Related papers: Generalized geometric speed limits for quantum obs…
The quantum speed limit indicates the maximal evolution speed of the quantum system. In this work, we determine speed limits on the informational measures, namely the von Neumann entropy, maximal information, and coherence of quantum…
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found…
Generalization is the ability of machine learning models to make accurate predictions on new data by learning from training data. However, understanding generalization of quantum machine learning models has been a major challenge. Here, we…
The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general…
We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the…
We derive generalizations of the energy-time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit…
Quantum computers are known to provide speedups over classical state-of-the-art machine learning methods in some specialized settings. For example, quantum kernel methods have been shown to provide an exponential speedup on a learning…
We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in…
Inequalities of Mandelstam-Tamm and Margolus-Levitin type provide lower bounds on the time it takes for a quantum system to evolve from one state into another. Knowledge of such bounds, called quantum speed limits, is of utmost importance…
In this work, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices. This bound itself is of interest, as we show that it satisfies the canonical criteria of a QFI…
The speed of quantum evolution is limited under finite energy resources. While most quantum speed limits (QSLs) are formulated in terms of quantum states, they can be extended to the evolution operator itself, and thus impose fundamental…
Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality,…
It is well known in quantum mechanics that a large energy gap between a Hilbert subspace of specific interest and the remainder of the spectrum can suppress transitions from the quantum states inside the subspace to those outside due to…
Quantum speed limit (QSL) is the study of fundamental limits on the evolution time of quantum systems. For instance, under the action of a time-independent Hamiltonian, the evolution time between an initial and a final quantum state obeys…
Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in…
We present a class of generalized entropic quantum speed limits based on $\alpha$-$z$-R\'{e}nyi relative entropy, a real-valued, contractive, two-parameter family of distinguishability measures. The quantum speed limit (QSL) falls into the…
We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the…
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher…