Quantum superposition in the context of Quantum cryptography

A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is meant to test our intuitions about morality or other fundamental philosophical questions.

Quantum information science is an interdisciplinary field that combines the principles of quantum mechanics, information theory, and computer science to explore how quantum phenomena can be harnessed for the processing, analysis, and transmission of information. Quantum information science covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it refers to the theoretical aspects of information processing and does not include experimental research.

At its core, quantum information science explores how information behaves when stored and manipulated using quantum systems. Unlike classical information, which is encoded in bits that can only be 0 or 1, quantum information uses quantum bits or qubits that can exist simultaneously in multiple states because of superposition. Additionally, entanglement—a uniquely quantum linkage between particles—enables correlations that have no classical counterpart.

In chemistry, tautomers (/ˈtɔːtəmər/) are subset of structural isomers (constitutional isomers) of chemical compounds that readily interconvert. The chemical reaction interconverting the two is called tautomerization. This conversion commonly results from the relocation of a hydrogen atom within the compound. The phenomenon of tautomerization is called tautomerism, also called desmotropism. Tautomerism is for example relevant to the behavior of amino acids and nucleic acids, two of the fundamental building blocks of life.

Care should be taken not to confuse tautomers with depictions of "contributing structures" in chemical resonance. Tautomers are distinct chemical species that can be distinguished by their differing atomic connectivities, molecular geometries, and physicochemical and spectroscopic properties, whereas resonance forms are merely alternative Lewis structure (valence bond theory) depictions of a single chemical species, whose true structure is a quantum superposition, essentially the "average" of the idealized, hypothetical geometries implied by these resonance forms.

In quantum mechanics, Schrödinger's cat is a thought experiment concerning quantum superposition. In the thought experiment, a hypothetical cat in a closed box may be considered to be simultaneously both alive and dead while it is unobserved, as a result of its fate being linked to a random subatomic event that may or may not occur. This experiment, viewed this way, is described as a paradox. This thought experiment was devised by physicist Erwin Schrödinger in 1935 in a discussion with Albert Einstein to illustrate what Schrödinger saw as the problems of Niels Bohr and Werner Heisenberg's philosophical views on quantum mechanics.

In Schrödinger's original formulation, a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal radiation monitor such as a Geiger counter detects radioactivity (a single atom decaying), the flask is shattered, releasing the poison, which kills the cat. If no decaying atom triggers the monitor, the cat remains alive. Mathematically, the wave function that describes the contents of the box is a combination, or quantum superposition, of these two possibilities. Yet, when one looks in the box, one sees the cat either alive or dead, not both alive and dead. This poses the question of when exactly quantum superposition ends and reality resolves into one possibility or the other.

A quantum computer is a (real or theoretical) computer that exploits superposed and entangled states. Quantum computers can be viewed as sampling from quantum systems that evolve in ways that may be described as operating on an enormous number of possibilities simultaneously, though still subject to strict computational constraints. By contrast, ordinary ("classical") computers operate according to deterministic rules. (A classical computer can, in principle, be replicated by a classical mechanical device, with only a simple multiple of time cost. On the other hand (it is believed), a quantum computer would require exponentially more time and energy to be simulated classically.) It is widely believed that a quantum computer could perform some calculations exponentially faster than any classical computer. For example, a large-scale quantum computer could break some widely used public-key cryptographic schemes and aid physicists in performing physical simulations. However, current hardware implementations of quantum computation are largely experimental and only suitable for specialized tasks.

The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in ordinary or "classical" computing. However, unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a linear combination of two states known as a quantum superposition. The result of measuring a qubit is one of the two states given by a probabilistic rule. If a quantum computer manipulates the qubit in a particular way, wave interference effects amplify the probability of the desired measurement result. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform this amplification.

A stationary state is a quantum state with all observables independent of time. It is an eigenvector of the energy operator (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences explained below.

In particle physics, a glueball (also gluonium, gluon-ball) is a hypothetical composite particle. It consists solely of gluons, without valence quarks. Such a state is possible because gluons carry color charge and experience the strong interaction between themselves. Glueballs are extremely difficult to identify in particle accelerators, because they mix with ordinary meson states. In pure gauge theory, glueballs are the only states of the spectrum and some of them are stable.

Theoretical calculations show that glueballs should exist at energy ranges accessible with current collider technology. However, due to the aforementioned difficulty (among others), they have so far not been observed and identified with certainty, although phenomenological calculations have suggested that an experimentally identified glueball candidate, denoted f₀(1710), has properties consistent with those expected of a Standard Model glueball.

The omega meson (ω) is a flavourless meson formed from a superposition of an up quark–antiquark and a down quark–antiquark pair. It is part of the vector meson nonet and mediates the nuclear force along with pions and rho mesons.

In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed ensembles of states. These arise in quantum mechanics in two different situations:

1. when the preparation of a system can randomly produce different pure states, and thus one must deal with the statistics of the ensemble of possible preparations; and
2. when one wants to describe a physical system that is entangled with another, without describing their combined state. This case is typical for a system interacting with some environment (e.g. decoherence). In this case, the density matrix of an entangled system differs from that of an ensemble of pure states that, combined, would give the same statistical results upon measurement.

Density matrices are thus crucial tools in areas of quantum mechanics that deal with mixed states (not to be confused with superposed states), such as quantum statistical mechanics, open quantum systems and quantum information.

In various interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an observation and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation.

In the Copenhagen interpretation, wave function collapse connects quantum to classical models, with a special role for the observer. By contrast, objective-collapse proposes an origin in physical processes. In the many-worlds interpretation, collapse does not exist; all wave function outcomes occur while quantum decoherence accounts for the appearance of collapse.

In quantum computing, a qubit (/ˈkjuːbɪt/) or quantum bit is a basic unit of quantum information; a binary qudit – the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

Within quantum technology, a quantum sensor utilizes quantum mechanical phenomena, such as quantum superposition, quantum entanglement, and quantum squeezing, to measure things. If a quantum system is measurable, and it interacts with its environment in a known way, then measurements of that system can provide information about its environment. Theoretically such sensor technology would have precision limited only by the uncertainty principle.The field of quantum sensing deals with the design and engineering of quantum mechanical systems and measurements with potential for better performance than any classical strategy in a number of technological applications. Of the wide range of quantum mechanical systems that can be used as a quantum sensor, most can be classified as photonic systems or solid state systems.

In quantum computing, a quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary states (represented by "1"s and "0"s), quantum memory stores a quantum state for later retrieval. These states hold useful computational information known as qubits. Unlike the classical memory of everyday computers, the states stored in quantum memory can be in a quantum superposition, giving much more practical flexibility in quantum algorithms than classical information storage.

Quantum memory is essential for the development of many devices in quantum information processing, including a synchronization tool that can match the various processes in a quantum computer, a quantum gate that maintains the identity of any state, and a mechanism for converting predetermined photons into on-demand photons. Quantum memory can be used in many aspects, such as quantum computing and quantum communication. Continuous research and experiments have enabled quantum memory to realize the storage of qubits.

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions. In a mathematical sense, these wave functions are the basis set of functions, the basis functions, which describe the electrons of a given atom. In chemical reactions, orbital wavefunctions are modified, i.e. the electron cloud shape is changed, according to the type of atoms participating in the chemical bond.

It was introduced in 1929 by Sir John Lennard-Jones with the description of bonding in the diatomic molecules of the first main row of the periodic table, but had been used earlier by Linus Pauling for H₂.