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Authors
Edward J. Gillis
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When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often overlook the possibility of entanglement between the measured system and the preparation apparatus. The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system. Since entanglement is a generic result of interaction, as shown by Gemmer and Mahler[1], and by Durt[2,3] one would expect some nonzero entanglement between apparatus and measured system, even though the amount of such entanglement is extremely small. Because the apparatus has an enormous number of degrees of freedom relative to the measured system, even a very tiny difference between the apparatus states that are correlated with the orthogonal states of the measured system can be sufficient to account for the perceived deviation from strict conservation of the quantity in question. Hence measurements need not violate conservation laws.
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Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the characteristic operator of this scenario is analytically provided, as well as the corresponding quantum Fisher information (QFI). As the application of this scenario, we focus on two classes of Hamiltonians: su(2) category and canonical category. Several specific physical systems in these two categories are discussed in detail. Besides, we also calculate an alternative form of QFI in this scenario.
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In statistical mechanics, a small system exchanges conserved quantities---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the conserved quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small systems long-time state was dubbed ``the non-Abelian thermal state (NATS). We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
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Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode selective losses, and minimal quantum systems, and the meteoric research on them has mainly focused on the wide range of novel functionalities they demonstrate. Here, we address the following questions: Does anything remain constant in the dynamics of such open systems? What are the consequences of such conserved quantities? Through spectral-decomposition method and explicit, recursive procedure, we obtain all conserved observables for general $mathcal{PT}$-symmetric systems. We then generalize the analysis to Hamiltonians with other antilinear symmetries, and discuss the consequences of conservation laws for open systems. We illustrate our findings with several physically motivated examples.
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