Related references: arXiv:1105.4014, arXiv:1112.3679, arXiv:1107.5139]]>

[2] Daniusis, Janzing,...: Inferring deterministic causal relations, UAI 2010.

[3] Janzing: On the entropy production of time-series with uni-directional linearity.Journ. Stat. Phys. 2010.]]>

Disclaimer: Up to some differences in the technical details, all of this is work of Bart Jacobs. (See arXiv:1205.3940)

probability"? De Finetti's theorem licenses the view that it is simply a

convenient metaphor for a certain class of knowledge about a series of

events. There are quantum versions for "unknown states" and "unknown

channels". I will explain how "unknown measurements" can be rehabilitated

too.

I will then move to a totally different topic. The Bloch sphere is handy

for representing qubit states, but the equivalent for two qubits is

15-dimensional! I will advocate instead drawing the set of states that Bob

can steer Alice to, the "steering ellipsoid". I will show how entanglement

and discord look from this perspective, and outline a geometric

classification of separable two qubit states.]]>

]]>

relativistic locality include the Bell's inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava-Lifshitz gravity. Here, we explore a recent proposal for a ``real ensemble'' non-local description of quantum mechanics, in which ``particles'' can copy each others' observables AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has (ordinary) quantum mechanics as a fixed point, where all particles with the same observables have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems (in our study) are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per observable, as well as systematic deviations from quantum mechanics, decay as ~ (EnergyXTime)^{-n}, where n > 2. Interestingly, this convergence is controlled by the absolute value of energy (and not energy difference). Finally, we discuss different issues related to this theory, as well as potential implications for early universe, and the cosmological constant problem.]]>

mechanics.]]>

tau. A time series of positions q,q',q'', ... has two classical

observables: position (q) and velocity (q'-q)/tau. They do not commute,

for observing position does not force the clock to tick, but observing

velocity does force the clock to tick. Thus if VQ denotes first observe

position, then observe velocity and QV denotes first observe velocity,

then observe position, we have

VQ: (q'-q)q/tau

QV: q'(q'-q)/tau

(since after one tick the position has moved from q to q').

Thus [Q,V]= QV - VQ = (q'-q)^2/tau. If we consider the equation

[Q,V] = k (a constant), then k = (q'-q))^2/tau and this is recognizably

the diffusion constant that arises in a process of Brownian motion.

Thus, starting with the simplest assumptions for discrete physics, we are

lead to recognizable physics. We take this point of view and follow it

in both physical and mathematical directions. A first mathematical

direction is to see how i, the square root of negative unity, is related

to the simplest time series: ..., -1,+1,-1,+1,... and making the

above analysis of time series more algebraic leads to the following

interpetation for i. Let e=[-1,+1] and e'=[+1,-1] denote, as ordered

pairs, two phase-shifted versions of the alternating series above.

Define an operator b such that eb = be' and b^2 = 1. Regard b as a time

shifting operator. The operator b shifts the alternating series by one

half its period. Regard e' = -e and ee' = [-1.-1] = -1 (combining term by

term). Then let i = eb. We have ii = (eb)(eb) = ebeb = ee'bb = -1. Thus ii = -1

through the definition of i as eb, a temporally sensitive entity that

shifts it phase in the course of interacting with (a copy of) itself.

By going to i as a discrete dynamical system, we can come back to the

general features of discrete dynamical systems and look in a new way at

the role of i in quantum mechanics. Note that the i we have constructed is

already part of a simple Clifford algebra generated by e and b with

ee = bb = 1 and eb + be = 0. We will discuss other mathematical physical

structures such as the Schrodinger equation, the Dirac equation and the

relationship of a simple logical operator (generalizing negation) with

Majorana Fermions.]]>

Related works:

-GC, Distinguishability and copiability of programs in general process theories, arXiv:1411.3035;

-Categorical purification, http://www.cs.ox.ac.uk/CQM2014/programme/Giulio.pdf

-GC, G. M. D'Ariano, and P. Perinotti, Probabilistic theories with purification, Phys. Rev. A 81, 062348 (2010)

> 2 bits are communicated by transmission of a system that locally

encodes at most one bit, and present protocols with N arbitrarily large. Our hyperdense coding protocols imply superadditive classical

capacities: two entangled systems can encode N > 2 bits, even though each system locally encodes at most one bit. Our protocols violate either a reversibility condition or tomographic locality.

]]>In this talk, I will introduce a novel operational approach to characterizing and reconstructing quantum theory which puts an observer’s information acquisition -- rather than the probability structure – centre stage. In particular, we consider an observer interrogating a system with binary questions and explain how an elementary set of rules governing the observer’s acquisition of information about the system leads to qubit quantum theory. The derivation is constructive, elucidating, among other things, the origin of entanglement, monogamy and more generally the correlation structure. This approach also yields a new characterization of pure states in terms of ‘conserved informational charges’ which, in turn, define the unitary group.

]]>framework: it is assumed that a physical system has some underlying ontic state and that quantum states correspond to probability distributions over these ontic states.

The first question is whether or not quantum states are necessarily real---that is, whether or not the distributions for different quantum states must be disjoint. The PBR theorem proves the reality of quantum states by making assumptions about the ontic structure of bipartite systems, assumptions that have been challenged. Recent work has therefore concentrated on single systems, producing theorems proving the existence of pairs of quantum states whose overlap region on the ontic state space is very small.

The second question is whether the ontology of a quantum system can be macro-realist---that is, can there be "macroscopic" quantities which always have determinate values? The Leggett-Garg inequalities claim to rule out this possibility, but this conclusion has been disputed.

The third question is less familiar: Must quantum superpositions be ontic? That is, for some superposition with respect to some orthonormal basis, must ontic states exist which can be obtained by preparing the superposition, but not by preparing any of the basis states? In other words, can Schrödinger's cat always be either alive xor dead?

]]>

]]>function solving the Schrödinger equation. In view of Feynman's criticism towards classical field theory one may wonder whether such a complex object as the wave function is needed to account for quantum phenomena. After all the value of the velocity field, i.e., of the wave function, is only needed in the vicinity of the configuration of the particle positions, however, it is defined everywhere in configuration space, even in places where the configuration might never roam. In a joint work with M. Hall and H. Wiseman we were able to formulate an approach to quantum mechanics that is capable to describe typical quantum phenomena like interference without a wave function, having only particles. This approach comes at the cost of introducing many classical worlds, hence the name Many-Interacting-Worlds approach (MIW). In MIW the force on each particle is given by 1) Newton's force describing the interaction within each world and 2) an additional force term describing an interaction between the worlds. Similar approaches have been suggested by B. Poirier and C. Sebens. I will give an overview on MIW, discuss the nature of its equations of motion, and its empirical import.

]]>However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many researchers over more than 80 years.

Here we introduce an information theoretic paradigm together with an intuitive geometric picture for decoding incompatible observables,

starting from two simple ideas: Every observable can only provide

limited information and information is monotonic under data

processing. By virtue of quantum estimation theory, we introduce a family of universal criteria for detecting incompatible observables and a natural measure of incompatibility, which are applicable to arbitrary number of arbitrary observables. Based on this framework, we derive a family of universal measurement uncertainty relations, provide a simple information theoretic explanation of quantitative wave--particle duality, and offer new perspectives for understanding Bell nonlocality, contextuality, and quantum precision limit.

]]>In this talk I introduce tools to quantify realistic descriptions of resources, applicable for example when we do not have perfect control over a physical system, when only the neighbourhood of a state or some of its properties are known, or when slight correlations cannot be ruled out.

Some resources, like entanglement, can be characterized in terms of copies of local states: we generalize this with operational ways to describe composition and copies of realistic resources, without assuming a tensor product structure. For others, like thermodynamic work, value is seen as a real function on physical states, like the height of a weight. While value is often expected to behave linearly, that simplification excludes many real-life resources: for example, the operational value of money, in terms of what can be done with it, is hardly linear on the amount of coin, and even has catalytic aspects above certain thresholds. We characterize resources that behave linearly and those that allow for investments - in the extreme, catalytic resources.

This work is an application of the framework introduced in arXiv:1511.08818.

]]>This talk is based on work with Antonios Varvitsiotis and Zhaohui Wei, arXiv:1507.00213 and arXiv:1506.07297. ]]>

]]>

principle carry quantum nonequilibrium. If they did indeed exist, nonequilibrium distributions would not only demonstrate the need to reevaluate the canonical quantum formalism, but also generate new phenomena that lie outside the domain of conventional quantum theory, potentially opening up a large domain for investigation. We will develop a simple, parameter free, quantum field theoretical model of spectral measurement, and use it to demonstrate some of the novel effects that could occur to the profiles of the line spectra of such relic particles. We find for instance, line broadening effects that scale with the resolution of the telescope, the possibility of line narrowing and other effects that could cause multiple bumps to form. We use this discussion to comment on possible implications on the indirect search for dark matter. ]]>

In this talk, we will introduce several types of nonclassical logical structures contained within the N-qubit Pauli group, corresponding in general to preparation and/or measurement schemes for systems of several qubits that demonstrate violation of some notion of classical reasoning. These structures are geometric in nature, and we identify the primitive elements from which more elaborate types are constructed. We will review the key types of structures that are available and explain their hierarchy. Finally we will use them to give simple and transparent proofs of entanglement correlations, quantum contextuality via the Kochen-Specker theorem, and quantum nonlocality via the Bell-GHZ theorem.

These structures have many applications in quantum information processing, but the real purpose of this talk is simply to introduce unfamiliar researchers to the simplest known logical proofs of these nonclassicality theorems, which can be understood using only the algebra of the Pauli spin matrices and simple counting arguments. ]]>

]]> ]]>

The paper introduces an extended Wigner's friend thought experiment, which makes use of Hardy's paradox to show that agents will necessarily reach contradictory conclusions - unless they take into account that they themselves may be in a superposition, and that their subjective experience of observing an outcome is not the whole story.

Frauchiger and Renner then put this experiment in context within a general framework to analyse physical theories. This leads to a theorem saying that a theory cannot be simultaneously (1) compliant with quantum theory, including at the macroscopic level, (2) single-world, and (3) self-consistent across different agents.

In this talk I will (1) describe the experiment and its immediate consequences, (2) quickly review how different interpretations react to it, (3) explain the framework and theorem in more detail.

]]>

[Unpublished results of E.W., Rob Spekkens, Tobias Fritz]

]]>Based on http://arxiv.org/abs/1607.05870.

]]>For a bipartite system (X,Y), the joint entropy can be written as an algebraic sum of three terms: the entropy of X alone, the entropy of Y alone, and the mutual information of X and Y, which comes with an opposite sign. This suggests a set-theoretical analogy: mutual information is a sort of "intersection", and joint entropy is a sort of "union".

The same picture cannot be generalized to three or more parts in a straightforward way, and the problem is still considered open. Is there a deep reason for why the set-theoretical analogy fails?

Category theory can give an alternative, conceptual point of view on the problem. As Shannon already noted, information appears to be related to symmetry. This suggests a natural lattice structure for information, which is compatible with a set-theoretical picture only for bipartite systems.

The categorical approach favors objects with a structure in place of just numbers to describe information quantities. We hope that this can clarify the mathematical structure underlying information theory, and leave it open to wider generalizations. ]]>

I will show how to construct such spaces following the original analysis by Mackay and also show that such modular spaces possess a beautiful geometrical structure that generalizes Riemanian geometry to phase space. A geometry we have named Born geometry. I hope this will open wild speculations on the nature of locality in the presence of quantum mechanics and more broadly the nature of classical reality viewed from a quantum perspective.

]]>For long-distance quantum communication we convert polarization entangled photons generated by a single quantum dot into time-bin entangled photons by sending them through a polarization-time-bin interface [5]. Importantly, this conversion is performed without loss of entanglement strength. Time-bin entanglement is more robust for long-distance quantum communication than polarization entanglement, since time-bin entangled photons are insensitive to thermal and mechanical disturbances in optical fibers.

**References**

[1] M. A. M. Versteegh, M. E Reimer, K. D Jöns, D. Dalacu, P. J. Poole, A. Gulinatti, A. Giudice, and V. Zwiller, *Nature Commun.* **5**, 5298 (2014).

[2] D. Dalacu, K. Mnaymneh, J. Lapointe, X. Wu, P. J. Poole, G. Bulgarini, V. Zwiller, and M. E. Reimer, *Nano Lett.* **12** (11), 5919-5923 (2012).

[3] M. E. Reimer *et al.*, *Phys. Rev. B* **93**, 195316 (2016).

[4] K. D. Jöns *et al.*, arXiv:1510.03897 (2015).

[5] M. A. M. Versteegh, M. E. Reimer, A. A. van den Berg, G. Juska, V. Dimastrodonato, A. Gocalinska, E. Pelucchi, and V. Zwiller, *Phys. Rev. A* **92**, 033802 (2015).

We develop a framework to do Operational Probabilistic Theories (OPT) with indefinite causal structure. For the interest of quantum gravity, this framework gives a general prescription to quantize causal structure, assuming linearity is intact. For the interest of quantum foundations, this framework can support new experimental tests about the validity of quantum theory in complex Hilbert space. It also offers opportunities for constructing new OPT models to substitute ordinary quantum theory. Along this direction, we identify principles that single out the complex Hilbert space theory within the general framework.

]]>We discuss first the geometry of the (N^2-1)--dimensional convex body

of mixed quantum states acting on an N--dimensional Hilbert space

and study projections of this set into 2- and 3-dimensional spaces.

For composed dimensions, N=K^2, one consideres the subset

of separable states and shows that it has a positive measure.

Analyzing its properties contributes to our understanding of

quantum entanglement and its time evolution. ]]>

This is joint work with Antonios Varvitsiotis and Zhaohui Wei.

References:

Phys. Rev. Lett. 117, 060401,

Phys. Rev. A, to appear. (ArXiv:1606.03878),

ArXiv:1609.01030.

]]>TRIGGER WARNING: category theory, blasphemy. ]]>

symmetry is irrevocably violated by quantization. Anomalies not only constrain the

space of classical theories than are consistent with quantum mechanics but are

responsible for rich, surprising and experimentally tested physical phenomena.

In this talk I will give a non-technical, bird's eye introduction to anomalies. ]]>

It is natural to wonder if using an infinite dimensional resource space and local operations, one can return the resource state exactly while producing an entangled state in their state space. Whether or not you can achieve this phenomenon of “perfect embezzlement of an entangled state” depends on which mathematical model one uses to describe “local”.

We prove that perfect embezzlement is impossible in the tensor model but is possible in the commuting model. We then relate this to current work on the conjectures of Connes and Tsirelson about different models for quantum conditional probabilities.

This talk is based on joint work with R. Cleve, L. Liu and S. Harris.

]]>However, this keeps us from gaining a deeper understanding of such concepts which can in turn help us build a theory based on truly foundational concepts.

In this talk I introduce an alternate description of physical reality based on a simple foundational concept that there exist things that influence one another.

A network of objects that influence one another form a partially-ordered set (poset) that is called the influence network is considered. By consistently quantifying such a network with respect to a distinguished chain of events that is called an embedded observer, I demonstrate in relevant special cases that influence events can only be quantified by the familiar mathematics of space-time (Minkowski metric and Lorentz transformations), influence gives rise to basic concepts in Euclidean geometry such as direction, dimension and subspaces as well as the Pythagorean theorem, the dot product and geometrical figures. Thus a discrete version of some of the Euclidean geometry’s fundamental concepts is derived in this picture. Finally I talk about the concept of influence in quantum mechanics and how the case of a free particle is identical to the Feynman checkerboard problem for the electron which is known to give rise to the Dirac equation.

]]>

Possible radical implications aside, performing an experiment like this would push the development of new technologies. The biggest problem would be to get sufficiently high rates wherein there has been a human induced switch at each end before a signal as to the new value of the setting could be communicated to the other end and, at the same time, a photon pair is detected. It looks like an experiment like this, while challenging, is just about feasible with current technologies.

]]>REFERENCE:

Alvaro Mozota Frauca and Rafael Dolnick Sorkin, How to Measure the Quantum Measure, Int J Theor Phys 56: 232-258 (2017), arxiv:1610.02087

]]>

[1] M.H.A. and Y. Nazarov, Phys. Rev. B 91, 104303 (2015)

[2] M.H.A. and Y. Nazarov, Phys. Rev. B 91, 174307 (2015)

]]>I am going to describe our results regarding the* formulation of rules for the update of states after measurement*. I will do it for systems of discrete prime dimensions and I will then give the idea on how to proceed in the non-prime dimensional case.

I will also depict the relationship between Spekkens’ model, stabiliser quantum mechanics and Gross' theory of discrete Wigner functions (they are equivalent theories in odd dimensions) in terms of measurement update rules.

I will conclude by briefly discussing a project we have been recently working on that consists of characterising sub theories of Spekkens’ model that are operationally equivalent to sub theories of QM (in particular in the case of qubits) and use them to represent the non-contextual classically simulable part of state-injection schemes of computation with contextuality as a resource.

]]>The MIW approach offers a direct “realist” description of nature that may be beneficial in interpreting quantum phenomena such as entanglement, measurement, spontaneous decay, etc. It provides a useful analysis of MWI, explaining how the illusion of world branching emerges in that context. Moreover, x(t, C) satisfies a trajectory-based action principle, which allows quantum theory (via the Euler-Lagrange equation and Noether’s theorem) to be placed on the same footing as classical theories. In this manner, a straightforward relativistic generalization can also be obtained [7,8], which offers a notion of global simultaneity even for accelerating observers. Whereas the original MIW theory is fully consistent with Schroedinger wave mechanics, the more recently developed flavors offer the promise of new experimental predictions. These and other developments, e.g. for many dimensions, multiple particles, and spin, may also be discussed.

[1] B. Poirier, Chem. Phys. 370, 4 (2010).

[2] M. J. W. Hall, D.-A. Deckert, and H. Wiseman, Phys. Rev. X 4, 041013 (2014)

[3] B. Poirier, Phys. Rev. X, 4, 040002 (2014).

[4] C. T. Sebens, Phil. Sci. 82, 266 (2015).

[5] P. Holland, Ann. Phys. 315, 505 (2005).

[6] J. Schiff and B. Poirier, J. Chem. Phys. 136, 031102 (2012).

[7] B. Poirier, arXiv:1208.6260 [quant-ph], (2012).

[8] H.-M. Tsai and B. Poirier, EmQM15: Emergent Quantum Mechanics 2015, ed. G. Grössing, (J. Physics, IOP, 2016) 701, 012013.

]]>

Conversely, we describe a protocol that smoothly interpolates between the two-point measurement work distribution for projective measurements and Allahverdyan's work quasi-probability for weak measurements, and show that the negativity of the latter is a direct signature of contextuality.

]]>We will further discuss ideas to experimentally test quantum mechanics by means of collapse models [3] by both matter-wave interferometry [4] and non-interferometric methods [5]. While first experimental bounds by non-interferometric tests have been achieved during the last year by a number of different experiments according to our idea [4], we at Southampton work on setting up the Nanoparticle Talbot Interferometer (NaTalI) to test the quantum superposition principle directly for one million atomic mass unit (amu) particles.

We will further discuss some ideas to probe the interplay between quantum mechanics and gravity by such levitated optomechanics experiments. One idea is to seek experimental evidence about the fundamentally quantum or classical nature of gravity by using the torsional motion of a non-spherical trapped particle [6], while a second idea is to test the effect of the gravity related shift of energy levels of the mechanical harmonic oscillator, which is predicted by semi-classical gravity (Schroedinger-Newton equation) [7] or thirdly try to pick up entanglement mediated by gravity [8].

]]>]]>

We introduce a framework for the non-asymptotic characterization of two related operational tasks, the distillation as well as environment-assisted distillation of quantum coherence. We establish a complete description of the achievable rates of distillation in the one-shot setting under several different classes of free operations, which we show to correspond to the optimization of smoothed entropic quantities as semidefinite programs. We introduce a class of coherence measures which quantify the best achievable fidelity of distillation, and use them to obtain an explicit analytical characterization of coherence distillation for all pure states. Further, we provide insight into the distillation of entanglement, revealing new operational similarities and differences between the resource theories of coherence and entanglement.

This talk is based on joint work with Kun Fang, Xin Wang, and Gerardo Adesso (arxiv:1711.10512) as well as with Ludovico Lami and Alexander Streltsov (in preparation).

]]>learning is entering the field as the latest buzzword. While it provides a more scalable alternative to convex programming and enables forming new conjectures, the outcome of learning methods remains uncertified. In this talk, I introduce the most important paradigms in machine learning for quantum information theory, give an overview of some earlier work in the field, argue for the importance of certifiable predictions of learning algorithms, and present some of our preliminary results. ]]>

We present results along two lines:

(i) Generalised Hong-Ou-Mandel interference as unambiguous state discrimination (arXiv:1806.01236, with S. Stanisic); we find optimised interferometers that discriminate between indistinguishable and interesting distinguishable states by projecting onto non-symmetric irreps of the unitary group of interferometers. We give analytic and numerical results for up to nine photons in nine modes.

(ii) Quantum simulation of noisy boson sampling (arXiv:1803.03657, with A. Moylett); we provide quantum circuits that simulate bosonic sampling with arbitrarily distinguishable particles, based on the quantum Schur-Weyl transform. This makes clear how particle distinguishabililty leads to decoherence in the standard quantum circuit model. We show how ideal samples can be postselected, how photon loss can also be modelled, and how standard results in the classical simulation of noisy quantum computations fail to apply to the boson sampling case. ]]>

One long standing question on quantum non-locality is the quest for an informational principle explaining quantum correlations. Many candidates for such a principle have been proposed with partial success, but none fully explaining quantum correlation. Most of these principles rely on the analysis of the multipartite conditional probabilities. In this talk I will briefly review a few results we had when, instead of analysing multipartite probabilities, we analysed sequences of results from non-local boxes. First, that non-local deterministic boxes cannot be computable. Second, that pseudorandom inputs allow for a local model explaining non-local correlations. Finally, I will present a simple principle that rules out many non-physical sequences of experiments, and a unified view of local and non-signalling correlations based on sequences.

]]>We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of the physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge.

]]>I'll also argue that subjective probabilities are unproblematic in the many-worlds setting by showing how the usual decision-theoretical axioms apply there, and finish by showing that together with a proper definition of measurement they suffice to derive the Born rule.

]]>theory that emerge as inherently nonclassical always involve properties that

are fine tuned, i.e. properties that hold at the operational level but break at the

ontological level (they only hold for fine tuned values of the ontic parameters). Famous

examples of fine tuned properties are noncontextuality and locality. We here

develop a precise theory-independent mathematical framework for characterizing

operational fine tunings. These are distinct from causal fine tunings — already

introduced by Wood and Spekkens — as they do not involve any assumption

on the underlying causal structure. We show how all the already known examples of

operational fine tunings fit into our framework, we discuss possibly new fine tunings

and we use the framework to shed new light on the relation between nonlocality

and generalized contextuality. The framework is set in the language of functors in category

theory and it aims at unifying the spooky properties of quantum theory as well as

accounting for new ones.

]]>