The lesson learned from this observation will be briefly discussed. The concept of objectivity, on the other hand, is closedly linked to that one of "an observer", thus, we can at least assign it as a primitive of the theory. Now agents are themselves physical systems, and we should take this into account when we specify the ground rules of what they can do.

## Department of Mathematics

On the one hand, we take agents and their communication as a primitive of the theory and then see which concepts can be derived from there. I give further details on a unification of the foundations of operational quantum theory with those of quantum field theory, coming out of a program that is also known as the positive formalism.

I will discuss status and challenges of this program, focusing on the central new concept of local quantum operation. Among the conceptual challenges I want to highlight the question of causality.

How do we know that future choices of measurement settings do not influence present measurement results? Should we enforce this, as in the standard formulation of quantum theory? Should this "emerge" from a fundamental theory? Does this question even make sense in a context without a fixed notion of time, such as quantum gravity? With a heavy dose of speculation put also grounded in very concrete evidence I find that fermionic theories might play an essential role.

Ognyan Oreshkov , Universite Libre de Bruxelles. Time-delocalized quantum subsystems and operations: on the existence of processes with indefinite causal structure in quantum mechanics.

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However, up until now, there has been no rigorous justification for the interpretation of such an experiment as a genuine realization of a process with indefinite causal structure as opposed to a simulation of such a process. Where exactly are the local operations of the parties in such an experiment? On what spaces do they act given that their times are indefinite?

Can we probe them directly rather than assume what they ought to be based on heuristic considerations? How can we reconcile the claim that these operations really take place, each once as required, with the fact that the structure of the presumed process implies that they cannot be part of any acyclic circuit?

Here, I offer a precise answer to these questions: the input and output systems of the operations in such a process are generally nontrivial subsystems of Hilbert spaces that are tensor products of Hilbert spaces associated with different times—a fact that is directly experimentally verifiable.

With respect to these time-delocalized subsystems, the structure of the process is one of a circuit with a cycle, which cannot be reduced to a possibly dynamical probabilistic mixture of acyclic circuits. This provides, for the first time, a rigorous proof of the existence of processes with indefinite causal structure in quantum mechanics.

I further show that all bipartite processes that obey a recently proposed unitary extension postulate, together with their unitary extensions, have a physical realization on such time-delocalized subsystems, and provide evidence that even more general processes may be physically admissible.

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These results unveil a novel structure within quantum mechanics, which may have important implications for physics and information processing. Paolo Perinotti , Universita degli Studi di Pavia. I nfinite composite systems and cellular automata in operational probabilistic theories. Cellular automata are a central notion for the formulation of physical laws in an abstract information-theoretical scenario, and lead in recent years to the reconstruction of free relativistic quantum field theory.

For this purpose, we construct infinite composite systems, illustrating the main features of their states, effects and transformations. We discuss the generalization of the concepts of homogeneity and locality, in an framework where space-time is not a primitive object. Ana Belen Sainz , Perimeter Institute. Almost quantum correlations violate the no-restriction hypothesis. To identify which principles characterise quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations.

We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalised probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost quantum correlations.

Therefore, any theory whose correlations are exactly, or very close to, the almost quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other non-signalling ones.

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## Quantum Information Theory and the Foundations of Quantum Mechanics

Lev Vaidman , Tel Aviv University. The protocols of full communication, including transmitting unknown quantum states were proposed only few years ago, but it was shown that in all these protocols the particle was leaving a weak trace in the transmission channel, the trace larger than the trace left by a single particle passing through the channel. However, a simple modification of these recent protocols eliminates the trace in the transmission channel and makes all these protocols truly counterfactual.

Dominic Verdon , University of Oxford. A compositional approach to quantum functions, and the Morita theory of quantum graph isomorphisms. We apply Morita-theoretical machinery within this framework to characterise, classify, and construct quantum strategies for the graph isomorphism game. This is joint work with Benjamin Musto and David Reutter, based on the papers Alexander Wilce , Susquehanna University.

The similarity of this derivation in some respects to the constructive one offered by Julian Schwinger c. One of the insights obtained from this reconstruction is that H5 is the one distinguishing the quantum probabilistic structure derived from a classical one. Hardy argues that this exercise helps point the way toward a modified version of quantum theory in which quantum gravity might be obtained, toward a broader such framework he was later to offer, cf.

That work attempted a reconstruction that is also based on five axioms stated here following Hardy's later analysis 63 of its full axiomatic structure : 1 Information, 2 Information locality, 3 Tomographic locality, 4 The existence of a reversible transformation between any pair of pure states, and 5 Gebit a generalized bit state spectrality; any state for a gebit can be written as a convex combination of a pair of maximally distinguishable states , with causality taken as a background assumption.

Hardy was later to point out shortcomings in this attempt, including some around the use of gebits, a special case of a state. Its five axioms are: MM1 In systems that carry one bit of information, each state is characterized by a finite set of outcome probabilities. MM2 The state of a composite system is characterized by the statistics of measurements on the individual components.

MM3 All systems that effectively carry the same amount of information have equivalent state spaces. MM4 Any pure state of a system can be reversibly transformed into any other. This reconstruction grapples with similar issues to those of refs. Notably, unlike ref. A central goal of the approach has been to minimize the number of axioms needed to derive quantum theory as distinct from other generalized theories of probability. In further pursuit of this goal, these workers have since shown that MM2 can be weakened and replaced by the requirements that gebits carry exactly one bit of information and that any system state be reversibly encodable in a sufficiently large number of generalized bits.

## Realism and Antirealism in Informational Foundations of Quantum Theory | Bilban | Quanta

A specific sort of quantum circuit model was introduced in this work that incorporates structures naturally connected with the operations they perform. The precise sense in which theory is said to be operationalist is the following.

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The analogous system of the bit in quantum theory is the qubit, having not only the two states 0 and 1, but also all their superpositions, corresponding to the possibility of having complementary properties which are absent in classical computer science. Therefore, we are left with states of qubits, namely pure quantum software: objects, matter, hardware, completely became vaporized.

The six principles used in the derivation are the following. All six principles apart from vi hold for both classical and quantum information: only the purification one singles out quantum theory. Principle iii relates probability and logic. Principle iv is the requirement that two transformations suffice to identify their composition. Principle v allows for subsystems. Principle vi allows any form of irreversibility or state mixing to correspond to discarding part of the environment of the system in question. A primary task for informational reconstructive approaches to quantum theory has long been to provide, at a minimum, an informatic motivation for the mathematical structures assumed in quantum mechanics, such as complex Hilbert state space, and Hermitian operators representing system properties, as seen in the previous examples discussed above.

In this case, the representability of every state of a system as a Hermitian operator on a complex Hilbert space of said dimension is achieved by showing the identity of the upper bounds on the probability of conclusive teleportation of an unknown state in terms of the maximal number of perfectly discriminable states and the dimension of the vector space spanned by system states. Holism in quantum mechanics is generally understood as exemplified by the existence of entangled states, entangled states being just those that are inseparable —that is, those that generally cannot be prepared by local operations.

In an OPT, the two are tantamount: Entangled states have the feature that the marginal probabilities pertaining to subsystems are mixed, with maximal knowledge of their composite without maximal knowledge of the parts, and the converse—that such maximal knowledge of the composite without that of the parts implies its being entangled. Principle ii implies that any two distinct states of a composite system have different joint probability distributions for some local measurement, allowing them to be distinguished by local measurements on the subsystems alone via the corresponding correlations and that the composite system dimension is the product of the subsystem state dimensions: The full information of the entangled state is that contained in these correlations.

From the perspective of this approach, Principle vi is that of greatest significance because it serves to distinguish quantum OPT from classical OPT. The basic idea is that every mixed state can be prepared by discarding part of a larger pure composite system state to which it belongs.

The principle can also be seen as capturing a law of conservation of information in that every irreversible process can be carried out uniquely via a reversible interaction of the system undergoing it with an environment in a pure state before interaction begins. A decade after his paper of , motivated in part by intervening work of refs. The key elements of this treatment are a maximal set of distinguishable states, namely, any set containing the maximum number of states for which there exists a maximal measurement, which is a measurement that can distinguish a state from the others of the maximal set in a single attempt, with a maximal effect being associated with its result.

As in the paper, quantum theory is here considered a sort of probability theory with quantum states represented by vectors of probabilities. It is shown that there are only two theories according with the set of operational postulates assembled here including names characterizing them 63 : P1 Sharpness. Associated with any given pure state is a unique maximal effect giving probability equal to one.

This maximal effect does not give probability equal to one for any other pure state. P2 Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. P3 Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components.