Seminar: Questions and progress in quantum information and causality (summer 2019)

Every Thursday, 10:00-11:30, IQOQI Kitchen (Boltzmanngasse 3).
Update June 2019:
Note that there will be no seminar on June 27. Instead, we will have two talks on June 13: one as usual from 10-11 in the IQOQI Kitchen, and another one at 12:00 noon in the IQOQI Seminar Room. See below.

Contact: Markus Müller

Goals and contents: Presentation of very recent research in quantum information theory and causality. There will be an alteration between invited international speakers, and student talks on current research. Note that "quantum information theory" is construed very broadly, including topics like e.g. quantum thermodynamics. For more detailed bureaucratic information, please see u:space.


List of talks

* March 14: Fabien Clivaz, Unifying paradigms of quantum refrigeration: A universal and attainable bound on cooling (Paper)
Cooling quantum systems is arguably one of the most important thermodynamic tasks connected to modern quantum technologies and an interesting question from a foundational perspective. It is thus of no surprise that many different theoretical cooling schemes have been proposed, differing in the assumed control paradigm, complexity and operating either in a single cycle or in steady state limits. Working out bounds on quantum cooling has since been a highly context dependent task with multiple answers and sometimes obscured assumptions. In this work we derive a universal bound for cooling quantum systems in the limit of infinite cycles (or steady state regimes) that is valid for any control paradigm and machine size. The bound only depends on a single parameter of the refrigerator and is theoretically attainable in all control paradigms. For qubit targets we prove that this bound is achievable in a single cycle and by autonomous machines.

* March 21: Ilya Kull, A spacetime area law bound on quantum correlations
Area laws are a far-reaching consequence of the locality of physical interactions, and they are relevant in a range of systems, from black holes to quantum many-body systems. Typically, these laws concern the entanglement entropy or the quantum mutual information of a subsystem at a single time. However, when considering information propagating in spacetime, while carried by a physical system with local interactions, it is intuitive to expect area laws to hold for spacetime regions. In this work, we prove such a law for quantum lattice systems. 
We consider two agents interacting in disjoint spacetime regions with a spin-lattice system that evolves in time according to a local Hamiltonian. In their respective spacetime regions, the two agents apply quantum instruments to the spins. By considering a purification of the quantum instruments, and analyzing the quantum mutual information between the ancillas used to implement them, we obtain a spacetime area law bound on the amount of correlation between the agents' measurement outcomes. Furthermore, this bound applies both to signaling correlations between the choice of operations on the side of one agent, and the measurement outcomes on the side of the other; as well as to the entanglement they can harvest from the spins by coupling detectors to them.

* March 28: Miguel Navascues, Theoretical research without projects (Paper)
We propose a research funding scheme by which each research unit (be it a single scientist, a group leader or a whole institute) applies for funding, but does not specify how much. The decision of how much funds (if any) must be awarded to each unit is taken by the funding agency, based on the recent scientific activity of the unit and its prior funding. To analyze the performance of this scheme, we introduce a mathematical model of the research system. In this model, each research unit possesses a “scientific productivity function” that relates how much science it can produce with the funds it holds to conduct research. These functions are unknown, i.e., neither the research agency nor the scientists themselves can tell how they look like. Relying on this model, we show that there exist systematic procedures to decide the budget distribution at each grant call, with the property that the total scientific production of the research community will be frequently not far off its maximum possible value. In contrast, "excellence schemes" concentrating funds in the hands of a few are shown to converge to configurations where the total scientific productivity is an arbitrarily small fraction of the maximum achievable.
    Joint work with Costantino Budroni

* April 4: David Trillo Fernandez, Remote time manipulation (Paper)
Harnessing the flow of proper time of arbitrary external systems over which we exert little or no control has been a recurring theme in both science and science-fiction. Unfortunately, all relativistic schemes to achieve this effect beyond mere time dilation are utterly unrealistic. In this work, we find that there exist non-relativistic scattering experiments which, if successful, freeze out, speed up or even reverse the free dynamics of any ensemble of quantum systems present in the scattering region. This "time warping" effect is universal, i.e., it is independent of the particular interaction between the scattering particles and the target systems, or the (possibly non-Hermitian) Hamiltonian governing the evolution of the latter. The protocols require careful preparation of the probes which are scattered, and success is heralded by projective measurements of these probes at the conclusion of the experiment. We fully characterize the possible time translations which we can effect on n target systems through a scattering protocol of fixed duration; the core result is that time can be freely distributed between the systems, and reversed at a small cost. For high n, our protocols allow one to quickly send a single system to its far future or past.

* April 11: Philipp Schüttelkopf, Quantum-coherent mixtures of causal relations (Slides: PDF, PowerPoint)
This talk gives an introduction to the paper by MacLean, Ried, Spekkens, and Resch (Nat. Commun. 8, 15149 (2017)). Abstract of the paper:
Understanding the causal influences that hold among parts of a system is critical both to explaining that system’s natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of
time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common cause acting on both. Here, we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum
version of Berkson’s effect, whereby two independent causes can become correlated upon observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell’s theorem and the search for quantum gravity.

* May 2: Alexander R. H. Smith (Dartmouth College, USA), Quantum clocks, conditional probabilities, and probabilistic time dilation
What allowed Einstein to transcend Newton's conception of an absolute time was his insistence on an operational definition of time as that which is measured by a clock. Quantum theory has yet to be liberated from this absolute notion of time as evidenced by the Schrödinger equation in which time appears as an external classical parameter. 

In this talk I will introduce an operational formulation of quantum theory known as the conditional probability interpretation of time (CPI) in which time is defined in terms of an observable on a quantum system functioning as a clock; in some contexts, the CPI is known as the Page and Wootters mechanism. This clock and a system of interest do not evolve with respect to an external time, but instead, they are entangled and as a consequence a relational dynamics between the system and clock emerges. I will present a generalization of the CPI relevant when the clock and system interact, which should be expected when the gravitational interaction between them is taken into account. I will demonstrate how such clock-system interactions result in a time-nonlocal modification to the Schrödinger equation. I will then examine relativistic particles with internal degrees of freedom which constitute a clock that tracks their proper time. By examining the conditional probability associated with two such clocks reading different proper times, I will show that these clocks exhibit both classical and quantum time dilation effects. Moreover, I will show that the Helstrom-Holevo lower bound requires that these clocks satisfy a time-energy uncertainty relation between the proper time they estimate and their rest mass.

* May 9: Miles Blencowe, The Wigner Current for Open Quantum Systems
We extend the Wigner current vector field (Wigner current) construct to single bosonic mode quantum systems interacting with an environment. In terms of the Wigner function quasiprobability density and associated Wigner current, the open system quantum dynamics can be concisely expressed as a continuity equation. Through the consideration of the harmonic oscillator and additively driven Duffing oscillator in the bistable regime as illustrative system examples, we show how the evolving Wigner current vector field on the system phase space yields useful geometric insights concerning how quantum states decohere away due to interactions with the environment, as well as how they may be stabilized through the counteracting effects of the system anharmonicity (i.e., nonlinearity).

* May 16: Karim Fabian Osman, Beyond Bell's Theorem: Correlation Scenarios
This will be an introduction to the framework as formulated by Tobias Fritz in this paper. The abstract of the paper is as follows:
Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a correlation scenario, and Bell's Theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from Bell scenarios, and we describe examples of (quantum) nonlocality in some of these scenarios, while posing many open problems along the way. Some of our scenarios have been considered before by mathematicians in the context of causal inference.

* May 23: Markus Müller, The second law in nanoscale thermodynamics and no-broadcasting of reference frame information
Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counter- part: the possibility of state transitions is not determined by free energy alone, but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow to extract less work reliably than what is expected from computing the free energy difference. However, these known results rely crucially on the assumption that the thermal machine is not only exactly preserved in every cycle, but also kept uncorrelated from the quantum systems on which it acts. Here we lift this restriction: we allow the machine to become correlated with the microscopic systems on which it acts, while still exactly preserving its own state. Surprisingly, we show that this restores the second law in its original form: free energy alone determines the possible state transitions, and the corresponding amount of work can be invested or extracted from single systems exactly and without any fluctuations.
While this result is true for block-diagonal (quasiclassical) states, we show that an analogous result cannot hold in the presence of quantum coherence. This is due to a general no-broadcasting theorem: coherence and other reference frame information cannot be transferred to other quantum systems without disturbing the reference frame, if that frame is finite-dimensional.
Based on Phys. Rev. X 8, 041051 (2018), and joint work with Matteo Lostaglio, to appear in PRL.

* June 6: Veronika Baumann and Flavio del Santo,  The quantum measurement problem: Wigner’s-friend-type experiments
 Despite its tremendous experimental success, Quantum Theory has always shown profound fundamental problems, of which one of the most long-standing is the “quantum measurement problem”. Formally quantum states evolve according to the unitary (deterministic) continuous time Schrödinger equation, but the actual operation of a measurement is then translated in the theoretical framework into what is usually referred to as the “collapse” of the quantum state, which is a probabilistic, non-unitary process. QT, however, does not state under which conditions, one has to apply either the unitary evolution of the state vector or “collapse” it (state-update rule). This issue becomes problematic when one considers becomes manifest in Wigner’s-friend-type gedankenexperiments, namely when one “observer” is in turn observed, and thus treated as a quantum system. In that case the tension between the unitary dynamics and the state-update rule directly leads to paradoxes.

Following recent more sophisticated variants of the Wigner’s friend gedankenexperiment, we will show that it is possible to formulate an alternative Born rule that, while reproducing all the same probabilities of standard quantum scenarios, it also provides a resolution of the paradoxes in Wigner’s-friend-type scenarios.
Moreover, we will discuss recent results that combine Bell’s inequalities and the Wigner’s friend gedankenexperiment to infer new no-go theorems that undermine the existence of observer-independent measurement outcomes. Finally, we will comment on the operational value of these proposals.

* June 13: Philipp Höhn, Quantum reference systems: a perspective-neutral approach
I will summarize a recent 'perspective-neutral' approach to quantum reference systems and quantum general covariance.
(Based on arXiv:1809.00556, 1809.05093, 1810.04153, 1811.00611)

* June 13, 12:00 noon, IQOQI Seminar Room: Matti Raasakka, Locally finite-dimensional quantum physics and spacetime structure
Gravitational entropy bounds suggest that any bounded quantum system should be describable by a finite-dimensional Hilbert space. I consider a formulation where the finite-dimensionality is implemented at the level of local operator algebras a la algebraic QFT. The requirement of local finite-dimensionality leads to modifications to the microscopic structure of spacetime, which I will explore. I will also discuss how local finite-dimensionality allows for spacetime geometry to be seen as an effective description of the statistical properties of quantum states, and for gravity to emerge as a statistical effect.