Information-theoretic derivation of energy and speed bounds
- URL: http://arxiv.org/abs/2403.13223v2
- Date: Mon, 25 Mar 2024 10:02:39 GMT
- Title: Information-theoretic derivation of energy and speed bounds
- Authors: Lorenzo Giannelli, Giulio Chiribella,
- Abstract summary: We provide a model where the dynamics originates from a condition of informational non-equilibrium.
We derive a notion of energy that captures the main features of energy in quantum theory.
Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions.
- Score: 0.2302001830524133
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Information-theoretic insights have proven fruitful in many areas of quantum physics. But can the fundamental dynamics of quantum systems be derived from purely information-theoretic principles, without resorting to Hilbert space structures such as unitary evolution and self-adjoint observables? Here we provide a model where the dynamics originates from a condition of informational non-equilibrium, the deviation of the system's state from a reference state associated to a field of identically prepared systems. Combining this idea with three basic information-theoretic principles, we derive a notion of energy that captures the main features of energy in quantum theory: it is observable, bounded from below, invariant under time-evolution, in one-to-one correspondence with the generator of the dynamics, and quantitatively related to the speed of state changes. Our results provide an information-theoretic reconstruction of the Mandelstam-Tamm bound on the speed of quantum evolutions, establishing a bridge between dynamical and information-theoretic notions.
Related papers
- A Theory of Quantum Jumps [44.99833362998488]
We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field.
Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
arXiv Detail & Related papers (2024-04-16T11:00:46Z) - Quantifying High-Order Interdependencies in Entangled Quantum States [43.70611649100949]
We introduce the Q-information: an information-theoretic measure capable of distinguishing quantum states dominated by synergy or redundancy.
We show that quantum systems need at least four variables to exhibit high-order properties.
Overall, the Q-information sheds light on novel aspects of the internal organisation of quantum systems and their time evolution.
arXiv Detail & Related papers (2023-10-05T17:00:13Z) - Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
We explore the applicability of quantum-data learning to practical problems in high-energy physics.
We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states.
The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
arXiv Detail & Related papers (2023-06-29T18:00:01Z) - Second Response Theory: A Theoretical Formalism for the Propagation of
Quantum Superpositions [0.0]
We expand a previously developed size-extensive formalism within coupled cluster theory, called second response theory, so it propagates quantum systems.
Our theory shows strong consistency with numerically exact results for the determination of quantum mechanical observables, probabilities, and coherences.
arXiv Detail & Related papers (2023-06-13T17:33:22Z) - A Quantum-Classical Model of Brain Dynamics [62.997667081978825]
Mixed Weyl symbol is used to describe brain processes at the microscopic level.
Electromagnetic fields and phonon modes involved in the processes are treated either classically or semi-classically.
Zero-point quantum effects can be incorporated into numerical simulations by controlling the temperature of each field mode.
arXiv Detail & Related papers (2023-01-17T15:16:21Z) - Non-Hermitian Hamiltonian Deformations in Quantum Mechanics [4.071207179756646]
We introduce a broader class of non-Hermitian Hamiltonian deformations in a nonrelativistic setting.
We relate the time evolution operator and the time-evolving density matrix in the undeformed and deformed theories.
As the dissipative evolution of a quantum system can be conveniently described in Liouville space, we discuss the spectral properties of the Liouvillians.
arXiv Detail & Related papers (2022-11-10T09:25:59Z) - Quantum computation of dynamical quantum phase transitions and
entanglement tomography in a lattice gauge theory [0.0]
Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe.
We compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory.
Results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer.
arXiv Detail & Related papers (2022-10-06T17:47:33Z) - Correspondence Between the Energy Equipartition Theorem in Classical
Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
In quantum mechanics, the energy per degree of freedom is not equally distributed.
We show that in the high-temperature regime, the classical result is recovered.
arXiv Detail & Related papers (2022-05-24T20:51:03Z) - From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation.
We describe quantum decays in a 2-level system as coherent and continuous processes.
arXiv Detail & Related papers (2021-07-29T18:27:38Z) - A kinetic theory for quantum information transport [0.0]
This is a framework aimed at describing how out of equilibrium open quantum systems move information around their state space.
The main goal is to build new mathematical tools, together with physical intuition, to improve our understanding of non-equilibrium phenomena in quantum systems.
arXiv Detail & Related papers (2021-06-01T10:45:18Z) - Non-Hermitian Physics [4.511923587827301]
Review is given on the foundations and applications of non-Hermitian classical and quantum physics.
In particular, we discuss rich and unique phenomena found therein, such as unidirectional invisibility.
Other topics related to non-Hermitian physics, including nonreciprocal transport, speed limits, nonunitary quantum walk, are also reviewed.
arXiv Detail & Related papers (2020-06-02T18:00:01Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.