Covariance and Quantum Physics-Need for a New Foundation of Quantum Theory?

Tristan Hübsch, Djordje Minić

In this article we present a new view on string theory that is rooted in quantum foundations extended to the domain of quantum gravity in the form of gravitized quantum theory, in which the canonical probability measure captured by the Born rule of quantum theory, turns out to be dynamical and contextual. We claim that this gravitization of quantum theory is the essence of string theory. String theory, according to this view, originates in foundations of quantum theory and Nambu's dynamics, which features in the non-perturbative definition of string theory in terms of a T-duality covariant and non-commutative formulation, called the metastring. Nambu's dynamics and the associated cubic and hypercubic objects also appear as the natural language for exploring the new observables and phenomena implied by a dynamical Born rule, including triple and higher order quantum interference, that can be investigated in experiments involving massive quantum probes, and that are also needed for direct empirical tests of the Born rule, a cornerstone of quantum theory.

Jan Naudts

Ernst Schmützer

Sisi Zhou, Zi-Wen Liu, Liang Jiang

Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important case being the Eastin–Knill theorem). The need for understanding the limits of covariant quantum error correction arises in various realms of physics including fault-tolerant quantum computation, condensed matter physics and quantum gravity. Here, we explore covariant quantum error correction with respect to continuous symmetries from the perspectives of quantum metrology and quantum resource theory, establishing solid connections between these formerly disparate fields. We prove new and powerful lower bounds on the infidelity of covariant quantum error correction, which not only extend the scope of previous no-go results but also provide a substantial improvement over existing bounds. Explicit lower bounds are derived for both erasure and depolarizing noises. We also present a type of covariant codes which nearly saturates these lower bounds.

Asher Peres, Daniel R. Terno

This article discusses the intimate relationship between quantum mechanics, information theory, and relativity theory. Taken together these are the foundations of present-day theoretical physics, and their interrelationship is an essential part of the theory. The acquisition of information from a quantum system by an observer occurs at the interface of classical and quantum physics. The authors review the essential tools needed to describe this interface, i.e., Kraus matrices and positive-operator-valued measures. They then discuss how special relativity imposes severe restrictions on the transfer of information between distant systems and the implications of the fact that quantum entropy is not a Lorentz-covariant concept. This leads to a discussion of how it comes about that Lorentz transformations of reduced density matrices for entangled systems may not be completely positive maps. Quantum field theory is, of course, necessary for a consistent description of interactions. Its structure implies a fundamental tradeoff between detector reliability and localizability. Moreover, general relativity produces new and counterintuitive effects, particularly when black holes (or, more generally, event horizons) are involved. In this more general context the authors discuss how most of the current concepts in quantum information theory may require a reassessment.

Egon Marx