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Quantum entanglement is a quantum mechanical phenomenon, in which the superposition of states of two or more systems allows the systems to influence one another regardless of their spatial separation. |
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Quantum entanglement is a quantum mechanical phenomenon in which the superposition of states of two or more systems allows the systems to influence one another regardless of their spatial separation. |
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Entanglement is one of the properties of quantum mechanics which caused Einstein and others to dislike the theory. In 1935, Einstein, Podolsky, and Rosen formulated the EPR paradox, demonstrating that entanglement makes quantum mechanics a non-local theory. Einstein famously derided entanglement as "spooky action at |
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Entanglement is one of the properties of quantum mechanics which caused Einstein and others to dislike the theory. In 1935, Einstein, Podolsky, and Rosen formulated the EPR paradox, demonstrating that entanglement makes quantum mechanics a non-local theory. Einstein famously derided entanglement as "spooky action at |
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In 1964, Bell? invented an experimental test, based on the EPR paradox, that could distinguish quantum entanglement from the effects of a broad class of hidden variable theories. Subsequent experiments verified the quantum mechanical approach. Since then, |
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In 1964, Bell? invented an experimental test, based on the EPR paradox, that could distinguish quantum entanglement from the effects of a broad class of hidden variable theories. Subsequent experiments verified the quantum mechanical approach. Since then, |
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Choose two basis vectors {|0>A, |1>A} of HA, and two basis vectors {|0>B, |1>B} of HA. An example of an entangled state is |
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Choose two basis vectors {|0>A, |1>A} of HA, and two basis vectors {|0>B, |1>B} of HB. This is an example of an entangled state: |
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:2-1/2 |0>A |1>B - |1>A|0>B |
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:2-1/2 ( |0>A |1>B - |1>A|0>B ) |
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Neither system A nor B are in a definite state; instead, their states are superposed with each other. In this sense, the systems are "entangled". |
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If the composite system is in this state, neither system A nor system B have a definite state. Instead, their states are superposed with one another. In this sense, the systems are "entangled". |
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ΩB performed by Bob always returns μ1. If the latter occurs, the measurement always returns μ0. Thus, system B has been altered by Alice performing her measurement on system A. This happens even if the systems A and B are widely separated, which is the foundation of the EPR paradox. |
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ΩB performed by Bob always returns μ1. If the latter occurs, Bob's measurement always returns μ0. Thus, system B has been altered by Alice performing her measurement on system A., even if the systems A and B are spatially separated. This is the foundation of the EPR paradox. |
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Because the outcome of Alice's measurement is random and cannot be controlled by Alice, no information can be transmitted from Alice to Bob in this manner. Causality is thus preserved, as we claimed. |
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Because the outcome of Alice's measurement is random and cannot be controlled by Alice, no information can be transmitted from Alice to Bob in this manner. Causality is thus preserved, as we claimed above. |
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:ρA = 1/2 (|0>A<0|A + |1>A<1|A) |
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:ρA = 1/2 ( |0>A<0|A + |1>A<1|A) |
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:S = - k Tr ρ ln ρ |
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:S = - k Tr ( ρ ln ρ ) |
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is (up to a proportionality factor) precisely the entropy of the system corresponding to H! |
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is precisely the entropy of the system corresponding to H! |
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The entropy of any pure state is zero, which is unsurprising as there is no uncertainty about the state of the system. The entropy of the entangled state discussed above is kln 2 (which can be shown to be the maximum entropy for a composition of two two-level systems.) Generally, the more entangled a system is, the larger its entropy. |
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The entropy of any pure state is zero, which is unsurprising since there is no uncertainty about the state of the system. The entropy of the entangled state discussed above is kln 2 (which can be shown to be the maximum entropy for a composition of two two-level systems.) Generally, the more entangled a system, the larger its entropy. |
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It can also be shown that [unitary operators]? acting on a state - including the time evolution operator obtained from Schrodinger's equation - leave the entropy unchanged. This associates the reversibility of a process with its resulting entropy change, which is a deep result linking quantum mechanics to information theory and thermodynamics. |
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It can also be shown that [unitary operators]? acting on a state (such as the time evolution operator obtained from Schrodinger's equation) leave the entropy unchanged. This associates the reversibility of a process with its resulting entropy change, which is a deep result linking quantum mechanics to information theory and thermodynamics. |
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