April 2020

We discuss a point, which from time to time has been doubted in the literature: all symmetries, such as those induced by the energy and momentum conservation laws, hold in quantum physics not just “on average”, as is sometimes claimed, but exactly in each “branch” of the wavefunction, expressed in the basis where the conserved observable is sharp. We note that for conservation laws to hold exactly for quantum systems in this sense (not just on average), it is necessary to assume the so-called “totalitarian property of quantum theory”, namely that any system capable of measuring a quantum observable must itself be quantised. Hence, if conservation laws are to hold exactly, the idea of a `classical measuring apparatus’ (i.e., not subject to the branching structure) is untenable. We also point out that any other principle having a well-defined formulation within classical physics, such as the Equivalence principle, is also to be extended to the quantum domain in exactly the same way, i.e., branch by branch.

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with $N$ depolarizing channels put in superposition of $M$ causal orders via quantum SWITCH. We calculate Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with $M$ and it is independent of $N$. For a qubit it never reaches $1$ if we are increasing $M$. On the other hand, the classical capacity decreases with the dimension $d$ of the message system. Further, for $N=3$ and $N=4$ we studied superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by cyclic permutation subgroup.

In a standard interfeQILab Rometry experiment, one measures the phase difference between two paths by recombining the two wave packets on a beam-splitter. However, it has been recently recognized that the phase can also be estimated via local measurements, by using an ancillary particle in a known superposition state. In this work, we further analyse these protocols for different types of particles (bosons or fermions, charged or uncharged), with a particular emphasis on the subtleties that arise when the phase is due to the coupling to an abelian gauge field. In that case, we show that the measurable quantities are spacetime loop integrals of the 4-vector potential, enclosed by two identical particles or by a particle-antiparticle pair. Furthermore, we generalize our considerations to scenarios involving an arbitrary number of parties performing local measurements on a general charged fermionic state. Finally, as a concrete application, we analyse a recent proposal by Marletto and Vedral (arXiv:1906.03440) involving the time-dependent Aharonov-Bohm effect.

When a noisy communication channel is used multiple times, the errors occurring at different times generally exhibit correlations. Classically, these correlations do not affect the evolution of individual particles: a single classical particle can only traverse the channel at a definite moment of time, and its evolution is insensitive to the correlations between subsequent uses of the channel. In stark contrast, here we show that a single quantum particle can sense the correlations between multiple uses of a channel at different moments of time. In an extreme example, we show that a channel that outputs white noise when the particle is sent at a definite time can exhibit correlations that enable a perfect transmission of classical bits when the particle is sent at a superposition of two times. In contrast, we show that, in the lack of correlations, a single particle sent at a superposition of two times undergoes an effective channel with classical capacity of at most 0.16 bits. When multiple transmission lines are available, time correlations can be used to simulate the application of quantum channels in a coherent superposition of alternative causal orders, and even to provide communication advantages that are not accessible through the superposition of causal orders.

Gauge-invariance is a fundamental concept in Physics — known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata. More precisely, the notions of gauge-invariance and gauge-equivalence in Cellular Automata are formalized. A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.

Table-top tests of quantum gravity (QG) have long been thought to be practically impossible. However, remarkably, due to rapid progress in quantum information science (QIS), such tests may soon be achievable. Here, we uncover an exciting new theoretical link between QG and QIS that also leads to a radical new way of testing QG with QIS experiments. Specifically, we find that only a quantum, not classical, theory of gravity can create non-Gaussianity, a QIS resource that is necessary for universal quantum computation, in the quantum field state of matter. This allows for tests based on QIS in which non-Gaussianity in matter is used as a signature of QG. In comparison to previous studies of testing QG with QIS where entanglement is used to witness QG when all other quantum interactions are excluded, our non-Gaussianity witness cannot be created by direct classical gravity interactions, facilitating tests that are not constrained by the existence of such processes. Our new signature of QG also enables tests that are based on just a single rather than multi-partite quantum system, simplifying previously considered experimental setups. We describe a table-top test of QG that uses our non-Gaussianity signature and which is based on just a single quantum system, a Bose-Einstein condensate (BEC), in a single location. In contrast to proposals based on opto-mechanical setups, BECs have already been manipulated into massive non-classical states, aiding the prospect of testing QG in the near future.