Abstract
Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The ...higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called “scrambling,” is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields’ notions of quantum-operation disagreement.
We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the ...presence of a Markovian heat bath. It has the form 'worst-case work = penalty-optimum'. The equality holds for all rates of changing the Hamiltonian and can be used to derive the optimum by setting the penalty to 0. The optimum term contains the max entropy of the initial state, rather than the von Neumann entropy, thus recovering recent results from single-shot statistical mechanics. Energy coherences can arise during the protocol but are assumed not to be present initially. We apply the equality to an electron box.
The difference ΔF between free energies has applications in biology, chemistry, and pharmacology. The value of ΔF can be estimated from experiments or simulations, via fluctuation theorems developed ...in statistical mechanics. Calculating the error in a ΔF estimate is difficult. Worse, atypical trials dominate estimates. How many trials one should perform was estimated roughly by Jarzynski Phys. Rev. E 73, 046105 (2006)PLEEE81539-375510.1103/PhysRevE.73.046105. We enhance the approximation with the following information-theoretic strategies. We quantify "dominance" with a tolerance parameter chosen by the experimenter or simulator. We bound the number of trials one should expect to perform, using the order-∞ Rényi entropy. The bound can be estimated if one implements the "good practice" of bidirectionality, known to improve estimates of ΔF. Estimating ΔF from this number of trials leads to an error that we bound approximately. Numerical experiments on a weakly interacting dilute classical gas support our analytical calculations.
We describe the formation of highly degenerate, Landau-level-like amplified states in a strained photonic honeycomb lattice in which amplification breaks the sublattice symmetry. As a consequence of ...the parity anomaly, the zeroth Landau level is localized on a single sublattice and possesses an enhanced or reduced amplification rate. The selection of the sublattice depends on the strain orientation but is independent of the valley. The spectral properties of the higher Landau levels are constrained by a generalized time-reversal symmetry. In the setting of two-dimensional photonic crystal lasers, the anomaly affects the mode selection and lasing threshold while in three-dimensional photonic lattices it can be probed via the beam dynamics.
Resource theory of quantum uncomplexity Yunger Halpern, Nicole; Kothakonda, Naga B. T.; Haferkamp, Jonas ...
Physical review. A,
12/2022, Letnik:
106, Številka:
6
Journal Article
Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times. The spins would serve as ...biological qubits. The qubits may resist decoherence longer when in Posner molecules. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model’s quantum-communication ability, we show how it can teleport information incoherently: A state’s weights are teleported. Dephasing results from the entangling operation’s simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model’s operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck–Kennedy–Lieb–Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.
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