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Recent work has shown that relativistic time dilation results in correlations between a particles internal and external degrees of freedom, leading to decoherence of the latter. In this note, we briefly summarize the results and address the comments and concerns that have been raised towards these findings. In addition to brief replies to the comments, we provide a pedagogical discussion of some of the underlying principles of the work. This note serves to clarify some of the counterintuitive aspects arising when the two theories are jointly considered.
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The physics of low-energy quantum systems is usually studied without explicit consideration of the background spacetime. Phenomena inherent to quantum theory on curved space-time, such as Hawking radiation, are typically assumed to be only relevant at extreme physical conditions: at high energies and in strong gravitational fields. Here we consider low-energy quantum mechanics in the presence of gravitational time dilation and show that the latter leads to decoherence of quantum superpositions. Time dilation induces a universal coupling between internal degrees of freedom and the centre-of-mass of a composite particle. The resulting correlations cause decoherence of the particles position, even without any external environment. We also show that the weak time dilation on Earth is already sufficient to decohere micron scale objects. Gravity therefore can account for the emergence of classicality and the effect can in principle be tested in future matter wave experiments.
We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the systems total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.
We formulate a novel approach to decoherence based on neglecting observationally inaccessible correlators. We apply our formalism to a renormalised interacting quantum field theoretical model. Using out-of-equilibrium field theory techniques we show that the Gaussian von Neumann entropy for a pure quantum state increases to the interacting thermal entropy. This quantifies decoherence and thus measures how classical our pure state has become. The decoherence rate is equal to the single particle decay rate in our model. We also compare our approach to existing approaches to decoherence in a simple quantum mechanical model. We show that the entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
Entanglement and quantum communication are paradigmatic resources in quantum information science leading to correlations between systems that have no classical analogue. Correlations due to entanglement when communication is absent have for long been studied in Bell scenarios. Correlations due to quantum communication when entanglement is absent have been studied extensively in prepare-and-measure scenarios in the last decade. Here, following up on a recent companion paper [arXiv:2103.10748], we set out to understand and investigate correlations in scenarios that involve both entanglement and communication, focusing on entanglement-assisted prepare-and-measure scenarios. We establish several elementary relations between standard classical and quantum communication and their entanglement-assisted counterparts. In particular, while it was already known that bits or qubits assisted by two-qubit entanglement between the sender and receiver constitute a stronger resource than bare bits or qubits, we show that higher-dimensional entanglement further enhance the power of bits or qubits. We also provide a characterisation of generalised dense coding protocols, a natural subset of entanglement-assisted quantum communication protocols, finding that they can be understood as standard quantum communication protocols in real-valued Hilbert space. Though such dense coding protocols can convey up to two bits of information, we provide evidence, perhaps counter-intuitively, that resources with a small information capacity, such as a bare qutrits, can sometimes produce stronger correlations. Along the way we leave several conjectures and conclude with a list of interesting open problems.
In this paper, we theoretically investigate the time dilation and Doppler effect in curved space-time from the perspective of quantum field theory (QFT). A Coordinate Transformation which Maintains the Period of Clocks is introduced, and such coordinate transformation is named as CTMPC throughout this paper. By analogy with the Lorentz transformation in Minkowski space-time, CTMPC is a correct transformation in curved space-times in a sense that it shows the correct relation between the time measured by the two observers, moreover, Lorentz transformation is just a special case of CTMPC applied in Minkowski space-time. We demonstrate that the Coordinate Transformation which Maintains the Local Metric (CTMLM) is one CTMPC, while the mathematical forms of physics formulas in QFT will be maintained. As applications of CTMLM, the time dilation and Doppler effect with an arbitrary time-dependent relative velocity in curved space-time are analysed. For Minkowski space-time, the time dilation and Doppler effect agree with the clock hypothesis. For curved space-time, we show that even if the emitted wave has a narrow frequency range, the Doppler effect may, in general, broaden the frequency spectrum and, at the meantime, shift the frequencies values. These new findings will deepen our understanding on the nature of space-time and the Doppler effect in curved space-time, they may also provide theoretical guidance in future astronomical observations.
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