Black Box Quantum Mechanics

J. E. Cunningham

Liam P. McGuinness

Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is truly random. However, existing demonstrations are not black-box, to avoid falsely certifying deterministic data, assumptions must be made on how the data was generated. Here we demonstrate genuine randomness certification in the black-box setting -- one in which no deterministic adversary, even with unlimited computational power, will succeed in getting their data certified. We use it to provably generate random numbers using only measurements on single particle states and without a random seed.

Peng Wang, Gang Xin, Yuwei Jiao

In recent decades, with the emergence of numerous novel intelligent optimization algorithms, many optimization researchers have begun to look for a basic search mechanism for their schemes that provides a more essential explanation of their studies. This paper aims to study the basic mechanism of an algorithm for black-box optimization with quantum theory. To achieve this goal, the Schroedinger equation is employed to establish the relationship between the optimization problem and the quantum system, which makes it possible to study the dynamic search behaviors in the evolution process with quantum theory. Moreover, to explore the basic behavior of the optimization system, the optimization problem is assumed to be decomposed and approximated. Then, a multilevel approximation quantum dynamics model of the optimization algorithm is established, which provides a mathematical and physical framework for the analysis of the optimization algorithm. Correspondingly, the basic search behavior based on this model is derived, which is governed by quantum theory. Comparison experiments and analysis between different bare-bones algorithms confirm the existence of the quantum mechanic based basic search mechanism of the algorithm on black-box optimization.

Bruce Cameron Reed

Mingsheng Ying

Radu Necsanu

This paper develops Quantum Box as a member of the Black Box Operator family. In this family, quantum mechanics is treated as a pre-existing reference member, while Quantum Box is constructed from a common operator grammar: statistical input, fixed input, dynamic input, distinguishability factor, black box, and output. The construction begins with a finite function box in which the black box remains common mode while surrounding inputs declare context, change, uncertainty, and readout. It then introduces probability bodies, chords, ledgers, and overlap as accounting terms for retaining statistical weight, relation, non-common contribution, and distinguishability. The manuscript checks the minimal object on three Stern-Gerlach reference outputs, applies the same family form to macroscopic process boxes, reads the resulting answers to measurement, uncertainty, readout, and collapse, and then extends the object in a controlled way for harder cases. A compact single readout law is given before a reduced 15-entry reference suite. The main manuscript records the calculation summaries and boxed recoveries, while the companion calculation file preserves the full step-by-step algebra. The observation is organizational: the family supplies a disciplined account of how declared data, common-mode action, relation, distinguishability, and output are connected. 1. Introduction If quantum mechanics allowed you to ask it three questions, what would those questions be? Write them down before reading further. We do not prescribe those questions. Instead, we build the Black Box Operator family and later return to the questions by reading what the construction says about measurement, uncertainty, readout, and collapse. We ask whether such questions can be organized at the level of the Black Box Operator family. The starting point is simple. A black box is the part that acts reliably as common mode. It is the stable action. It is not rewritten by the surrounding inputs. The surrounding inputs declare how the box is supplied, held, changed, distinguished, and read. We first build this idea as a finite mathematical function. No physical language is needed for that part. We then use the same structure to define Quantum Box. Methodological note. We present the construction first as a clean-room finite box: declared inputs, common-mode action, and declared output appear before any physical reading is attached. The extended terminology register is kept in Appendix A; the global definitions needed for the paper are stated below. 1.1 Main result We construct a Black Box Operator family and then define Quantum Box as the quantum-facing member of that family. The family separates five roles that are often compressed in ordinary notation: statistical supply, fixed context, dynamic change, distinguishability, common-mode action, and declared output. Within Quantum Box, we further represent statistical weight by probability bodies, relational contribution by chords, non-common contribution by ledgers, and retained relational accessibility by overlap. The main result is the following. Once the Quantum Box object is declared, the same readout grammar calculates the three elementary Stern-Gerlach cases, two macroscopic process boxes, and a reduced 15-entry suite of nontrivial 4 reference cases. The claim is not that the paper derives every physical law from first principles. The claim is narrower and testable: Quantum Box gives an executable account in which declared records, common-mode action, non-common ledger content, distinguishability, and output are connected by one calculational discipline. In this sense the extended suite is included as a not-a-toy-model test. It asks whether the same small set of objects continues to calculate once the paper leaves the elementary spin examples. A case receives the status “Calculated here” in the companion calculation file only when the input, Quantum Box declaration, algebraic calculation, output, and reference comparison are all displayed. The main manuscript reports the recovered result and points to the corresponding companion case. arXiv endorsement request.Readers who are eligible and willing to support arXiv submission access may endorse this work in the relevant category: Mathematical Physics: https://arxiv.org/auth/endorse?x=MTM7WLQuantum Physics: https://arxiv.org/auth/endorse?x=E9768LGeneral Relativity and Quantum Cosmology: https://arxiv.org/auth/endorse?x=KWIKJQ