In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist. The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. The no-cloning theorem concerns only pure states whereas the generalized statement regarding mixed states is known as the no-broadcast theorem.
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
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 to complete the quantum teleportation, classical information needs to be sent from sender to receiver. Because classical information needs to be sent, quantum teleportation cannot 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 the 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 not present in classical mechanics.
In quantum mechanics, a density matrix is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while those can only represent pure states, density matrices can also represent mixed states. Mixed states arise in quantum mechanics in two different situations: first when the preparation of the system is not fully known, and thus one must deal with a statistical ensemble of possible preparations, and second when one wants to describe a physical system which is entangled with another, without describing their combined state.
Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wave function is used to explain various quantum effects. As long as there exists a definite phase relation between different states, the system is said to be coherent. A definite phase relationship is necessary to perform quantum computing on quantum information encoded in quantum states. Coherence is preserved under the laws of quantum physics.
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 computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements.
The Bell states or EPR pairs are specific quantum states of two qubits that represent the simplest examples of quantum entanglement; conceptually, they fall under the study of quantum information science. The Bell states are a form of entangled and normalized basis vectors. This normalization implies that the overall probability of the particle being in one of the mentioned states is 1: . Entanglement is a basis-independent result of superposition. Due to this superposition, measurement of the qubit will "collapse" it into one of its basis states with a given probability. Because of the entanglement, measurement of one qubit will "collapse" the other qubit to a state whose measurement will yield one of two possible values, where the value depends on which Bell state the two qubits are in initially. Bell states can be generalized to certain quantum states of multi-qubit systems, such as the GHZ state for 3 or more subsystems.
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet.
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that, at first glance, suggest the possibility of communication faster-than-light. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. These results can be applied to understand the so-called paradoxes in quantum mechanics, such as the EPR paradox, or violations of local realism obtained in tests of Bell's theorem. In these experiments, the no-communication theorem shows that failure of local realism does not lead to what could be referred to as "spooky communication at a distance".
LOCC, or local operations and classical communication, is a method in quantum information theory where a local (product) operation is performed on part of the system, and where the result of that operation is "communicated" classically to another part where usually another local operation is performed conditioned on the information received.
BB84 is a quantum key distribution scheme developed by Charles Bennett and Gilles Brassard in 1984. It is the first quantum cryptography protocol. The protocol is provably secure, relying on two conditions: (1) the quantum property that information gain is only possible at the expense of disturbing the signal if the two states one is trying to distinguish are not orthogonal ; and (2) the existence of an authenticated public classical channel. It is usually explained as a method of securely communicating a private key from one party to another for use in one-time pad encryption.
Quantum cloning is a process that takes an arbitrary, unknown quantum state and makes an exact copy without altering the original state in any way. Quantum cloning is forbidden by the laws of quantum mechanics as shown by the no cloning theorem, which states that there is no operation for cloning any arbitrary state perfectly. In Dirac notation, the process of quantum cloning is described by:
In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. It is a time-reversed dual to the no-cloning theorem, which states that arbitrary states cannot be copied. This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust. Physicist Arun K. Pati along with Samuel L. Braunstein proved this theorem.
SARG04 is a 2004 quantum cryptography protocol derived from the first protocol of that kind, BB84.
Entanglement distillation is the transformation of N copies of an arbitrary entangled state into some number of approximately pure Bell pairs, using only local operations and classical communication.
Quantum complex networks are complex networks whose nodes are quantum computing devices. Quantum mechanics has been used to create secure quantum communications channels that are protected from hacking. Quantum communications offer the potential for secure enterprise-scale solutions.
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and the environment. This is a fundamental consequence of the linearity and unitarity of quantum mechanics. Thus, information is never lost. This has implications in black hole information paradox and in fact any process that tends to lose information completely. The no-hiding theorem is robust to imperfection in the physical process that seemingly destroys the original information.
In quantum physics, the "monogamy" of quantum entanglement refers to the fundamental property that it cannot be freely shared between arbitrarily many parties.
