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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Convolution Properties I01:20

Convolution Properties I

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Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:
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Transfer Function to State Space01:23

Transfer Function to State Space

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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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The Entropy as a State Function01:14

The Entropy as a State Function

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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Convolution: Math, Graphics, and Discrete Signals01:24

Convolution: Math, Graphics, and Discrete Signals

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In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
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Preparation of Entangled States through Hilbert Space Engineering.

Y Lin1, J P Gaebler1, F Reiter2

  • 1National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA.

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Summary

Researchers used quantum Zeno dynamics to create entangled states in trapped atomic ions. This method achieved high fidelities for two-ion Bell states and three-ion W-states, showing robustness against laser intensity fluctuations.

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Area of Science:

  • Quantum Information Science
  • Atomic Physics
  • Quantum Computing

Background:

  • Quantum entanglement is crucial for quantum computing and information processing.
  • Trapped atomic ions are promising qubits for quantum technologies.
  • Previous methods for entanglement generation in trapped ions faced challenges with imperfections.

Purpose of the Study:

  • To prepare entangled states of two and three trapped atomic ions.
  • To utilize quantum Zeno dynamics for controlled quantum state preparation.
  • To assess the fidelity and robustness of the entanglement generation method.

Main Methods:

  • Applying laser fields to trapped atomic ions to control quantum dynamics.
  • Using a global microwave field to drive transitions between an initial product state and a target entangled state.
  • Implementing the quantum Zeno effect to constrain quantum evolution.

Main Results:

  • Successfully prepared entangled states of two and three trapped ^{9}Be^{+} ions.
  • Achieved high Bell state fidelities (up to 0.990) for two ions.
  • Obtained a W-state fidelity of 0.910 for three ions.

Conclusions:

  • Quantum Zeno dynamics provides an effective method for preparing entangled states in trapped ions.
  • The developed procedure demonstrates high fidelity entanglement generation.
  • This approach exhibits relative insensitivity to laser intensity fluctuations, enhancing its practical applicability.