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In theoretical physics, quantum nonlocality is the phenomenon by which measurements made at a microscopic level contradict a collection of notions known as local realism that are regarded as intuitively true in classical mechanics. Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory. Many entangled quantum states produce such correlations when measured, as demonstrated by Bell's theorem. Experiments have generally favoured quantum mechanics as a description of nature, over local hidden variable theories. Any physical theory that supersedes or replaces quantum theory must make similar experimental predictions and must therefore also be nonlocal in this sense; quantum nonlocality is a property of the universe that is independent of our description of nature. The terms however must be defined properly. Using the proper physical definition of locality, special relativity has the principle of locality included in its very definition. Therefore, this principle is also included in relativistic quantum field theories as the "principle of locality" saying mainly that on two regions of spacetime, separated by a space-like interval, the observables defined on each of the two regions commute, therefore are independent and can be defined simultaneously in an experiment. This is the generally accepted definition of locality. Phenomena like entanglement or quantum superposition are in perfect agreement with this definition of locality and are therefore strictly local. The rest of this article discusses quantum correlation effects which are not to be associated to the principle of locality. In fact, any relativistic form of quantum mechanics is fundamentally local. Whilst quantum nonlocality improves the efficiency of various computational tasks,〔Gilles Brassard, Richard Cleve, Alain Tapp, "(The cost of exactly simulating quantum entanglement with classical communication )".〕 it does not allow for faster-than-light communication, and hence is compatible with special relativity. However, it prompts many of the foundational discussions concerning quantum theory. == Example == Imagine two experimentalists, Alice and Bob, situated in separate laboratories. They conduct a simple experiment in which Alice chooses and pushes one of two buttons, A0 and A1, on her apparatus, and Bob observes on his apparatus one of two indicating lamps, b0 and b1, lighting. In this case there are four possible events that could occur in the experiment: (A0,b0), (A0,b1), (A1,b0) and (A1,b1). Suppose that after many runs of the experiment, only the events (A0,b0) and (A1,b1) occur; this is good evidence that A has an influence on b. Indeed, Alice could easily send messages to Bob by encoding those messages into sequences of 0's and 1's, and causing the b0 or b1 lamp to light up respectively. More realistically, suppose that the four events occur with (conditional) probabilities P(b0|A0), P(b1|A0) = 1 - P(b0|A0), P(b0|A1) and P(b1|A1) = 1 - P(b0|A1). Here P(b0|A0) is the probability that Bob's b0 lamp lit up, given that Alice pushed the button A0. We can still rigorize the notion that A has an influence on B in this setting: if P(b0|A0) differs from P(b0|A1) then Alice's choice of button still affects the probabilistic outcome on Bob's side, and it is still possible for Alice to send Bob messages with low probability of error. For example, if P(b0|A0) = and P(b0|A1) = , then after 100 runs of the experiment in which Alice pushed the same button, Bob can tell with high probability which button it was by looking at how often b0 occurred. Here is a more complicated scenario: Alice pushes one of two buttons, A0 and A1, and Bob also pushes one of two buttons, B0 and B1. Alice observes one of two outcomes, a0 and a1, and Bob also observes one of two outcomes, b0 and b1. There are 24 = 16 possible combinations of these 4 events: :: where each of X,Y,x,y is 0 or 1. Suppose that of these 16, only 8 combinations actually occur, with the following (conditional) probabilities: :: where denotes addition modulo 2 (XOR) and the juxtaposition "XY" denotes multiplication (AND). Then if A1 and B1 are both pressed () the outcomes with nonzero probability (note that ) are perfectly anticorrelated, either (a0,b1) or (a1,b0), with an equal probability for both occurrences. In all other cases ( the two outcomes with nonzero probability (note that ) are perfectly correlated (either (a0,b0) or (a1,b1), again, equiprobably. Do these outcomes imply that some influence exists (A on b, or B on a), or not? The question is important, since the answer depends on our fundamental assumptions about how mathematical theories describe physical reality. On the one hand, Alice cannot send a message to Bob, using her buttons A0, A1 and his indicators b0, b1 (nor Bob to Alice), since it is easily checked that P(bx|A0) = P(bx|A1) for both x = 0 and x = 1 in the above example. That is to say, this particular set of probabilities is non-signalling. In this sense, there is no influence of A on b, or of B on a. On the other hand, it is provably impossible for two separated parties to simulate this outcome without any kind of interaction or communication between them.〔 Thorough logical analysis reveals that the above outcome can only occur if there is some direct influence between A and B, if we assume local realism and, arguably, counterfactual definiteness. These fundamental assumptions, deeply rooted in our physical intuition, are incompatible with quantum theory. Different interpretations of quantum mechanics reject different parts of local realism and/or counterfactual definiteness (for detail, see Principle of locality). A classical definition of nonlocality, i.e. direct influence of one object on another, distant object, normally takes local realism and counterfactual definiteness for granted. The standard formulation of basic quantum mechanics is fundamentally local and, using a more recent terminology, non-realistic. This is one piece of information used for decades, starting with the construction of Feynman's path integrals. Other interpretations are usually incapable of describing all the effects of quantum mechanics properly or overstate some maximality bounds imposed by measurements. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「quantum nonlocality」の詳細全文を読む スポンサード リンク
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