Quantum computing is a type of computation that harnesses the collective properties of quantum states, such as superposition, interference, and entanglement, to perform calculations. The devices that perform quantum computations are known as quantum computers. Though current quantum computers are too small to outperform usual (classical) computers for practical applications, they are believed to be capable of solving certain computational problems, such as integer factorization, substantially faster than classical computers. The study of quantum computing is a subfield of quantum information science.
Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation is commonly portrayed in science fiction as a means to transfer physical objects from one location to the next, quantum teleportation only transfers quantum information. The sender does not have to know the particular quantum state being transferred. Moreover, the location of the recipient can be unknown, but classical information needs to be sent from sender to receiver to complete the teleportation. Because classical information needs to be sent, teleportation can not occur faster than the speed of light.
In quantum computing, a qubit or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state 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 states can be taken to be the vertical polarization and the horizontal 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 both states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.
Quantum entanglement is a physical phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lacking in classical mechanics.
Bell's theorem is a term encompassing a number of closely-related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories. The "local" in this case refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields can only occur at speeds no greater than the speed of light. "Hidden variables" are hypothetical properties possessed by quantum particles, properties that are undetectable but still affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."
Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault-tolerant quantum computation that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements.
A local hidden-variable theory in the interpretation of quantum mechanics is a hidden-variable theory that has the added requirement of being consistent with local realism. It refers to all types of the theory that attempt to account for the probabilistic features of quantum mechanics by the mechanism of underlying inaccessible variables, with the additional requirement from local realism that distant events be independent, ruling out instantaneous interactions between separate events.
The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state , the conditional entropy is written , or , depending on the notation being used for the von Neumann entropy. The quantum conditional entropy was defined in terms of a conditional density operator by Nicolas Cerf and Chris Adami, who showed that quantum conditional entropies can be negative, something that is forbidden in classical physics. The negativity of quantum conditional entropy is a sufficient criterion for quantum non-separability.
A Tsirelson bound is an upper limit to quantum mechanical correlations between distant events. Given that quantum mechanics is non-local, a natural question to ask is "how non-local can quantum mechanics be?", or, more precisely, by how much can the Bell inequality be violated within quantum mechanics. The answer is precisely the Tsirelson bound for the particular Bell inequality in question. In general, this bound is lower than the bound that would be obtained if more general theories, only constrained by "no-signalling", were considered, and much research has been dedicated to the question of why this is the case.
Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment".
Quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, particularly exploiting quantum entanglement and quantum squeezing. This field promises to develop measurement techniques that give better precision than the same measurement performed in a classical framework. Together with quantum hypothesis testing, it represents an important theoretical model at the basis of quantum sensing.
In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not admit an interpretation in terms of a local realistic theory. Quantum nonlocality has been experimentally verified under different physical assumptions. Any physical theory that aims at superseding or replacing quantum theory should account for such experiments and therefore cannot fulfill local realism; quantum nonlocality is a property of the universe that is independent of our description of nature.
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed due to wave function collapse. This could be used to detect eavesdropping in quantum key distribution (QKD).
In quantum information theory, quantum state merging is the transfer of a quantum state when the receiver already has part of the state. The process optimally transfers partial information using entanglement and classical communication. It allows for sending information using an amount of entanglement given by the conditional quantum entropy, with the Von Neumann entropy, . It thus provides an operational meaning to this quantity.
The noisy-storage model refers to a cryptographic model employed in quantum cryptography. It assumes that the quantum memory device of an attacker (adversary) trying to break the protocol is imperfect (noisy). The main goal of this model is to enable the secure implementation of two-party cryptographic primitives, such as bit commitment, oblivious transfer and secure identification.
Quantum contextuality is a feature of the phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured. More formally, the measurement result of a quantum observable is dependent upon which other commuting observables are within the same measurement set.
Quantum illumination is a paradigm for target detection that employs quantum entanglement between a signal electromagnetic mode and an idler electromagnetic mode, as well as joint measurement of these modes. The signal mode is propagated toward a region of space, and it is either lost or reflected, depending on whether a target is absent or present, respectively. In principle, quantum illumination can be beneficial even if the original entanglement is completely destroyed by a lossy and noisy environment.
Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states can be used for quantum metrology, as they can provide a better precision for estimating a rotation angle than classical interferometers.
Quantum foundations is a discipline of science that seeks to understand the most counter-intuitive aspects of quantum theory, reformulate it and even propose new generalizations thereof. Contrary to other physical theories, such as general relativity, the defining axioms of quantum theory are quite ad hoc, with no obvious physical intuition. While they lead to the right experimental predictions, they do not come with a mental picture of the world where they fit.
Relativistic quantum cryptography is a sub-field of quantum cryptography, in which in addition to exploiting the principles of quantum physics, the no-superluminal signalling principle of relativity theory stating that information cannot travel faster than light is exploited too. Technically speaking, relativistic quantum cryptography is a sub-field of relativistic cryptography, in which cryptographic protocols exploit the no-superluminal signalling principle, independently of whether quantum properties are used or not. However, in practice, the term relativistic quantum cryptography is used for relativistic cryptography too.
