Lifeboat Foundation

In the general formulation of quantum information, quantum states are represented by a special class of matrices called density matrices. This lesson describes the basics of how density matrices work and explains how they relate to quantum state vectors. It also introduces the Bloch sphere, which provides a useful geometric representation of qubit states, and discusses different types of correlations that can be described using density matrices.

0:00 — Introduction.
1:46 — Overview.
2:55 — Motivation.
4:40 — Definition of density matrices.
9:55 — Examples.
12:58 — Interpretation.
15:37 — Connection to state vectors.
20:13 — Probabilistic selections.
25:23 — Completely mixed state.
28:41 — Probabilistic states.
32:03 — Spectral theorem.
37:36 — Bloch sphere (introduction)
38:36 — Qubit quantum state vectors.
41:30 — Pure states of a qubit.
43:52 — Bloch sphere.
47:38 — Bloch sphere examples.
51:36 — Bloch ball.
55:40 — Multiple systems.
56:46 — Independence and correlation.
1:00:55 — Reduced states for an e-bit.
1:04:16 — Reduced states in general.
1:08:53 — The partial trace.
1:12:23 — Conclusion.

Continue reading “Lesson 09: Density Matrices | Understanding Quantum Information & Computation” »

Since Nobel-Prize-winning physicist Frank Wilczek first proposed his theory over a decade ago, researchers have been on the search for elusive “time crystals”—many-body systems composed of particles and quasiparticles like excitons, photons, and polaritons that, in their most stable quantum state, vary periodically in time.

Wilczek’s theory centered around a puzzling question: Can the most stable state of a quantum system of many particles be periodic in time? That is, can it display temporal oscillations characterized by a beating with a well-defined rhythm?

It was quite rapidly shown that time crystal behavior cannot occur in isolated systems (systems which do not exchange energy with the surrounding environment). But far from closing the subject, this disturbing question motivated scientists to search for the conditions under which an open system (i.e., one that exchanges energy with the environment) may develop such time crystal behavior.

Transferring information from one location to another without transmitting any particles or energy seems to run counter to everything we’ve learned in the history of physics.

Yet there is some solid reasoning that this ‘counterfactual communication’ might not only be plausible, but depending on how it works could reveal fundamental aspects of reality that have so far been hidden from view.

Counterfactual physics isn’t a new thing in itself, describing a way of deducing activity by an absence of something. In one sense, it’s pretty straight forward. If your dog barks at strangers, and you hear silence when the front door opens, you’ve received information that says a familiar person has entered your house in spite of the absence of sound.

The true nature of time has eluded physicists for centuries, but a new theoretical model suggests it may only exist due to entanglement between quantum objects.

By Karmela Padavic-Callaghan

Proposed set-up might help reconcile gravity with quantum descriptions of the other fundamental forces – a long sought-after goal in physics.

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Previous guest and friend of the show, Sir Roger Penrose, argues that human consciousness is not algorithmic and, therefore, cannot be modeled by Turing machines. In fact, he believes in a quantum mechanical understanding of human consciousness. However, as with any issue related to human consciousness, many disagree with him. One of his opponents is Daniel Dennett, with whom I recently had the pleasure of talking. Tune in to find out why Dennett thinks Penrose is wrong!

Continue reading “Dan Dennett: Sir Roger Penrose Is WRONG About Human Consciousness!” »

A research team has developed a novel “pulse-shaped” light method to enhance the electrical conductivity of PbS quantum dot solar cells. This new technique, which replaces the lengthy traditional heat treatment process, generates substantial energy at regular intervals, significantly improving efficiency and addressing defects caused by light, heat, and moisture exposure. PbS quantum dots, known for their wide absorption range and low processing costs, are now more viable for commercial use. This advancement is expected to facilitate the broader application of quantum dot technology in optoelectronic devices. Credit: SciTechDaily.com.

A research team headed by Professor Jongmin Choi from the Department of Energy Science and Engineering at Daegu Gyeongbuk Institute of Science and Technology has successfully developed a “PbS quantum dot” capable of quickly improving the electrical conductivity of solar cells. This collaborative effort involved Professor Changyong Lim of the Department of Energy Chemical Engineering at Kyungpook National University, led by President Wonhwa Hong, and Professor Jongchul Lim from the Department of Energy Engineering at Chungnam National University, under the leadership of President Jeongkyoum Kim.

The team identified a method to enhance electrical conductivity through the use of “pulse-shaped” light, which generates substantial energy in a concentrated manner at regular intervals. This method could replace the heat treatment process, which requires a significant amount of time to achieve the same result. This approach is expected to facilitate the production and commercialization of PbS quantum dot solar cells in the future.

Researchers from Lancaster University and Radboud University Nijmegen have managed to generate propagating spin waves at the nanoscale and discovered a novel pathway to modulate and amplify them.

Recently, a team of chemists, mathematicians, physicists and nano-engineers at the University of Twente in the Netherlands developed a device to control the emission of photons with unprecedented precision. This technology could lead to more efficient miniature light sources, sensitive sensors, and stable quantum bits for quantum computing.