The density matrix of a pure quantum state ly) is defined as p = 1)land the density matrix of the collection of pure states ) with the corresponding probabilities p, is defined as p = Σ. Ρ|Ψ;}ψι|. (a) Find a density matrix of 4) =(100) + |11)) and show that this density matrix corresponds a pure state (by using the purity). (b) Find a density matrix composed of quantum states ₁) = (100) + |11)), 2)=(101) +110)) with corresponding probabilities P₁ = P₂ = 1/2. Show that the density matrix is in a mixed state.
The density matrix of a pure quantum state ly) is defined as p = 1)land the density matrix of the collection of pure states ) with the corresponding probabilities p, is defined as p = Σ. Ρ|Ψ;}ψι|. (a) Find a density matrix of 4) =(100) + |11)) and show that this density matrix corresponds a pure state (by using the purity). (b) Find a density matrix composed of quantum states ₁) = (100) + |11)), 2)=(101) +110)) with corresponding probabilities P₁ = P₂ = 1/2. Show that the density matrix is in a mixed state.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![The density matrix of a pure quantum state ) is defined as p = 1)land the density matrix of the
collection of pure states ) with the corresponding probabilities p, is defined as
ρ = Σ; pi|Ψ}(Ψ.|.
(a) Find a density matrix of 4) = (100) + |11)) and show that this density matrix corresponds a
pure state (by using the purity).
(b) Find a density matrix composed of quantum states ₁) = (100) + 111)),
142)=(101) + |10)) with corresponding probabilities p₁ = P2 = 1/2.
Show that the density matrix is in a mixed state.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe43bca3-718e-44ea-b76f-859b595de7a8%2F45f43c90-0cae-4ba4-a9e2-7fa274d911dd%2F8arg9op_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The density matrix of a pure quantum state ) is defined as p = 1)land the density matrix of the
collection of pure states ) with the corresponding probabilities p, is defined as
ρ = Σ; pi|Ψ}(Ψ.|.
(a) Find a density matrix of 4) = (100) + |11)) and show that this density matrix corresponds a
pure state (by using the purity).
(b) Find a density matrix composed of quantum states ₁) = (100) + 111)),
142)=(101) + |10)) with corresponding probabilities p₁ = P2 = 1/2.
Show that the density matrix is in a mixed state.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY