Quantum Candies and Quantum Cryptography

Abstract

The field of quantum information is becoming more known to the general public. However, effectively demonstrating the concepts underneath quantum science and technology to the general public can be a challenging job. We investigate, extend, and much expand here "quantum candies" (invented by Jacobs), a pedagogical model for intuitively describing some basic concepts in quantum information, including quantum bits, complementarity, the no-cloning principle, and entanglement. Following Jacob's quantum candies description of the well known quantum key distribution protocol BB84, we explicitly demonstrate various additional quantum cryptography protocols using quantum candies in an approachable manner. The model we investigate can be a valuable tool for science and engineering educators who would like to help the general public to gain more insights about quantum science and technology: most parts of this paper, including many protocols for quantum cryptography, are expected to be easily understandable by a layperson without any previous knowledge of mathematics, physics, or cryptography.

Digital Signatures with Quantum Candies

“…In particular, as also shown previously in [12] and even more so in [13], the qandy model (i.e., a "superpositionless" variant of quantum theory) is sufficiently strong for presenting interesting features of quantum protocols while being able to fully avoid the usage of superpositions or phases. In the following sections, we will see how these characteristics of qandies allow us to successfully achieve our goal of creating secure signature schemes.…”

“…Those properties have significant information-theoretic consequences (e.g., the nocloning theorem), and the notion of quantum candies helps explaining some of those properties in a simple and mathematics free manner [12,13]. In the conference version [12],…”

“…We now present the notion of quantum candies (or qandies) as presented in [ 12 , 13 ]. The concept of qandies was first proposed by Jacobs [ 21 ]—see a detailed description of Jacobs qandies in [ 12 , 13 ].…”

“…In an attempt to improve accessibility to this important field of science, an idea for a simplified model was first proposed by Jacobs—the “Quantum Candy” model. The model was later greatly expanded and defined in [ 12 , 13 ].…”

“…In essence, the “Qandy Model” abandons the notion of quantum bits (qubits) in favor of “Quantum Candies” (qandies)—mystical candies that, similarly to classical bits, only have a discrete set of possible states, but unlike classical bits do behave essentially “quantumly”. It is shown and discussed in [ 12 , 13 ], that many concepts from QIP, and especially quantum cryptographic protocols, can be interpreted and defined in the qandy model. However, not many quantum-information protocols can be defined without using superpositions, unitary transformations, and phases.…”