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Quantum information and special relativity

Asher Peres·Daniel R. Terno
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Abstract

Relativistic effects affect nearly all notions of quantum information theory. The vacuum behaves as a noisy channel, even if the detectors are perfect. The standard definition of a reduced density matrix fails for photon polarization because the transversality condition behaves like a superselection rule. We can however define an effective reduced density matrix which corresponds to a restricted class of positive operator-valued measures. There are no pure photon qubits, and no exactly orthogonal qubit states. Reduced density matrices for the spin of massive particles are well-defined, but are not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning. The distinguishability of quantum signals and their entanglement depend on the relative motion of observers.

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Asher Peres, Daniel R. Terno. 2003-01-15. Quantum information and special relativity. https://arxiv.org/abs/quant-ph/0301065

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