Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
The Entropy as a State Function01:14

The Entropy as a State Function

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...
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
Second Law of Thermodynamics02:49

Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Integrability and chaos via fractal analysis of spectral form factors: Gaussian approximations and exact results.

Physical review. E·2026
Same author

Invested and Potential Magic Resources in Measurement-Based Quantum Computation.

Physical review letters·2025
Same author

Unscrambling Quantum Information with Clifford Decoders.

Physical review letters·2024
Same author

Stabilizer Rényi Entropy.

Physical review letters·2022
Same author

Isospectral Twirling and Quantum Chaos.

Entropy (Basel, Switzerland)·2021
Same author

García-Pintos, Hamma, and del Campo Reply.

Physical review letters·2021

Related Experiment Video

Updated: May 18, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Quantum entanglement in random physical states.

Alioscia Hamma1, Siddhartha Santra, Paolo Zanardi

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, N2L 2Y5, Waterloo, Ontario, Canada.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Most quantum states are entangled, but not physically accessible. This study shows that random quantum circuits create accessible entangled states obeying area and volume laws, approaching a mixed state with increased circuit length.

More Related Videos

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Related Experiment Videos

Last Updated: May 18, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Information Science
  • Statistical Mechanics
  • Many-Body Physics

Background:

  • Most quantum states in Hilbert space are maximally entangled, a property useful for statistical mechanics.
  • However, these states are typically not physically accessible in quantum many-body systems.

Purpose of the Study:

  • To define and investigate physically accessible entangled states using random quantum circuits.
  • To analyze the typicality of entanglement in these accessible states.

Main Methods:

  • Defining physical ensembles of states via random circuits of independent unitaries with local support.
  • Studying entanglement typicality using the purity of the reduced state.
  • Analyzing subsystem entanglement scaling with system size and circuit depth.

Main Results:

  • For short circuits (k=O(1)), typical purity follows an area law, saturating upper bounds on average.
  • Subsystems exhibit volume law entanglement when local evolution time scales with subsystem size.
  • For large circuit depths (large k), the reduced state approaches a completely mixed state.

Conclusions:

  • Random quantum circuits provide a pathway to physically accessible, entangled states.
  • The study demonstrates the emergence of area and volume laws for entanglement in such systems.
  • The findings suggest that long random evolutions lead to thermalization, approaching a mixed state.