Causal structure in the presence of sectorial constraints, with application to the quantum switch

Existing work on quantum causal structure assumes that one can perform arbitrary operations on the systems of interest. But this condition is often not met. Here, we extend the framework for quantum causal modelling to situations where a system can suffer sectorial constraints, that is, restrictions on the orthogonal subspaces of its Hilbert space that may be mapped to one another. Our framework (a) proves that a number of different intuitions about causal relations turn out to be equivalent; (b) shows that quantum causal structures in the presence of sectorial constraints can be represented with a directed graph; and (c) defines a fine-graining of the causal structure in which the individual sectors of a system bear causal relations. As an example, we apply our framework to purported photonic implementations of the quantum switch to show that while their coarse-grained causal structure is cyclic, their fine-grained causal structure is acyclic. We therefore conclude that these experiments realize indefinite causal order only in a weak sense. Notably, this is the first argument to this effect that is not rooted in the assumption that the causal relata must be localized in spacetime.

Quantum-Enhanced Learning of Continuous-Variable Quantum States

Efficient characterization of continuous-variable quantum states is important for quantum communication, quantum sensing, quantum simulation and quantum computing. However, conventional quantum state tomography and recently proposed classical shadow tomography require truncation of the Hilbert space or phase space and the resulting sample complexity scales exponentially with the number of modes. In this paper, we propose a quantum-enhanced learning strategy for continuous-variable states overcoming the previous shortcomings. We use this to estimate the point values of a state characteristic function, which is useful for quantum state tomography and inferring physical properties like quantum fidelity, nonclassicality and quantum non-Gaussianity. We show that for any continuous-variable quantum states $rho$ with reflection symmetry – for example Gaussian states with zero mean values, Fock states, Gottesman-Kitaev-Preskill states, Schr”odinger cat states and binomial code states – on practical quantum devices we only need a constant number of copies of state $rho$ to accurately estimate the square of its characteristic function at arbitrary phase-space points. This is achieved by performinig a balanced beam splitter on two copies of $rho$ followed by homodyne measurements. Based on this result

Nonclassicality in correlations without causal order

Causal inequalities are device-independent constraints on correlations realizable via local operations under the assumption of definite causal order between these operations. While causal inequalities in the bipartite scenario require nonclassical resources within the process-matrix framework for their violation, there exist tripartite causal inequalities that admit violations with classical resources. The tripartite case puts into question the status of a causal inequality violation as a witness of nonclassicality, i.e., there is no a priori reason to believe that quantum effects are in general necessary for a causal inequality violation. Here we propose a notion of classicality for correlations–termed deterministic consistency–that goes beyond causal inequalities. We refer to the failure of deterministic consistency for a correlation as its antinomicity, which serves as our notion of nonclassicality. Deterministic consistency is motivated by a careful consideration of the appropriate generalization of Bell inequalities–which serve as witnesses of nonclassicality for non-signalling correlations–to the case of correlations without any non-signalling constraints. This naturally leads us to the classical deterministic limit of the process matrix framework as the appropriate analogue of a local hidden variable model. We then define a hierarchy of sets of correlations–from the classical to the most nonclassical–and prove strict inclusions between them. We also propose a measure for the antinomicity of correlations–termed ‘robustness of antinomy’–and apply our framework in bipartite and tripartite scenarios. A key contribution of this work is an explicit nonclassicality witness that goes beyond causal inequalities, inspired by a modification of the Guess Your Neighbour’s Input (GYNI) game that we term the Guess Your Neighbour’s Input or NOT (GYNIN) game.

Graphical CSS Code Transformation Using ZX Calculus

In this work, we present a generic approach to transform CSS codes by building upon their equivalence to phase-free ZX diagrams. Using the ZX calculus, we demonstrate diagrammatic transformations between encoding maps associated with different codes. As a motivating example, we give explicit transformations between the Steane code and the quantum Reed-Muller code, since by switching between these two codes, one can obtain a fault-tolerant universal gate set. To this end, we propose a bidirectional rewrite rule to find a (not necessarily transversal) physical implementation for any logical ZX diagram in any CSS code. We then focus on two code transformation techniques: $textit{code morphing}$, a procedure that transforms a code while retaining its fault-tolerant gates, and $textit{gauge fixing}$, where complimentary codes can be obtained from a common subsystem code (e.g., the Steane and the quantum Reed-Muller codes from the [[15,1,3,3]] code). We provide explicit graphical derivations for these techniques and show how ZX and graphical encoder maps relate several equivalent perspectives on these code transforming operations.

Matrix Mechanics Mis-Prized: Max Born’s Belated Nobelization

We examine evaluations of the contributions of Matrix Mechanics and Max Born to the formulation of quantum mechanics from Heisenberg’s Helgoland paper of 1925 to Born’s Nobel Prize of 1954. We point out that the process of evaluation is continuing in the light of recent interpretations of the theory that deemphasize the importance of the wave function.

Relational interpretation of quantum mechanics and Alexander Bogdanov’s worldview

There is a surprising parallel between the conceptual step taken by the theoretical physicists who discovered quantum mechanics in the 1920s and the philosophical work of Alexander Bogdanov. Both were under the direct cultural influence of the ideas of Ernst Mach. Even more surprisingly, there are aspects of the current debate on the physical interpretation of the quantum formalism that closely mirror the Lenin-Bogdanov debate, in particular on the confusion between subjectivity and relationality. It seems to me that the ideas of Alexander Bogdanov can still bring clarity and be fertile today when applied to open issues in the foundations of physics.

Temporal witnesses of non-classicality in a macroscopic biological system

Exciton transfer along a polymer is essential for many biological processes, for instance light harvesting in photosynthetic biosystems. Here we apply a new witness of non-classicality to this phenomenon, to conclude that, if an exciton can mediate the coherent quantum evolution of a photon, then the exciton is non-classical. We then propose a general qubit model for the quantum transfer of an exciton along a polymer chain, also discussing the effects of environmental decoherence. The generality of our results makes them ideal candidates to design new tests of quantum features in complex bio-molecules.

A toy model provably featuring an arrow of time without past hypothesis

The laws of Physics are time-reversible, making no qualitative distinction between the past and the future — yet we can only go towards the future. This apparent contradiction is known as the `arrow of time problem’. Its resolution states that the future is the direction of increasing entropy. But entropy can only increase towards the future if it was low in the past, and past low entropy is a very strong assumption to make, because low entropy states are rather improbable, non-generic. Recent works, however, suggest we can do away with this so-called `past hypothesis’, in the presence of reversible dynamical laws featuring expansion. We prove that this is the case for a toy model, set in a 1+1 discrete spacetime. It consists in graphs upon which particles circulate and interact according to local reversible rules. Some rules locally shrink or expand the graph. Generic states always expand; entropy always increases — thereby providing a local explanation for the arrow of time.

Relational superposition measurements with a material quantum ruler

In physics, it is crucial to identify operational measurement procedures to give physical meaning to abstract quantities. There has been significant effort to define time operationally using quantum systems, but the same has not been achieved for space. Developing an operational procedure to obtain information about the location of a quantum system is particularly important for a theory combining general relativity and quantum theory, which cannot rest on the classical notion of spacetime. Here, we take a first step towards this goal, and introduce a model to describe an extended material quantum system working as a position measurement device. Such a “quantum ruler” is composed of N harmonically interacting dipoles and serves as a (quantum) reference system for the position of another quantum system. We show that we can define a quantum measurement procedure corresponding to the “superposition of positions”, and that by performing this measurement we can distinguish when the quantum system is in a coherent or incoherent superposition in the position basis. The model is fully relational, because the only meaningful variables are the relative positions between the ruler and the system, and the measurement is expressed in terms of an interaction between the measurement device and the measured system.