Characterizations of symmetric monotone metrics on the state space of quantum systems

2006 ◽  
Vol 6 (7) ◽  
pp. 597-605
Author(s):  
F. Hansen
Keyword(s):  
State Space ◽  
Quantum System ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Classical Case ◽  
Riemannian Metric ◽  
Quantum Systems ◽  
The State ◽  
Stochastic Mappings

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

scholarly journals ON THE CURVATURE OF A CERTAIN RIEMANNIAN SPACE OF MATRICES

2000 ◽  
Vol 03 (02) ◽  
pp. 199-212 ◽  
Author(s):  
PETER W. MICHOR ◽  
DÉNES PETZ ◽  
ATTILA ANDAI
Keyword(s):  
Scalar Curvature ◽  
State Space ◽  
Quantum System ◽  
Curvature Tensor ◽  
Riemannian Space ◽  
Riemannian Metric ◽  
Positive Definite ◽  
The State ◽  
Inner Product ◽  
Positive Definite Matrices

Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov–Kubo–Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

scholarly journals Flows in non-equilibrium quantum systems and quantum photosynthesis

2017 ◽  
Vol 20 (04) ◽  
pp. 1750021 ◽  
Author(s):  
S. V. Kozyrev ◽  
A. A. Mironov ◽  
A. E. Teretenkov ◽  
I. V. Volovich
Keyword(s):  
Quantum System ◽  
Stationary State ◽  
Quantum Systems ◽  
The State ◽  
State Of The Environment ◽  
Non Equilibrium

A three-level quantum system interacting with non-equilibrium environment is investigated. The stationary state of the system is found (both for non-coherent and coherent environment) and relaxation and decoherence to the stationary state is described. The stationary state of the system will be non-equilibrium and will generate flows. We describe the dependence of the flows on the state of the environment. We also discuss application of this model to the problem of quantum photosynthesis, in particular, to the description of flows of excitons and generation of excitonic coherences.

scholarly journals The D-CTC Condition is Generically Fulfilled in Classical (Non-quantum) Statistical Systems

2021 ◽  
Vol 51 (5) ◽  
Author(s):  
Jürgen Tolksdorf ◽  
Rainer Verch
Keyword(s):  
State Space ◽  
General Model ◽  
Quantum Systems ◽  
The State ◽  
Closed Timelike Curves ◽  
Original Proof ◽  
Quantum Nature ◽  
Model Independent ◽  
Quantum Statistical ◽  
Statistical Systems

AbstractThe D-CTC condition, introduced by David Deutsch as a condition to be fulfilled by analogues for processes of quantum systems in the presence of closed timelike curves, is investigated for classical statistical (non-quantum) bi-partite systems. It is shown that the D-CTC condition can generically be fulfilled in classical statistical systems, under very general, model-independent conditions. The central property used is the convexity and completeness of the state space that allows it to generalize Deutsch’s original proof for q-bit systems to more general classes of statistically described systems. The results demonstrate that the D-CTC condition, or the conditions under which it can be fulfilled, is not characteristic of, or dependent on, the quantum nature of a bi-partite system.

Optimal temperature estimation for a XXZ spin-1 2 chain coupled locally to independent thermal baths

2020 ◽  
Vol 34 (36) ◽  
pp. 2050425
Author(s):  
Chao-Quan Wang
Keyword(s):  
Quantum System ◽  
Fisher Information ◽  
Open Quantum System ◽  
Quantum Fisher Information ◽  
Steady States ◽  
Optimal Time ◽  
Quantum Master Equation ◽  
Optimal Temperature ◽  
Temperature Estimation ◽  
Open Quantum

Temperature as an environmental parameter influences the evolution of an open quantum system. In detail, temperature lies in Lindblad operator of quantum master equation that the evolution of an open quantum system follows. Hence, one can implement a temperature estimation of thermal baths through a measurement of quantum Fisher information about temperature brought from quantum states. Such a method by calculating quantum Fisher information about a parameter to estimate its value avoids measuring the parameter directly and it does not change the value of the parameter due to making measurements. In this paper, we consider a model consisting of a XXZ spin-[Formula: see text] chain coupled locally to independent thermal baths with different temperature. Based on the model, we investigate optimal temperature estimation for thermal baths with respect to an open quantum system subjected to non-steady states. We first study optimal probe time for temperature estimation in the case of non-steady states and find that the optimal time shows different features for different types of system variables. It proves that in a certain duration there exists a tradeoff between the trial times and the attaining amount of Fisher information in each trial. In addition, we pay attention to an issue on optimal probe states. We demonstrate that in many cases the optimal states are not always the maximally entangled states and even maybe the separable states, which is related with the measuring time, system couplings.

scholarly journals The shape of higher-dimensional state space: Bloch-ball analog for a qutrit

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 485
Author(s):  
Christopher Eltschka ◽  
Marcus Huber ◽  
Simon Morelli ◽  
Jens Siewert
Keyword(s):  
State Space ◽  
Quantum System ◽  
Dimensional Space ◽  
Three Dimensional ◽  
The State ◽  
Level System ◽  
Three Dimensional Model ◽  
System A ◽  
Dimensional State Space ◽  
Geometric Intuition

Geometric intuition is a crucial tool to obtain deeper insight into many concepts of physics. A paradigmatic example of its power is the Bloch ball, the geometrical representation for the state space of the simplest possible quantum system, a two-level system (or qubit). However, already for a three-level system (qutrit) the state space has eight dimensions, so that its complexity exceeds the grasp of our three-dimensional space of experience. This is unfortunate, given that the geometric object describing the state space of a qutrit has a much richer structure and is in many ways more representative for a general quantum system than a qubit. In this work we demonstrate that, based on the Bloch representation of quantum states, it is possible to construct a three dimensional model for the qutrit state space that captures most of the essential geometric features of the latter. Besides being of indisputable theoretical value, this opens the door to a new type of representation, thus extending our geometric intuition beyond the simplest quantum systems.

scholarly journals Fisher Information in Noisy Intermediate-Scale Quantum Applications

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 539
Author(s):  
Johannes Jakob Meyer
Keyword(s):  
Fisher Information ◽  
Quantum Algorithms ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Quantum Sensing ◽  
Near Term

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

scholarly journals Quantum Fisher Information of W and GHZ State Superposition under Decoherence

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Quantum System ◽  
Recent Work ◽  
Fisher Information ◽  
Quantum Fisher Information ◽  
Ghz State ◽  
Noisy Channels ◽  
Noise Parameters ◽  
Ghz States

We study the changes in quantum Fisher information (QFI) values for one quantum system consisting of a superposition of W and GHZ states. In a recent work [6], QFI values of this mentioned system studied. In this work, we extend this problem for the changes of QFI values in some noisy channels. We show the change in QFI depending on noise parameters. We report interesting results for different type of decoherence channels.

scholarly journals Quantum Fisher Information of Decohered W and GHZ Superposition States with Arbitrary Relative Phase

2017 ◽  
Author(s):  
Volkan Erol
Keyword(s):  
Quantum System ◽  
Recent Work ◽  
Fisher Information ◽  
Relative Phase ◽  
Quantum Fisher Information ◽  
Phase Sensitivity ◽  
Quantum Metrology ◽  
Noisy Channels ◽  
Noise Parameters ◽  
Superposition States

Quantum Fisher Information (QFI) is a very useful concept for analyzing situations that require phase sensitivity. It become a popular topic especially in Quantum Metrology domain. In this work, we study the changes in quantum Fisher information (QFI) values for one relative arbitrary phased quantum system consisting of a superposition of N Qubits W and GHZ states. In a recent work [7], QFI values of this mentioned system for N qubits were studied. In this work, we extend this problem for the changes of QFI values in some noisy channels for the studied system. We show the changes in QFI depending on noise parameters. We report interesting results for different type of decoherence channels. We show the general case results for this problem.

Sign in / Sign up

Export Citation Format

Share Document