Information and the Reconstruction of Quantum Physics

Abstract

The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra-mathematical content. Here, a representative series of specifically information-based treatments-from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems-is reviewed.The most basic physical principle of quantum mechanics is that of state superposition: Any sum of physical state vectors is also a physical state, with these states lying in a Hilbert space or related mathematical structure; cf., for example, ref.[1]. The standard view recently has been that superposition lends striking features to quantum informationthat is, information encoded entirely via quantum systems-that are not found in its classical counterpart, that is, information encoded in classical mechanical states. The most striking of the features of the quantum state itself are those associated with entanglement, which arises with the interaction or joint appearance of systems via another basic quantum physical rule, that which assigns the tensor-product space of the linear spaces of the subsystems composing a larger system; as its consequence, quantum signal-state correlations are possible that are stronger than those between classical states-these correlations being often called "nonlocal" because they violate Bell-type inequalities and enable communication and information processing tasks to be accomplished that either cannot be done as efficiently or cannot be done at all using only classical mechanical signals; cf., for example, ref. [2].That nonclassical phenomena involving correlation can arise when quantum systems are entangled was evident early in the history of quantum mechanics to Albert Einstein [3] and to Erwin Schrödinger, [4,5] who named entanglement, even before the explorations of David Bohm, [6] John S. Bell, [7] Abner Shimony, [1] and others, for whom the understanding of nonlocal correlations was a great pursuit and who devised the first ...

No Preferred Reference Frame at the Foundation of Quantum Mechanics

“…As a result, there are many programs designed to interpret quantum mechanics (QM), i.e., reveal what QM is telling us about Nature. We will not review such attempts here (the interested reader is referred to Drummond’s 2019 overview of QM interpretations [ 3 ]), rather in this paper we will explain how axiomatic reconstructions of QM based on information-theoretic principles (e.g., see [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ] or the review by Jaeger [ 24 ]) contain a surprising advance in the understanding of QM. Specifically, we will show how the principle of Information Invariance and Continuity [ 8 ]: The total information of one bit is invariant under a continuous change between different complete sets of mutually complementary measurements.…”

“…Nonetheless, they all reveal directly or indirectly that the key difference between classical and quantum probability theories resides in the continuity of reversible transformations between pure states ( Section 2 ). In what is considered the first axiomatic reconstruction of QM [ 24 ], Hardy notes that by adding the single word “continuous” to his reversibility axiom, one obtains quantum probability theory instead of classical probability theory [ 4 ]. Indeed, many authors emphasize this point [ 12 , 19 , 22 , 42 ], e.g., Koberinski and Müller write [ 23 ]: We suggest that (continuous) reversibility may be the postulate which comes closest to being a candidate for a glimpse on the genuinely physical kernel of “quantum reality”.…”

Still Minding the Gap? Reflecting on Transitions between Concepts of Information in Varied Domains

“…An example of the continuing penetration of information concepts into physics is given in the demonstration that the third law of thermodynamics, generally expressed as the impossibility of reaching absolute zero, is related to the maximum speed with which information can be erased [21]. There has also been continuing interest in reconstructing the formalism of quantum theory in information terms [22,23].…”

The Physics of Information

“…Could we get it from bit ? A number of researcher investigate this possibility, and several of their attempts to recover physical laws from the principles governing information are reported about in this special issue on physics of information . The articles by Gregg Jaeger, by Ariel Caticha, and by John Skilling and Kevin Knuth address the reconstruction of quantum mechanics from information theory. Furthermore, Kevin Knuth and James Walsh show how to recover space‐time from particles sending each others signals in an initially geometry‐free setting.…”