quantum state

A quantum state is like mountain weather: it changes with every glance. To estimate its uncertainty, physicists make copies and take measurements. Each copy is a thermometer that breaks after use.

A quantum computer isn't just a bunch of qubits: it's a whole city, where each resident is one of the machine's possible states. Residents get to know each other through weak interactions between qubits: if one state can transition to another, a thread of acquaintance is drawn between them.

A washing machine sometimes tears clothes. To get a whole shirt, you wash several and then piece one together from the survivors. A quantum computer treats 'magic states'—special ingredients without which complex computations are impossible — in much the same way. These states are extremely fragile. The slightest noise, and the magic evaporates.

In a hall with a thousand spectators, applause blends into a general noise, but if someone falls out of rhythm — a ripple runs through the crowd. The quantum world works similarly: atoms in a trap can behave as a single whole, or they can fall apart into independent individuals.

Imagine a huge puzzle where each piece is a quantum particle. To complete the picture, you don't just fit the pieces together: you need to entangle them in a special way. Usually, this is done by carefully applying operations one after another, like assembling the puzzle strictly by the instructions, row by row.

Two tiny diamonds float in a vacuum, separated by a distance that light cannot cross during the experiment. Inside each, like a frozen spark, resides an entangled spin — a quantum state linking them into a single whole. Now the diamonds begin to move, but not just any motion: each one seems to split, existing in two places at once.

Quantum mechanics allows a particle to be in two places at once: this is called superposition. But massive objects, like a dust grain or a ball, don't behave that way: their position is always definite. Why? One idea is that it's an illusion: the particle is constantly "jittering" from random environmental kicks, and the blurred picture averages out.

A camera looks at two distant sparks. They're so close together that they merge into a single fuzzy blob. It seems impossible to tell them apart — the classic limit of optical microscopy has been reached. But quantum mechanics hints that the light field still holds a secret about where each spark sits.

In a tight row of atoms, spaced closer than the wavelength of light, a remarkable state hides. The excitation is distributed among all particles so that their radiation cancels itself out. This quantum 'silence' is an ideal vault for a photon: it can be stored there hundreds of times longer than usual.

The quantum world is a constant buzz of activity. Particles exchange energy, become entangled, and influence one another. You'd think that the more players in this game, the harder it is to predict the outcome. But sometimes, order emerges from chaos. Physicists took a close look at the SYK model — a mathematical playground for studying quantum chaos.

In the big world, there's a simple rule: energy density can't be negative, and its flow can't outrun light. In a café, that would look like this: a waiter can't deliver orders faster than he can run. Physicists call this restriction the energy dominance condition. But in the microworld, where quanta rule and spacetime can bend, energy starts acting up.

Seven dancers step onto the stage. They join hands so that any trio or quartet moves in perfect harmony with the rest — no group falls out of the overall rhythm. In the quantum world, this is called an absolutely maximally entangled state (AME for short). It's a perfect knot where every part knows everything about the whole.

A quantum computer based on neutral atoms is like a city where couriers, laser tweezers, physically carry packages between addresses. While one courier drags an atom across the entire chip, the others sit idle. This is slow and error-prone. The new architecture replaces couriers with a shared radio wave.

Imagine a postal service where couriers suddenly stop moving. It would seem that letters would stop arriving and communication between cities would break down. But what if the envelopes themselves suddenly gained the ability to change shape and transmit messages through a shared web without moving an inch?

Two dancers on stage must move in perfect sync, but if one hesitates, the whole routine is ruined. That's roughly how quantum computers with neutral atoms work: two atoms are entangled by putting them into a Rydberg state (as huge as a balloon compared to an ordinary atom), and then you wait for them to 'dance' their part.

Gravity in our world is curved spacetime. That's how Einstein's general theory of relativity describes it. But what happens to gravity at the level of atoms and particles, where quantum mechanics rules? This question has remained unanswered for nearly a century.

A delicate watermark on wet paper, and a fogged-up glass before your eyes. That's roughly what reading quantum states of light looks like: fragile photon patterns get distorted by losses, and detectors catch only a small fraction of the signal.

A tiny magnetized sphere floats in a vacuum, held by invisible fields. It starts to spin around the axis of the magnetic field, just like a top that's been given a gentle nudge. That's precession. But when the sphere becomes really small, quantum laws come into play.

A quantum computer relies on two forces: entanglement (particles behaving as a single whole) and "magic"—a measure of how far a state is from familiar classical physics. But how these two resources relate as a many-particle system evolves in time has remained a puzzle. The authors approached the problem through time.

Quantum entanglement — a phenomenon where the states of two or more particles become interconnected regardless of the distance between them — usually links intrinsic properties such as spin or polarization. However, a new experiment has for the first time realized entanglement of the positions of two atoms in space.

A magnetic field holds a tiny particle in mid-air, like an invisible dance partner. A special tuning of the field creates a trap with two "positions." In the ordinary world, a dancer occupies only one, but in the quantum world — both at once. Physicists have learned to achieve this for dust grains weighing trillionths of a gram.

The quantum vacuum is not a dead void but a boiling cauldron of probabilities. In some theories, our Universe is frozen in a metastable state: like superheated water, it's ready to explode into steam at the slightest nudge.

According to Einstein's general theory of relativity Albert Einstein, a massive rotating body drags the fabric of spacetime along with it, much like a spoon twirled in a jar sets thick honey flowing.

Quantum entanglement often behaves like a synchronized dance visible from only one angle. Change the way you observe it, and the particles appear disconnected. This limits secure communications. Now physicists have created a pair of photons whose 'dance' is flawless from all perspectives.

At temperatures billionths of a degree above absolute zero, a Bose–Einstein condensate emerges — a state where thousands of atoms march in a single quantum key.

A regular object moves along a predictable path, like a ball. In the quantum world, a particle is smeared into a probability cloud. To find order in this fog, scientists have recast Schrödinger's equation in the language of flowing water.

Quantum computers make mistakes. Each step of a computation introduces a tiny inaccuracy, and if left uncorrected, the result degenerates into noise. One of the main challenges is rotating a phase by an arbitrary angle. The standard approach is to assemble the desired rotation from a set of simple operations, like a mosaic.

Light or sound can be confined in a tiny region of a crystal, like a pearl in a shell. Usually, two methods are used. The first is like a heavy ball in a pit: a particle with large mass simply cannot roll out. The second is a perfect cage of mirrors, where waves cancel each other everywhere except in the trap itself.

In the lab, there's a trap, an invisible 'pit' made of electric fields, where a charged dust grain about a hundred nanometers across levitates. It oscillates back and forth like a pendulum in a clock.

In quantum mechanics, everything is fuzzy: a particle is not at a single point but smeared across space, and an event does not happen at a single moment. Yet our everyday world is full of definiteness — the coin landed heads, the light bulb turned on, a note appeared in the notebook.

A pebble falls into a pond, and ripples spread across the water. In the quantum world, the pond is not made of water but of many identical particles, and the pebble is also a particle, just a foreign one. Such a foreign particle is called a Fermi polaron.

Two pendulums hang from the same crossbar. A push, and they start swinging, gradually falling into and out of sync. In a topological qubit, Majorana particles, special excitations that can store quantum information, play the role of these pendulums.

Gravitational-wave observatories are like a keen ear listening for distant rumbles of cosmic catastrophes. To catch the faint whisper of merging black holes, detectors of gravitational waves use specially prepared light — known as squeezed vacuum.

In the mountains, there is a saddle — a point where the trail from one valley crosses over into another. Standing exactly on it, you take a step and are already descending the new slope. In chemistry, such a place is called the transition state: a brief moment when atoms are frozen on the threshold of transformation.

A thrown stone follows a smooth arc: its path is easy to predict. But if the stone skips across water, the trajectory becomes jagged and far more interesting. Quantum particles behave much the same way when their state is not a calm wave with fixed energy but a turbulent mix of several waves at once.

Two dice lie in different rooms. If they are 'entangled,' a roll of one instantly determines the outcome of the other — even at a distance. In the quantum world, such a link is called steering: one party, by performing measurements on their side, seems to dictate the state of the partner.

A boiling kettle with the lid on doesn’t show the bubbling, but the sound and vibration betray the intensity of the water boiling.

A quantum cat is a special state of light, the idea of which was proposed by Erwin Schrödinger in his famous thought experiment.

An ordinary magnet is like a compass: its needle points north. But a quantum compass can look in both directions at once. If a magnet floating in a vacuum is gently spun, its electron 'tops' synchronize so the whole piece of metal starts living by the rules of the microworld — freezes in a superposition, like a split pointer.

A single camera shot stores both a normal picture and a hidden map of how light rippled through the scene. Quantum entanglement makes this possible. Pairs of linked photons are generated: one visits the object, its twin takes a detour. Later, measuring the twin one way pulls out the brightness information.