# All

Tracking the behaviour of stochastic systems is a crucial task in the

statistical sciences. It has recently been shown that quantum models can

faithfully simulate such processes whilst retaining less information about the

past behaviour of the system than the optimal classical models. We extend these

results to general temporal and symbolic dynamics. Our systematic protocol for

quantum model construction relies only on an elementary description of the

dynamics of the process. This circumvents restrictions on corresponding

In previous work we proved that, for categories of free finite-dimensional

modules over a commutative semiring, linear compact-closed symmetric monoidal

structure is a property, rather than a structure. That is, if there is such a

structure, then it is uniquely defined (up to monoidal equivalence). Here we

provide a novel unifying category-theoretic notion of symmetric monoidal

structure with local character, which we prove to be a property for a much

broader spectrum of categorical examples, including the infinite-dimensional

The observations the dc voltage on asymmetric superconducting ring testify

that one of the ring segments is a dc power source. The persistent current

flows against the total electric field in this segment. This paradoxical

phenomenon is observed when the ring or its segments are switched between

superconducting and normal state by non-equilibrium noises. We demonstrate that

the dc voltage and the power increase with the number of the identical rings

connected in series. Large voltage and power sufficient for practical

We test the principles of classical modal logic in fully quantum settings.

Modal logic models our reasoning in multi-agent problems, and allows us to

solve puzzles like the muddy children paradox. The Frauchiger-Renner thought

experiment highlighted fundamental problems in applying classical reasoning

when quantum agents are involved; we take it as a guiding example to test the

axioms of classical modal logic. In doing so, we find a problem in the original

formulation of the Frauchiger-Renner theorem: a missing assumption about

Quantum self-testing addresses the following question: is it possible to

verify the existence of a multipartite state even when one's measurement

devices are completely untrusted? This problem has seen abundant activity in

the last few years, particularly with the advent of parallel self-testing

(i.e., testing several copies of a state at once), which has applications not

only to quantum cryptography but also quantum computing. In this work we give

the first error-tolerant parallel self-test in a three-party (rather than

Physical systems in the time domain may exhibit analogous phenomena in real

space, such as time crystals, time-domain Fresnel lenses, and modulational

interference in a qubit. Here we report the experimental realization of

time-domain grating using a superconducting qutrit in periodically modulated

probe and control fields via two schemes: Simultaneous modulation and

complementary modulation. Both experimental and numerical results exhibit

modulated Autler-Townes (AT) and modulation-induced diffraction (MID) effects.

A notion of morphism that is suitable for the sheaf-theoretic approach to

contextuality is developed, resulting in a resource theory for contextuality.

The key features involve using an underlying relation rather than a function

between measurement scenarios, and allowing for stochastic mappings of outcomes

to outcomes. This formalizes an intuitive idea of using one empirical model to

simulate another one with the help of pre-shared classical randomness. This

A method for the implementation of a universal set of fault-tolerant logical

gates is presented using homological product codes. In particular, it is shown

that one can fault-tolerantly map between different encoded representations of

a given logical state, enabling the application of different classes of

transversal gates belonging to the underlying quantum codes. This allows for

the circumvention of no-go results pertaining to universal sets of transversal

We employ a quasirandom methodology, recently developed by Martin Roberts, to

estimate the separability probabilities, with respect to the Bures (minimal

monotone/statistical distinguishability) measure, of generic two-qubit and

two-rebit states. This procedure, based on generalized properties of the golden

ratio, yielded, in the course of almost fifteen billion iterations, two-qubit

estimates repeatedly agreeing to close to nine decimal places with

$\frac{25}{341} =\frac{5^2}{11 \cdot 31} \approx 0.07331378299$. The

We review the physical foundations of Landauer's Principle, which relates the

loss of information from a computational process to an increase in

thermodynamic entropy. Despite the long history of the Principle, its

fundamental rationale and proper interpretation remain frequently

misunderstood. Contrary to some misinterpretations of the Principle, the mere

transfer of entropy between computational and non-computational subsystems can

occur in a thermodynamically reversible way without increasing total entropy.