Emergence of Constructor-Based Irreversibility in Quantum Systems: Theory and Experiment.

How irreversibility arises in a universe with time-reversal symmetric laws is a central problem in physics. In this Letter, we discuss a radically different take on the emergence of irreversibility, adopting the recently proposed constructor theory framework. Irreversibility is expressed as the requirement that a task is possible, while its inverse is not. We prove the compatibility of such irreversibility with quantum theory's time-reversal symmetric laws, using a dynamical model based on the universal quantum homogenizer. We also test the physical realizability of this model by means of an experimental demonstration with high-quality single-photon qubits.

Temporal teleportation with pseudo-density operators: How dynamics emerges from temporal entanglement.

We show that, by using 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 generalized temporal and spatial Bell inequalities and verifying agreement with theoretical predictions to a high degree of accuracy, in high-quality photon qubits.

Non-Monogamy of Spatio-Temporal Correlations and the Black Hole Information Loss Paradox.

Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a theoretical proposal to extend quantum theory with these pseudo-states to describe the statistics arising in black-hole evaporation. We also provide an experimental demonstration of this theoretical proposal, using a simulation in optical regime, that tomographically reproduces the correlations of the pseudo-density matrix describing this physical phenomenon.

Aharonov-Bohm Phase is Locally Generated Like All Other Quantum Phases.

In the Aharonov-Bohm (AB) effect, a superposed charge acquires a detectable phase by enclosing an infinite solenoid, in a region where the solenoid's electric and magnetic fields are zero. Its generation seems therefore explainable only by the local action of gauge-dependent potentials, not of gauge-independent fields. This was recently challenged by Vaidman, who explained the phase by the solenoid's current interacting with the electron's field (at the solenoid). Still, his model has a residual nonlocality: it does not explain how the phase, generated at the solenoid, is detectable on the charge. In this Letter, we solve this nonlocality explicitly by quantizing the field. We show that the AB phase is mediated locally by the entanglement between the charge and the photons, like all electromagnetic phases. We also predict a gauge-invariant value for the phase difference at each point along the charge's path. We propose a realistic experiment to measure this phase difference locally, by partial quantum state tomography on the charge, without closing the interference loop.

Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators.

Closed timelike curves are striking predictions of general relativity allowing for time-travel. They are afflicted by notorious causality issues (e.g. grandfather's paradox). Quantum models where a qubit travels back in time solve these problems, at the cost of violating quantum theory's linearity-leading e.g. to universal quantum cloning. Interestingly, linearity is violated even by open timelike curves (OTCs), where the qubit does not interact with its past copy, but is initially entangled with another qubit. Non-linear dynamics is needed to avoid violating entanglement monogamy. Here we propose an alternative approach to OTCs, allowing for monogamy violations. Specifically, we describe the qubit in the OTC via a pseudo-density operator-a unified descriptor of both temporal and spatial correlations. We also simulate the monogamy violation with polarization-entangled photons, providing a pseudo-density operator quantum tomography. Remarkably, our proposal applies to any space-time correlations violating entanglement monogamy, such as those arising in black holes.

Constructor theory of probability.

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalizing and improving upon the so-called 'decision-theoretic approach', I shall recast that problem in the recently proposed constructor theory of information-where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove that the unpredictability of measurement outcomes (to which constructor theory gives an exact meaning) necessarily arises in superinformation theories. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements can arise under superinformation theories. And I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch-Wallace-type argument-thus defining a class of decision-supporting superinformation theories. This broadens the domain of applicability of that argument to cover constructor-theory compliant theories. In addition, in this version some of the argument's assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

Constructor theory of information.

We propose a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible-i.e. in constructor-theoretic terms. It includes conjectured, exact laws of physics expressing the regularities that allow information to be physically instantiated. Although these laws are directly about information, independently of the details of particular physical instantiations, information is not regarded as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. This theory solves a problem at the foundations of existing information theory, namely that information and distinguishability are each defined in terms of the other. It also explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and locally inaccessible information (as in entangled systems).

Constructor theory of life.

Neo-Darwinian evolutionary theory explains how the appearance of purposive design in the adaptations of living organisms can have come about without their intentionally being designed. The explanation relies crucially on the possibility of certain physical processes: mainly, gene replication and natural selection. In this paper, I show that for those processes to be possible without the design of biological adaptations being encoded in the laws of physics, those laws must have certain other properties. The theory of what these properties are is not part of evolution theory proper, yet without it the neo-Darwinian theory does not fully achieve its purpose of explaining the appearance of design. To this end, I apply constructor theory's new mode of explanation to express exactly within physics the appearance of design, no-design laws, and the logic of self-reproduction and natural selection. I conclude that self-reproduction, replication and natural selection are possible under no-design laws, the only non-trivial condition being that they allow digital information to be physically instantiated. This has an exact characterization in the constructor theory of information. I also show that under no-design laws an accurate replicator requires the existence of a 'vehicle' constituting, together with the replicator, a self-reproducer.

Peierls distortion and quantum solitons.

Peierls distortion and quantum solitons are two hallmarks of 1-dimensional condensed-matter systems. Here we propose a quantum model for a one-dimensional system of nonlinearly interacting electrons and phonons, where the phonons are represented via coherent states. This model permits a unified description of Peierls distortion and quantum solitons. The nonlinear electron-phonon interaction and the resulting deformed symmetry of the Hamiltonian are distinctive features of the model, of which that of Su, Schrieffer, and Heeger can be regarded as a special case.

Effects of reduced measurement independence on Bell-based randomness expansion.

With the advent of quantum information, the violation of a Bell inequality is used to witness the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's theorem is the existence of experimental "free will," meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a no-signaling model with reduced "free will" and bound the adversary's capabilities in the task of randomness expansion.