Daisuke Ida, Takahiro Okamoto, Miyuki Saito
We consider the quantum state seen by an observer in the diamond-shaped region, which is a globally hyperbolic open submanifold of the Minkowski space-time. It is known from the operator-algebraic argument that the vacuum state of the quantum field transforming covariantly under the conformal group looks like a thermal state on the von Neumann algebra generated by the field operators on the diamond-shaped region of the Minkowski space-time. Here, we find that such a state can in fact be identified with a certain entangled quantum state. By doing this, we obtain the thermodynamic quantities such as the Casimir energy and the von Neumann entropy of the thermal state in the diamond-shaped region. We further speculate on a possible information-theoretic interpretation of the entropy in terms of the probability density functions naturally determined from the Tomita-Takesaki modular flow in the diamond-shaped region.
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http://arxiv.org/abs/1211.3525
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