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.
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.
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.
We consider the quantum version of inferring the causal relation between events. There has been recent progress towards identifying minimal interventions and observations needed. We here show, by means of constructing an explicit scheme, that quantum observations alone are sufficient for quantum causal inference for the case of a bipartite quantum system with measurements at two times. Our scheme involves the derivation of a closed-form expression for the space-time pseudo-density matrix associated with many times and qubits. This matrix can be determined by coarse-grained quantum observations alone. We show that from this matrix one can infer the causal structure via the sign of a particular function called a causal monotone. Our results show that for quantum processes one can infer the causal structure solely from correlations between observations at different times.
The quest for complete observables in general relativity has been a longstanding open problem. We employ methods from descriptive set theory to show that no complete observable is Borel definable. In fact, we show that it is consistent with the Zermelo-Fraenkel and Dependent Choice axioms that no complete observable exists whatsoever. In a nutshell, this implies that the Problem of Observables is to`analysis’ what the Delian Problem was to `straightedge and compass’. Our results remain true even after restricting the space of solutions to vacuum solutions. In other words, the issue can be traced to the presence of local degrees of freedom in general relativity.
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.
Locality is a central notion in modern physics, but different disciplines understand it in different ways. Quantum field theory focusses on relativistic locality, enforced by microcausality, while quantum information theory focuses on subsystem locality, which regulates how information and causal influences propagate in a system, with no direct reference to spacetime notions. Here we investigate how microcausality and subsystem locality are related. The question is relevant for understanding whether it is possible to formulate quantum field theory in quantum information language, and has bearing on the recent discussions on low-energy tests of quantum gravity. We present a first result in this direction: in the quantum dynamics of a massive scalar quantum field coupled to two localised systems, microcausality implies subsystem locality in a physically relevant approximation.
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, we show that, given nonlocal quantum measurements, for any $k$-mode continuous-variable states $rho$ having reflection symmetry, we only require $O(log M)$ copies of $rho$ to accurately estimate its characteristic function values at any $M$ phase-space points. Furthermore, the number of copies is independent of $k$. This can be compared with restricted conventional approach, where $Omega(M)$ copies are required to estimate the characteristic function values at $M$ arbitrary phase-space points.
Non-abelian symmetries play a central role in many areas in physics, and have been recently argued to result in distinct quantum dynamics and thermalization. Here we unveil the effect that the non-abelian SU(2) symmetry, and the rich Hilbert space structure that it generates for spin 1/2 systems, has on the average entanglement entropy of random pure states and of highly-excited Hamiltonian eigenstates. Focusing on the zero magnetization sector (J_z=0) for different fixed spin J, we show that the entanglement entropy has a leading volume law term whose coefficient s_A depends on the spin density j=2J/L, with s_A(j –> 0)=ln(2) and s_A(j –> 1)=0. We also discuss the behavior of the first subleading corrections.
It is shown that any theory that has certain properties has a measurement problem, in the sense that it makes predictions that are incompatible with measurement outcomes being absolute (that is, unique and non-relational). These properties are Bell Nonlocality, Information Preservation, and Local Dynamics. The result is extended by deriving Local Dynamics from No Superluminal Influences, Separable Dynamics, and Consistent Embeddings. As well as explaining why the existing Wigner’s-friend-inspired no-go theorems hold for quantum theory, these results also shed light on whether a future theory of physics might overcome the measurement problem. In particular, they suggest the possibility of a theory in which absoluteness is maintained, but without rejecting relativity theory (as in Bohm theory) or embracing objective collapses (as in GRW theory).
