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Workshop on "Incompatible Quantum Measurements"

Dates: 09.-12.09.2013

One of the fundamental and most striking implications of quantum mechanics, and a stark contrast to classical physics, is the existence of incompatible experimental setups. As originally found by Heisenberg, the measurements of position and of momentum of a quantum particle cannot be performed simultaneously without introducing imprecisions. The fact that these quantities are not experimentally compatible reflects the very properties of the quantum theory.

The Opening day on "Quantum Measurement Theory" (9.9.) will be devoted more generally to the theory of quantum measurements. The specific topics on Incompatible quantum measurements, which have seen a surge of research interest in recent years, will be the topic of the of the more specialized Workshop on the following days (10.-12.9.).

The Workshop will address, but is not strictly limit to, the following topics:
  • Coexistence and its relation to fundamental effects of quantum mechanics such as entanglement, uncertainty relations and/or no-cloning theorem and more generally to the chain of impossible devices,
  • Coexistence and joint measurability provide a good framework that is applicable and related to quantum communication protocols and especially invesigations of communication security,
  • How do the operational differences between the different incompatibility notions show up in real-world scenarios?

We welcome any researchers interested to participate in the workshop. If you would like to attend, please send us an email (including dates of attendance, and title and abstract of talk if desired). Unfortunately, we can provide financial support only for invited speakers.

Timetable

Monday (09.09.2013): Opening day on "Quantum Measurement Theory"
  • 13:45 Prof. Michael Wolf: Welcome and Opening
  • 14:00 Robert W. Spekkens: Unscrambling the omelette: distinguishing reality from information in quantum theory
  • 15:00 Coffee break
  • 15:30 Teiko Heinosaari: Quantum Incompatibility
  • 16:30 Coffee break
  • 17:00 Paul Busch: Heisenberg Uncertainty for Joint Measurements
  • 19:00 Social dinner
Tuesday-Thursday (10.-12.09.2013): Specialist Workshop on "Incompatible Quantum Measurements"

Tuesday, 10.9.
Traditional Day
Wednesday, 11.9.
Wild Day
Thursday, 12.9.
SIC Day
10:00 - 11:00 David Reeb Michael Keyl Tom Bullock
(start at 10:15)
11:00 - 11:30 Coffee break Coffee break Coffee break
11:30 - 12:30 Alessandro Toigo Takayuki Miyadera Claudio Carmeli
12:30 - 14:00 Lunch Lunch Lunch
14:00 - 14:45 Jussi Schulz Erkka Haapasalo Open questions
14:45 - 15:15 Coffee break Coffee break Coffee break
15:15 - 16:15 Jukka Kiukas Paolo Perinotti Concluding talk:
Mario Ziman
16:15 - 16:45 Coffee break Coffee break
16:45 - 17:45 Daniel Reitzner Neil Stevens Open-air discussion
19:00 Dinner Dinner

Talks

  • Tom Bullock: On the Operational Link between MUBs and SIC POVMs

We present here a physically motivated connection between the two concepts of mutually unbiased bases and symmetric informationally complete positive operator valued measures. This is done by generalising these two concepts into those of mutually unbiased POVMs and symmetric informationally complete systems, respectively, and then showing that in the case of prime-power dimensions these constructs can be used to go from a SIC POVM (assuming it exists for d > 67) to a complete set of MUBs, and vice versa.

  • Paul Busch: Heisenberg Uncertainty for Joint Measurements

The Uncertainty Principle, conceived by W. Heisenberg in 1927, epitomises the fundamental philosophical implications of quantum mechanics and its radical departure from classical physics. For decades, there has been an air of vagueness and perhaps even mystique around its formulation and interpretation, which may have contributed to the media hype in 2012 when it was announced that the principle had been experimentally violated. In this lecture I survey precise formulations of Heisenberg’s principle as trade-off relation for measurement errors and disturbance due to measurement. Recent claims about experimental refutations of the principle are shown to be untenable and found to have arisen from the unwarranted extrapolation of classical physical intuitions about measurement inaccuracies and measures of disturbance.

  • Claudio Carmeli: MUness and SICness from Covariant Phase Space Observables

We show how, in any prime power dimension, covariant phase space observables give a complete family of mutually unbiased POVMs that are smearings of MUBs. We give an operational characterization of SIC phase space observables.

  • Erkka Haapasalo: When do pieces determine the whole? Extreme marginals of a completely positive map

We will consider completely positive maps defined on tensor products of von Neumann algebras and taking values in the algebra of bounded operators on a Hilbert space and particularly certain convex subsets of the set of such maps. We show that when one of the marginal maps of such a map is an extreme point, then the marginals uniquely determine the map. We will further prove that when both of the marginals are extreme, then the whole map is extreme. We show that this general result is the common source of several well-known results dealing with, e.g., jointly measurable observables. We also obtain new insight especially in the realm of quantum instruments and their marginal observables and channels as well as a novel criterion for locality of a quantum channel connecting bipartite systems.

  • Teiko Heinosaari: Quantum Incompatibility

Two things are often called incompatible if they are not consistent with each other, for instance, a flat-head screwdriver is incompatible with a hex socket screw. In the context of a physical theory, two things, A and B, described by the theory are called incompatible if the theory does not allow for the existence of a third thing C that would have both A and B as its components. Incompatibility is a fascinating aspect of many physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as ’no-cloning’ and ’no information without disturbance’; these can be all seen as statements about incompatibility of certain devices. This talk develops the incompatibility point of view in quantum theory, giving several examples on the nature of this concept. It will be argued that incompatibility should be seen as resource rather than a hindrance.

  • Michael Keyl: Optimal cloning of quantum states — an overview

This talk will give a survey of optimal quantum cloning and its relation to state estimation. Related topics like optimal purification or, more generally, the simulation of positive but not completely positive maps, will be discussed as well. Apart from the description of the problem and a summary of the most important previous result, we will also have a look on some open problems like cloning of mixed states.

  • Jukka Kiukas: Coexistence of effects from an algebra of two projections

We characterise the coexistence of an arbitrary pair of effects belonging to a von Neumann algebra generated by two projections. As an application we formulate different operational degrees of incompatibility for binary projective measurements, containing, as a special case, the degree of nonclassicality given by the maximal allowed CHSH Bell inequality violation.

  • Takayuki Miyadera: Qualitative Information-Disturbance Relation

Classical and quantum post-processings yield physically meaningful relations in the sets of observables and channels, respectively. When lifted to the sets of equivalence classes, these relations become partial orderings. The partial orderings can be seen as abstract and general ways to describe information (noise) and disturbance. We have proved that the fundamental information-disturbance connection of quantum measurements takes a very natural form in this framework without any specific quantification of information (noise) and disturbance. This talk is based on a work with Teiko Heinosaari.

  • Paolo Perinotti: Complementarity in operational probabilistic theories

We review the framework of operational probabilistic theories, formalising the language of tests and operations. In presenting the formulation of Quantum Theory as a special kind of operational probabilistic theory, we introduce the notions of causality, determinism and complementarity. We show how cloning and discrimination are equivalent under very general assumptions, thus relating no-cloning to complementarity. We then discuss hidden variable models for causal theories, showing the relation between "spookiness" and the existence of complementary measurements.

  • David Reeb: Coexistence does not imply Joint Measurability

First, I will introduce the notions of "coexistence" and "joint measurability" for quantum observables, going back to Ludwig and Lahti, and then prove by an example that the first one is strictly more general than the latter. This resolves a puzzling open question, as both notions have been known to be equivalent for large classes of observables. I will show how the previous example implies that the notions of coexistence and joint measurability have some inherent stability features. Furthermore, I will explain how to check by semidefinite programming (SDP) whether a set of observables is jointly measurable and/or coexistent. Finally, I will outline a way how to construct all pairs of coexistent observables with 2 resp. 3 outcomes. (arXiv:1307.6986, joint work with Daniel Reitzner and Michael Wolf)

  • Daniel Reitzner: Measuring non-coexistence of two projections

Following the definitions and results from the previous talk we will provide further intuition about the measure of non-coexistence of two projections with possibility of extending to sharp observables. To exemplify the theory, we will analyze specific scenarios in various dimensions. We will also show some other operationally meaningful ways of making two simple projective measurements coexistent and put the results into perspective by comparing them to other known conditions of coexistence.

  • Jussi Schultz: Functional coexistence under symmetry constraints

Given that two quantum observables are functionally coexistent, i.e., functions of a common observable, a POVM realizing this common observable is typically highly nonunique. If there is some symmetry in the system respected by the two observables, it is desirable to be able to choose the common observable with the same symmetry. We prove a general fixed point theorem ensuring the existence of such choices, and use it to obtain characterizations for some concrete special cases.

  • Rob Spekkens: Unscrambling the Omelette: Distinguishing Reality from Information in Quantum Theory

E.T. Jaynes famously remarked of the standard quantum formalism that "it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature - all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble." This talk will review some recent efforts to unscramble Jaynes’s omelette. The first effort is a bottom-up approach. It considers theories that are essentially classical but where there is a fundamental restriction on how much knowledge can be acquired about the physical state of any system. Such theories can reproduce a surprisingly large part of quantum theory. The second approach is top-down and argues that the formalism of quantum theory is naturally interpreted as a noncommutative generalization of the theory of Bayesian inference, with quantum states summarizing an agent’s degrees of belief. After identifying all the aspects of the formalism that are about knowledge or inference, what remains can be safely identified as containing the physics. In particular, it will be argued that a unitary is a feature of reality, as is a subtle distinction between spatial relations and temporal relations in quantum theory.

  • Neil Stevens: Generalised models, steering, and correlations

The framework of generalised probabilistic models offer a way to define and analyse certain properties of a theory, independent of a particular formalism. This method can then be used to identify the properties that are possessed by certain theories, such as classical probability or quantum mechanics, that lead them to exhibit known phenomena. This talk will shed light upon a link between incompatibility of observables and ‘non-local’ correlations, through the notion of steering.

  • Alessandro Toigo: On the coexistence of conjugated observables on locally compact abelian groups

For two locally compact abelian groups G and H in duality, conjugated observables are defined in terms of their properties of covariance under the Weyl-Heisenberg representation of the product group G x H. We show that, for two such conjugated observables, joint measurability is equivalent to the existence of a Weyl-Heisenberg covariant joint observables. Some consequences of this fact are discussed in the two cases: 1) G = H = R, in which conjugated observables are fuzzy versions of canonical position and momentum; 2) G = H = Zd, where conjugated observables are unsharp versions of mutually unbiased bases. In case 2), we focus on pairs of unsharp mutually unbiased bases which are smeared with uniform noise, and explicitly find out the minimal amount of noise that is necessary in order to achieve joint measurability.

  • Mário Ziman: Concluding talk

This week in München fifteen-plus trained scholars used incompatible tools to save their 10ets. First, opening day was opened by Michael’s opening welcome and the target was fired by Rob’s unscrambled omelette, Teiko’s flat-head screwdriver and Paul’s trade-off relation. Uniquely “traditional” second day combined forces of David’s coexistence, Alessandro’s covariant joint, Jussi’s fixed point, Jukka’s projections and Daniel’s sharp observables. Third “wild” day focused secret powers of Michael’s purification, Takayuki’s partial ordering, Errka’s extreme marginals, Paolo’s hidden variable and Neil’s steering. Finally, Claudio’s phase space and Tom’s prime power helped to reach the phase of Suddenly Incompatible Coexistence. Everyone will remember this as SIC day. Your untrained observer is there mapping the situation. His conclusions are uncertain, consequences are unpredictable, but everyone (including the organizers) is hoping for the best.

Location

The workshop will take place at the Zentrum Mathematik of the TU München (Garching campus, metro stop "Garching-Forschungszentrum" U6) in Hörsaal 2 (Monday) and in room MA 03.10.011 (Tuesday-Thursday)
Directions

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Hotels:
Hoyacker Hof Pfeil
Motel One Pfeil

Organization and Contact

This workshop is supported by

 Pfeil

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