Monogamy of Correlations vs. Monogamy of Entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous.Comment: 12 pages, 2 figures. Invited submission to a special issue of Quantum Information Processing. v2: Published version. Open acces

Completely real? A critical note on the claims by Colbeck and Renner

In a series of papers Colbeck and Renner claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer, Landsman and Leegwater, I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed

Completely real? A critical note on the claims by Colbeck and Renner

In a series of papers Colbeck and Renner (2011, 2015a,b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer (2014), Landsman (2015) and Leegwater (2016), I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed

An Interpretation of Relativistic Spin Entanglement Using Geometric Algebra

Entangled states are often given as one of the most bizarre examples of “weirdness” described as inherent to quantum mechanics. The present work reinterprets entanglement as not being a property of states at all, but rather as a relationship between the reference frames in which the states reside, which proposes to reduce “weirdness” of interpretation. Using the geometric Algebra of Physical Space, it has been shown that a classical form of the Dirac equation can be satisfied by any eigenspinor, which is a Lorentz transformation operator describing the relative velocity and relative orientation of the rest frame of a system as seen from a particular lab frame from which it is described. The real linear nature of the Dirac equation means any real linear superposition of such eigenspinors are also solutions. Thus, with entanglement modelled as an operator consisting of a linear superposition of rotation operators describing the possible relative orientations of a particular particle frame and the frame from which it is observed, it too can satisfy a bipartite form of the Dirac equation. To investigate this model, the present work applies relativistic boost transformations to the entangling operator in various ways, including as an identical boost of both parts in the same direction, and also as equal and oppositely-directed boosts. The resulting “entangling eigenspinors” are then analyzed in various ways, including the application to specific spin states — only to discover that doing this results in a reduction of the information, which can be interpreted as a reduction in the amount of entanglement. By comparing this to the treatment of the Dirac equation in APS, it may be concluded that the application of the entangling eigenspinor to a state — which models the typical approach of simply boosting an entangled state — gives an incomplete account of what is happening. The full information is thus contained within the entangling eigenspinor, justifying the interpretation of the entanglement in terms of geometric information relating the reference frames, rather than as a property of the state

Doing Research - Wissenschaftspraktiken zwischen Positionierung und Suchanfrage

Forschung wird zunehmend aus Sicht ihrer Ergebnisse gedacht - nicht zuletzt aufgrund der Umwälzungen im System Wissenschaft. Der Band lenkt den Fokus jedoch auf diejenigen Prozesse, die Forschungsergebnisse erst ermöglichen und Wissenschaft konturieren. Dabei ist der Titel Doing Research als Verweis darauf zu verstehen, dass forschendes Handeln von spezifischen Positionierungen, partiellen Perspektiven und Suchbewegungen geformt ist. So knüpfen alle Beitragenden auf reflexive Weise an ihre jeweiligen Forschungspraktiken an. Ausgangspunkt sind Abkürzungen - die vermeintlich kleinsten Einheiten wissenschaftlicher Aushandlung und Verständigung. Der in den Erziehungs-, Sozial-, Medien- und Kunstwissenschaften verankerte Band zeichnet ein vieldimensionales Bild gegenwärtigen Forschens mit transdisziplinären Anknüpfungspunkten zwischen Digitalität und Bildung

Doing Research - Wissenschaftspraktiken zwischen Positionierung und Suchanfrage

Forschung wird zunehmend aus Sicht ihrer Ergebnisse gedacht - nicht zuletzt aufgrund der Umwälzungen im System Wissensschaft. Der Band lenkt den Fokus jedoch auf diejenigen Prozesse, die Forschungsergebnisse erst ermöglichen und Wissenschaft konturieren. Dabei ist der Titel Doing Research als Verweis darauf zu verstehen, dass forschendes Handeln von spezifischen Positionierungen, partiellen Perspektiven und Suchbewegungen geformt ist. So knüpfen alle Beitragenden auf reflexive Weise an ihre jeweiligen Forschungspraktiken an. Ausgangspunkt sind Abkürzungen - die vermeintlich kleinsten Einheiten wissenschaftlicher Aushandlung und Verständigung. Der in den Erziehungs-, Sozial-, Medien- und Kunstwissenschaften verankerte Band zeichnet ein vieldimensionales Bild gegenwärtigen Forschens mit transdisziplinären Anknüpfungspunkten zwischen Digitalität und Bildung

Doing Research. Wissenschaftspraktiken zwischen Positionierung und Suchanfrage

Forschung wird zunehmend aus Sicht ihrer Ergebnisse gedacht - nicht zuletzt aufgrund der Umwälzungen im System Wissensschaft. Der Band lenkt den Fokus jedoch auf diejenigen Prozesse, die Forschungsergebnisse erst ermöglichen und Wissenschaft konturieren. Dabei ist der Titel Doing Research als Verweis darauf zu verstehen, dass forschendes Handeln von spezifischen Positionierungen, partiellen Perspektiven und Suchbewegungen geformt ist. So knüpfen alle Beitragenden auf reflexive Weise an ihre jeweiligen Forschungspraktiken an. Ausgangspunkt sind Abkürzungen - die vermeintlich kleinsten Einheiten wissenschaftlicher Aushandlung und Verständigung. Der in den Erziehungs-, Sozial-, Medien- und Kunstwissenschaften verankerte Band zeichnet ein vieldimensionales Bild gegenwärtigen Forschens mit transdisziplinären Anknüpfungspunkten zwischen Digitalität und Bildung. (DIPF/Orig.