for fully characterized measurements. We extend it to the device-independent framework by exhibiting sets of two-party correlations that self-test pure three-qubit states.
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In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced density with a global $n$-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of $n$-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension $n$.
Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows from Bell non-locality. There exist other scenarios, known as semidevice-independent, in which assumptions are made on the devices, such as their dimension, and non-classicality is associated to the observation of other types of correlations with no classical analogue. More recently, the use of trusted quantum inputs for certification has been introduced. The goal of this work is to study the power of this formalism and describe self-testing protocols in various settings using trusted quantum inputs. We also relate these different types of self-testing to some of the most basic quantum information protocols, such as quantum teleportation. Finally, we apply our findings to quantum networks and provide methods for estimating the quality of the whole network, as well as of parts of it.
Testing theories of angular-momentum acquisition of rotationally supported disc galaxies is the key to understand the formation of this type of galaxies. The tidal-torque theory tries to explain this acquisition process in a cosmological framework and predicts positive autocorrelations of angular-momentum orientation and spiral-arm handedness on distances of 1Mpc/h. This disc alignment can also cause systematic effects in weak-lensing measurements. Previous observations claimed discovering such correlations but did not account for errors in redshift, ellipticity and morphological classifications. We explain how to rigorously propagate all important errors. Analysing disc galaxies in the SDSS database, we find that positive autocorrelations of spiral-arm handedness and angular-momentum orientations on distances of 1Mpc/h are plausible but not statistically significant. This result agrees with a simple hypothesis test in the Local Group, where we find no evidence for disc alignment. Moreover, we demonstrate that ellipticity estimates based on second moments are strongly biased by galactic bulges, thereby corrupting correlation estimates and overestimating the impact of disc alignment on weak-lensing studies. Finally, we discuss the potential of future sky surveys. We argue that photometric redshifts have too large errors, i.e., PanSTARRS and LSST cannot be used. We also discuss potentials and problems of front-edge classifications of galaxy discs in order to improve estimates of angular-momentum orientation.
Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements. In other words it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output behaviour and is known to be possible in several cases. Here we introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, we ask whether within a particular causal structure there are tasks that can only be performed in theories that have the same correlations as quantum mechanics in any scenario. We present a candidate task for such a correlation self-test and analyse it in a range of generalised probabilistic theories (GPTs), showing that none of these perform better than quantum theory. A generalisation of our results showing that all non-quantum GPTs are strictly inferior to quantum mechanics for this task would point to a new way to axiomatise quantum theory, and enable an experimental test that simultaneously rules out such GPTs.
Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Due to the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-particle quantum entanglement. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
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