Entanglement Criteria for Continuous-Variable Systems
In 1935, Einstein, Podolsky, and Rosen (EPR) questioned the completeness of quantum theory in their seminal work . The argument is based on two spatially separated systems, which are prepared into a bipartite wavefunction and then cease to interact with each other. According to quantum mechanics, a measurement on system I will reduce system II into certain wavefunction. A different measurement setting will reduce system II into another wavefunction. These two wavefunctions could be eigenfunctions of noncommuting operators. On the one hand, localism states that the choice of measurement in system I should not change system II. On the other hand, without disturbance, the eigenfunction of an operator provides the value of the physical quantity with certain, which corresponds to an element of physical reality. So by choosing different measurement settings, two noncommuting physical quantities could have simultaneous reality, which obviously contradicts with the uncertainty relation. Therefore, EPR argued that the wave function description in quantum theory cannot be complete.
KeywordsEntangle State Uncertainty Relation Separable State Schwarz Inequality High Order Moment
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