Papers QISS1

We show that, by utilising temporal quantum correlations as expressed by pseudo-density operators (PDOs), it is possible to recover formally the standard quantum dynamical evolution as a sequence of teleportations in time. We demonstrate that any completely positive evolution can be formally reconstructed by teleportation with different temporally correlated states. This provides a different interpretation of maximally correlated PDOs, as resources to induce quantum time-evolution. Furthermore, we note that the possibility of this protocol stems from the strict formal correspondence between spatial and temporal entanglement in quantum theory. We proceed to demonstrate experimentally this correspondence, by showing a multipartite violation of generalised temporal and spatial Bell inequalities and verifying agreement with theoretical predictions to a high degree of accuracy, in high-quality photon qubits.

In a seminal paper, Page found the exact formula for the average entanglement entropy for a pure random state. We consider the analogous problem for the ensemble of pure fermionic Gaussian states, which plays a crucial role in the context of random free Hamiltonians. Using recent results from random matritheory, we show that the average entanglement entropy of pure random fermionic Gaussian states in a subsystem of $N_A$ out of $N$ degrees of freedom is given by $langle S_Arangle_mathrm{G}!=!(N!-!tfrac{1}{2})Psi(2N)!+!(tfrac{1}{4}!-!N_A)Psi(N)!+!(tfrac{1}{2}!+!N_A!-!N)Psi(2N!-!2N_A)!-!tfrac{1}{4}Psi(N!-!N_A)!-!N_A$, where $Psi$ is the digamma function. Its asymptotic behavior in the thermodynamic limit is given by $langle S_Arangle_mathrm{G}!=! N(log 2-1)f+N(f-1)log(1-f)+tfrac{1}{2}f+tfrac{1}{4}log{(1-f)},+,O(1/N)$, where $f=N_A/N$. Remarkably, its leading order agrees with the average over eigenstates of random quadratic Hamiltonians with number conservation, as found by Lydzba, Rigol and Vidmar. Finally, we compute the variance in the thermodynamic limit, given by the constant $lim_{Ntoinfty}(Delta S_A)^2_{mathrm{G}}=frac{1}{2}(f+f^2+log(1-f))$.

In physical experiments, reference frames are standardly modelled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e. spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum $j$ and introduce the transformations between them by upgrading the Euler angles occurring in classical $textrm{SO}(3)$ spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large $j$, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is the first development of the quantum reference frame formalism for a non-Abelian group.

Research on indefinite causal structures is a rapidly evolving field that has a potential not only to make a radical revision of the classical understanding of space-time but also to achieve enhanced functionalities of quantum information processing. For example, it is known that indefinite causal structures provide exponential advantage in communication complexity when compared to causal protocols. In quantum computation, such structures can decide whether two unitary gates commute or anticommute with a single call to each gate, which is impossible with conventional (causal) quantum algorithms. A generalization of this effect to $n$ unitary gates, originally introduced in M. Ara’ujo et al., Phys. Rev. Lett. 113, 250402 (2014) and often called Fourier promise problem (FPP), can be solved with the quantum-$n$-switch and a single call to each gate, while the best known causal algorithm so far calls $O(n^2)$ gates. In this work, we show that this advantage is smaller than expected. In fact, we present a causal algorithm that solves the only known specific FPP with $O(n log(n))$ queries and a causal algorithm that solves every FPP with $O(nsqrt{n})$ queries. Besides the interest in such algorithms on their own, our results limit the expected advantage of indefinite causal structures for these problems.

Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on constructor-information-theoretic ideas, which offers a robust foundation for recently proposed table-top tests of non-classicality in gravity. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical. Hall and Reginatto claimed that there are classical systems that can entangle two quantum systems, thus violating our proposed witness. Here we refute that claim, explaining that the counterexample proposed by Hall and Reginatto in fact validates the witness, vindicating the witness of non-classicality in its full generality.

Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter’, and features a global symmetry. One then extends the theory so as make the global symmetry into a local one (a.k.a gauge-invariance). We formalise a discrete counterpart of this process, known as gauge extension, within the Computer Science framework of Cellular Automata (CA). We prove that the CA which admit a relative gauge extension are exactly the globally symmetric ones (a.k.a the colour-blind). We prove that any CA admits a non-relative gauge extension. Both constructions yield universal gauge-invariant CA, but the latter allows for a first example where the gauge extension mediates interactions within the initial CA.

In this paper, we continue the analysis of the effective model of quantum Schwarzschild black holes recently proposed by some of the authors in [1,2]. In the resulting spacetime the central singularity is resolved by a black-to-white hole bounce, quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon and classical geometry is approached asymptotically. This is the case independently of the relation between the black and white hole masses, which are thus freely specifiable independent observables. A natural question then arises about the phenomenological implications of the resulting non-singular effective spacetime and whether some specific relation between the masses can be singled out from a phenomenological perspective. Here we focus on the thermodynamic properties of the effective polymer black hole and analyse the corresponding quantum corrections as functions of black and white hole masses. The study of the relevant thermodynamic quantities such as temperature, specific heat and horizon entropy reveals that the effective spacetime generically admits an extremal minimal-sized configuration of quantum-gravitational nature characterised by vanishing temperature and entropy. For large masses, the classically expected results are recovered at leading order and quantum corrections are negligible, thus providing us with a further consistency check of the model. The explicit form of the corrections depends on the specific relation among the masses. In particular, a first-order logarithmic correction to the entropy is obtained for a quadratic mass relation. The latter corresponds to the case of proper finite length effects which turn out to be compatible with a minimal length generalised uncertainty principle associated with an extremal Planck-sized black hole.

Since the appearance of Einstein’s paper {em”On the Electrodynamics of Moving Bodies”} and the birth of special relativity, it is understood that the theory was basically coded within Maxwell’s equations. The celebrated mass-energy equivalence relation, $E=mc^2$, is derived by Einstein using thought experiments involving the kinematics of the emission of light (electromagnetic energy) and the relativity principle. Text book derivations often follow paths similar to Einstein’s, or the analysis of the kinematics of particle collisions interpreted from the perspective of different inertial frames. All the same, in such derivations the direct dynamical link with hypothetical fundamental fields describing matter (e.g. Maxwell theory or other) is overshadowed by the use of powerful symmetry arguments, kinematics, and the relativity principle. Here we show that the formula can be derived directly form the dynamical equations of a massless matter model confined in a bo(which can be thought of as a toy model of a composite particle). The only assumptions in the derivation are that the field equations hold and the energy-momentum tensor admits a universal interpretation in arbitrary coordinate systems. The mass-energy equivalence relation follows from the inertia or (taking the equivalence principle for granted) weight of confined field radiation. The present derivation offers an interesting pedagogical perspective on the formula providing a simple toy model on the origin of mass and a natural bridge to the foundations of general relativity.

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime QRF, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of describing the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the evolution parameter coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition. Concretely, we consider N relativistic quantum particles in a weak gravitational field and introduce a timeless formulation in which the global state of the N particles appears “frozen”, but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fithe QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, keeping the proper time in the local frame of the particle. This fully relational construction shows how the remaining particles evolve from the perspective of the QRF and includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we observe a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations in the QRF.

A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner’s theorem. Wigner’s theorem establishes that every symmetry of the quantum state space must be either a unitary transformation, or an antiunitary transformation. Here we extend Wigner’s theorem from quantum states to quantum evolutions, including both the deterministic evolution associated to the dynamics of closed systems, and the stochastic evolutions associated to the outcomes of quantum measurements. We prove that every symmetry of the space of quantum evolutions can be decomposed into two state space symmetries that are either both unitary or both antiunitary. Building on this result, we show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions. Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes. Here we propose a time symmetric formulation of quantum theory where the allowed quantum evolutions are restricted to a suitable set, which includes both unitary evolution and projective measurements, but excludes the deterministic preparation of pure states. The standard operational formulation of quantum theory can be retrieved from this time symmetric version by introducing an operation of conditioning on the outcomes of past experiments.