Information theory, which was developed by Claude Shannon starting in the late 1940s, deals with questions such as how quickly information can be sent over a noisy communications channel. Both the information carriers (e.g., photons) and the channel (e.g., optical fiber cable) are assumed to be classical systems, with well-defined, perfectly distinguishable states.
In the past two decades, physicists have been developing a quantum version of information theory in which the internal state of each information carrier has quantum properties, such as superposition—the ability to occupy two or more classical states at once. But the transmission lines are generally still assumed to be classical, so that the path taken by messages in space is always well-defined.
Now in a new paper, physicists Giulio Chiribella and Hlér Kristjánsson at the University of Oxford and the University of Hong Kong have proposed a second level of quantization, in which both the information carriers and the channels can be in quantum superposition. In this new paradigm of communication, the information carriers can travel through multiple channels simultaneously.
Adapted from: Physicists propose a second level of quantization for quantum Shannon theory by Lisa Zyga , Phys.org
Adapted from Quanta Magazine: https://www.quantamagazine.org/
Mathematicians long wondered whether it’s possible to express the number 33 as the sum of three cubes — that is, whether the equation 33 = x³+ y³+ z³ has a solution. They knew that 29 could be written as 3³ + 1³ + 1³, for instance, whereas 32 is not expressible as the sum of three integers each raised to the third power. But the case of 33 went unsolved for 64 years.
Read the whole article here: Sum-of-Three-Cubes Problem Solved for ‘Stubborn’ Number 33
je suis a la recherche du temps perdu
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First Day of School
He goes to class. There is an empty seat in front. He sits in the seat. He looks around. There are different people. He says “hi” to the girl next to him. She smiles. The teacher comes in. She closes the door. Everyone is silent. The first day of school begins.
Water on the Floor
She is thirsty. She gets a glass of water. She begins to walk. She drops the glass. There is water on the floor. The puddle is big. She gets a mop. She wipes the water off. The floor is clean. She gets another glass of water. She drinks it. She is happy.
Casey wants a new car. She needs money. She decides to babysit. She takes care of the child. She feeds him lunch. She reads him a story. The story is funny. The child laughs. Casey likes him. The child’s mom comes home. The child kisses Casey. Casey leaves. She will babysit him again.
Jill and Jodi are twins. They look the same. But they act differently. Jill likes sports. She is good at basketball and golf. She is also loud. She talks all day. Jodi likes reading. She can read 300 pages a day. She is also quiet. She does not like to talk. Jill and Jodi still love each other.
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The math of superposition and quantum states.
Huge thanks to my friend Evan Miyazono, both for encouraging me to do this project, and for helping me understand many things along the way.
This is a simple primer for how the math of quantum mechanics, specifically in the context of polarized light, relates to the math of classical waves, specifically classical electromagnetic waves.
I will say, if you *do* want to go off and learn the math of quantum mechanics, you just can never have too much linear algebra, so check out the series I did at http://3b1b.co/essence-of-linear-algebra
Mistakes: As several astute commenters have pointed out, the force arrow is pointing the wrong way at 2:18
. Thanks for the catch!
*Note on conventions: Throughout this video, I use a single-headed right arrow to represent the horizontal direction. The standard in quantum mechanics is actually to use double-headed arrows for describing polarization states, while single-headed arrows are typically reserved for the context of spin.
What’s the difference? Well, using a double-headed arrow to represent the horizontal direction emphasizes that in a quantum mechanical context, there’s no distinction between left and right. They each have the same measurable state: horizontal (e.g. they pass through horizontally oriented filters). Once you’re in QM, these kets are typically vectors in a more abstract space where vectors are not necessarily spatial directions but instead represent any kind of state.
Because of how I chose to motivate things with classical waves, where it makes sense for this arrow to represent a unit vector in the right direction, rather than the more abstract idea of a horizontal state vector, I chose to stick with the single-headed notation throughout, though this runs slightly against convention.
Music by Vincent Rubinetti:
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you’re into that).
Various social media stuffs:
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