No-communication theorem
In physics, the no-communication theorem 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, 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 suggest the possibility of instantaneous communication. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible. In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening to a common radio station: it is impossible for one of the listeners to use their radio receiver to send messages to the other listener. Informal Overview[edit] Formulation[edit] where Ti and Si are operators on HA and HB. The term
Density matrix
Explicitly, suppose a quantum system may be found in state with probability p1, or it may be found in state with probability p2, or it may be found in state with probability p3, and so on. The density operator for this system is[1] By choosing a basis (which need not be orthogonal), one may resolve the density operator into the density matrix, whose elements are[1] For an operator (which describes an observable is given by[1] In words, the expectation value of A for the mixed state is the sum of the expectation values of A for each of the pure states Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Pure and mixed states[edit] In quantum mechanics, a quantum system is represented by a state vector (or ket) . is called a pure state. and a 50% chance that the state vector is . A mixed state is different from a quantum superposition. Example: Light polarization[edit] An example of pure and mixed states is light polarization. . and . . .
Quantum information
In physics and computer science, quantum information is information that is held in the state of a quantum system. Quantum information is the basic entity that is studied in the growing field of quantum information theory, and manipulated using the engineering techniques of quantum information processing. Much like classical information can be processed with digital computers, transmitted from place to place, manipulated with algorithms, and analyzed with the mathematics of computer science, so also analogous concepts apply to quantum information. Quantum information[edit] Quantum information differs strongly from classical information, epitomized by the bit, in many striking and unfamiliar ways. Among these are the following: A unit of quantum information is the qubit. The study of all of the above topics and differences comprises quantum information theory. Quantum information theory[edit] How is information stored in a state of a quantum system? Journals[edit] See also[edit]
Information theory
Overview[edit] The main concepts of information theory can be grasped by considering the most widespread means of human communication: language. Two important aspects of a concise language are as follows: First, the most common words (e.g., "a", "the", "I") should be shorter than less common words (e.g., "roundabout", "generation", "mediocre"), so that sentences will not be too long. Such a tradeoff in word length is analogous to data compression and is the essential aspect of source coding. Second, if part of a sentence is unheard or misheard due to noise — e.g., a passing car — the listener should still be able to glean the meaning of the underlying message. Note that these concerns have nothing to do with the importance of messages. Information theory is generally considered to have been founded in 1948 by Claude Shannon in his seminal work, "A Mathematical Theory of Communication". Historical background[edit] With it came the ideas of Quantities of information[edit] Entropy[edit] . that
Physicists add 'quantum Cheshire Cats' to list of quantum paradoxes
(Phys.org) —Given all the weird things that can occur in quantum mechanics—from entanglement to superposition to teleportation—not much seems surprising in the quantum world. Nevertheless, a new finding that an object's physical properties can be disembodied from the object itself is not something we're used to seeing on an everyday basis. In a new paper, physicists have theoretically shown that this phenomenon, which they call a quantum Cheshire Cat, is an inherent feature of quantum mechanics and could prove useful for performing precise quantum measurements by removing unwanted properties. The physicists, Yakir Aharonov at Tel Aviv University in Tel Aviv, Israel, and Chapman University in Orange, California, US, and his coauthors have published a paper on quantum Cheshire Cats in a recent issue of the New Journal of Physics. The physicists begin their paper with an excerpt from Lewis Carroll's 1865 novel Alice in Wonderland: 'Well! Disturbing measurements Reviving the paradox
