What is Quantum Entanglement?
Quantum entanglement is a property of the quantum mechanical state of a system containing two or more objects, where the objects that make up the system are linked in such a way that one cannot adequately describe the quantum state of any member of the system without full mention of the other members of the system, even if the individual objects are spatially separated. Quantum entanglement is at the heart of the EPR paradox that was described by Albert Einstein, Boris Podolsky, and Nathan Rosen in 1935, and it was experimentally verified for the first time in 1972 by Stuart Freedman and John Clauser
Entanglement is a strikingly non-classical property of quantum mechanics, that arguably led to an unease with the theory by many of the early scientists. As put by Erwin Schrödinger in his seminal paper: [Entanglement] is not one, but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.
Einstein was perhaps the most famous of the opponents of quantum theory, and was particularly displeased with its inherently random nature. In 1935, responding to Niels Bohr's advocacy that quantum mechanics as a theory was complete, together with Podolsky and Rosen, he formulated the EPR paradox. The quantum mechanical thought experiment used the properties of an entangled system to (incorrectly) make predictions that were forbidden by quantum mechanics. Therefore, there are physical properties that can be predicted outside quantum mechanics, and thus quantum mechanics is incomplete. Einstein famously derided entanglement as "spukhafte Fernwirkung" or "spooky action at a distance".
The flaw in EPR's reasoning was not pinned down exactly until 1964, when John Stewart Bell showed that one of their key assumptions, the principle of locality, was not compatible with quantum theory. Specifically, he developed an upper limit, known as Bell's inequality, on the strength of correlations for any theory obeying local realism, and showed that there are quantum systems — called "entangled systems" — that violate this limit.
His inequality is experimentally testable, and there have been numerous tests, starting with the pioneering work of Freedman and Clauser in 1972 and Aspect's experiments in 1982. They all showed agreement with quantum mechanics and discarded the principle of local realism. However, they are not free of controversy, as there are some philosophical problems (known as loopholes) that could put in question the validity of the tests.
The remarkable work of Bell switched the focus of the discussion from the confused musings of EPR to the possibility of using these superstrong correlations as a resource for communication. It led to the discovery of quantum key distribution protocols, most famously BB84 by Bennet and Brassard and E91 by Artur Ekert. Interestingly, BB84 does not use entanglement, but Ekert's protocol uses the violation of Bell's inequality as a proof of security.
Entanglement is the pure quantum relation of two or more systems that cannot occur with classical ones. Appropriate measures of entanglement distinguish classical from quantum. For example, if both systems are in a pure state as described by unique wave function, then a good measure of entanglement is the entropy of one of these systems, which vanishes in classical case, yet can be positive in quantum mechanics. For a mixed system some people use mutual entropy, but this is not a good measure for it can be positive even in classical case. Appropriate measure of entanglement for mixed systems is negativity as introduced by Asher Peres. When particles decay into other particles, these decays must obey the various conservation laws. As a result, pairs of particles can be generated that are required to be in certain quantum states. For ease of understanding, consider the situation where a pair of these particles are created, have a two state spin and one must be spin up and the other must be spin down. As described in the introduction, these two particles can now be called entangled since you can not fully describe one particle without mentioning the other. This type of entangled pair where the particles always have opposite spin is known as the spin anti-correlated case. The case where the spins are always the same is known as spin correlated. Now that entangled particles have been created, quantum mechanics also holds that an observable, for example spin, is indeterminate until a measurement is made of that observable. At that instant, all of the possible values that the observable might have had "collapse" to the value that is measured. Consider, for now, just one of these created particles. In the singlet state of two spin, it is equally likely that this particle will be observed to be spin-up or spin-down. Meaning if you were to measure the spin of many like particles, the measurement will result in an unpredictable series of measurements that will tend to a 50% probability of the spin being up or down. However, the results are quite different if you examine both of the entangled particles in this experiment. When each of the particles in the entangled pair is measured in the same way, the results of their spin measurement will be correlated. Measuring one member of the pair tells you what the spin of the other member is without actually measuring its spin.
The controversy surrounding this topic comes in once you consider the ramifications of this result. Normally under the Copenhagen interpretation, the state a particle occupies is determined the moment the state is measured. However, in an entangled pair when the first particle is measured, the state of the other is known at the same time without measurement, regardless of the separation of the two particles. This knowledge of the second particle's state is at the heart of the debate. If the distance between particles is large enough, information or influence might be traveling faster than the speed of light which violates the principle of special relativity. One experiment that is in agreement with the effect of entanglement "traveling faster than light" was performed in 2008. This experiment found that the "speed" of quantum entanglement has a minimum lower bound of 10,000 times the speed of light. However, because the method involves uncontrollable observation rather than controllable changing of state, no actual information is transmitted in this process. Therefore, the speed of light remains the communication speed limit.
Theories involving hidden variables have been proposed in order to explain this result. These hidden variables would account for the spin of each particle, and would be determined when the entangled pair is created. It may appear then that the hidden variables must be in communication no matter how far apart the particles are, that the hidden variable describing one particle must be able to change instantly when the other is measured. If the hidden variables stop interacting when they are far apart, the statistics of multiple measurements must obey an inequality (called Bell's inequality), which is, however, violated both by quantum mechanical theory and experimental evidence.
If each particle departs the scene of its "entangled creation", however, with properties that would unambiguously determine the value of the quality to be subsequently measured, then the postulated instantaneous transmission of information across space and time would not be required to account for the result of both particles having the same value for that quality. The Bohm interpretation postulates that a guide wave exists connecting what are perceived as individual particles such that the supposed hidden variables are actually the particles themselves existing as functions of that wave.
Applications of entanglement
Entanglement has many applications in quantum information theory. With the aid of entanglement, otherwise impossible tasks may be achieved. Among the best-known applications of entanglement are superdense coding, quantum teleportation, information exchanges through time, and the creation of a quantum computer. Efforts to quantify this property are often termed entanglement theory. Quantum entanglement has many different applications in the emerging technologies of quantum computing and quantum cryptography, and has been used to realize quantum teleportation experimentally. At the same time, it prompts some of the more philosophically-oriented discussions concerning quantum theory. The correlations predicted by quantum mechanics and observed in experiment reject the principle of local realism, which is that information about the state of a system can only be mediated by interactions in its immediate surroundings and that the state of a system exists and is well-defined before any measurement. Different views of what is actually occurring in the process of quantum entanglement can be grounded in different interpretations of quantum mechanics. In the common Copenhagen interpretation, quantum mechanics is neither "real" (since measurements do not state, but instead prepare properties of the system) nor "local" (since the state vector comprises the simultaneous probability amplitudes for all positions, e.g. );
The Reeh-Schlieder theorem of quantum field theory is sometimes seen as an analogue of quantum entanglement.
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