No Arabic abstract
Quantum technologies, i.e., technologies benefiting from the features of quantum physics such as objective randomness, superposition, and entanglement, have enabled an entirely different way of distributing and processing information. The enormous progress over the last decades has also led to an urgent need for young professionals and new educational programs. However, the lack of intuitive analogies and the necessity of complex mathematical frameworks often hinder teaching and learning efforts. Thus, novel education methods, such as those involving gamification, are promising supplements to traditional teaching methods. Here, we present a strategic card game in which the building blocks of a quantum computer can be experienced. While playing, participants start with the lowest quantum state, play cards to program a quantum computer, and aim to achieve the highest possible quantum state. By extending the game to high-dimensional quantum systems, i.e., systems that can take more than two possible values, and by developing different multi-player modes, the game can be used as an introduction to quantum computational tasks for students. As such, it can also be used in a classroom environment to increase the conceptual understanding, interest, and motivation of a student. Therefore, the presented game contributes to the ongoing efforts on gamifying quantum physics education with a particular focus on the counter-intuitive features which quantum computing is based on.
Precise measurement or perfect cloning of unknown quantum states is forbidden by the laws of quantum mechanics. Yet, quantum teleportation in principle allows for a faithful and disembodied transmission of unknown quantum states between distant quantum systems using entanglement. There have been numerous experiments on teleportation of quantum states of single photons, atoms, trapped ions, defects in solid states, and superconducting circuits. However, all demonstrations to date were limited to a two-dimensional subspace$-$so-called qubit$-$of the quantized multiple levels of the quantum systems. In general, a quantum particle can naturally possess not only multiple degrees of freedom, but also, many degrees of freedom can have high quantum number beyond the simplified two-level subspace. Here, making use of multiport beam-splitters and ancillary single photons, we propose a resource-efficient and extendable scheme for teleportation of arbitrarily high-dimensional photonic quantum states. We report the first experimental teleportation of a qutrit, which is equivalent to a spin-1 system. Measurements over a complete set of 12 states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), well above the optimal single-copy qutrit-state-estimation limit of 1/2. The fidelity also exceeds the limit of 2/3, the maximum possible for explanation through qubits only. Thus, we strictly prove a genuine three-dimensional, universal, and highly non-classical quantum teleportation. Combining previous methods of teleportation of two-particle composite states and multiple degrees of freedom, our work provides a complete toolbox for teleporting a quantum particle intact. We expect that our results will pave the way for quantum technology applications in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.
Teleportation is a quantum information processes without classical counterparts, in which the sender can disembodied transfer unknown quantum states to the receiver. In probabilistic teleportation through a partial entangled quantum channel, the transmission is exact (with fidelity 1), but may fail in a probability and simultaneously destroy the state to be teleported. We propose a scheme for nondestructive probabilistic teleportation of high-dimensional quantum states. With the aid of an ancilla in the hands of sender, the initial quantum information can be recovered when teleportation fails. The ancilla acts as a quantum apparatus to measure the senders subsystem, and erasing the information it records can resumes the initial state.
A transformative approach to addressing complex social-environmental problems warrants reexamining our most fundamental assumptions about sustainability and progress, including the entrenched imperative for limitless economic growth. Our global resource footprint has grown in lock-step with GDP since the industrial revolution, spawning the climate and ecological crises. Faith that technology will eventually decouple resource use from GDP growth is pervasive, despite there being practically no empirical evidence of decoupling in any country. We argue that complete long-term decoupling is, in fact, well-nigh impossible for fundamental physical, mathematical, logical, pragmatic and behavioural reasons. We suggest that a crucial first step toward a transformative education is to acknowledge this incompatibility, and provide examples of where and how our arguments may be incorporated in education. More broadly, we propose that foregrounding SDG 12 with a functional definition of sustainability, and educating and upskilling students to this end, must be a necessary minimum goal of any transformative approach to sustainability education. Our aim is to provide a conceptual scaffolding around which learning frameworks may be developed to make room for diverse alternative paths to truly sustainable social-ecological cultures.
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is possible with more abstract representations. It was written for a Masters and PhD lecture given yearly at the University of Basel, Switzerland. The goal is to give a language to the student in which to speak about quantum physics in more detail, and to start the student on a path of fluency in this language. On our journey we approach questions such as: -- You already know how to calculate the energy eigenstates of a single particle in a simple one-dimensional potential. How can such calculations be generalized to non-trivial potentials, higher dimensions, and interacting particles? -- You have heard that quantum mechanics describes our everyday world just as well as classical mechanics does, but have you ever seen an example where such behavior is calculated in detail and where the transition from classical to quantum physics is evident? -- How can we describe the internal spin structure of particles? How does this internal structure couple to the particles motion? -- What are qubits and quantum circuits, and how can they be assembled to simulate a future quantum computer?
In economics duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called `leader-follower model. We give a quantum perspective on Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in static form of duopoly also known as Cournots duopoly. We find two qubit quantum pure states required for this purpose.