phenomenon

quantum correlation

Non-classical correlations between quantum systems enabling coordination, imaging, or energy extraction.
13 related articles · 5 formulas

Description

Quantum correlation refers to statistical dependencies between measurements on separate quantum systems that cannot be explained by classical physics. Unlike ordinary correlations, which arise from shared causes or direct influences, quantum correlations can be stronger than any local hidden-variable model permits, a phenomenon famously quantified by Bell inequalities. These correlations are the resource behind quantum entanglement, where the state of one particle is intrinsically linked to another regardless of distance, and they underpin protocols like quantum teleportation and superdense coding.

History

The concept was formalized in the 1930s through the Einstein-Podolsky-Rosen paradox, and John Bell's 1964 theorem turned it into a testable prediction. Alain Aspect's experiments in the 1980s confirmed the violation of Bell inequalities, establishing quantum correlations as a real physical phenomenon.

How it works

Quantum correlations emerge from the superposition principle: a composite system can exist in a state that is not a simple product of individual states, meaning the particles do not have definite properties until measured. When measured, the outcomes are random individually but perfectly or strongly correlated jointly, violating classical bounds. This arises because the wavefunction describes the whole system, not just its parts, and measurement collapses it globally, instantaneously linking the results.

In practice

Quantum correlations enable secure quantum key distribution, quantum teleportation, and enhanced imaging techniques like ghost imaging, where an image is formed from photons that never interacted with the object.

Fun fact

Quantum correlations can be so strong that they allow two parties to generate shared random numbers that are provably private, even if an eavesdropper has unlimited computational power.

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Formulas

$$S_q = k \frac{1 - \sum_{i=1}^W p_i^q}{q-1}$$
Generalized entropy for non-extensive systems with parameter q.
What is in the formula
qvariableentropic index characterizing non-extensivity — entropic index
p_ivariableprobability of microstate i — probability
Wvariablenumber of accessible microstates — number of states
S_qvariableTsallis entropy — entropy joule per kelvin
kconstantBoltzmann constant (or a generalized constant depending on context) — boltzmann constant = 1.380649e-23 joule per kelvin
∑operatorsum over all microstates — summation
s_q=k\frac{1-\sum_{i=1}^wp_i^q}{q-1} · 2606.27985
$$[\text{X/Y}] = a[\text{Z/Y}] + b$$
Linear correlation between elemental abundances indicates different nucleosynthetic sources.
What is in the formula
[\text{X/Y}]variableAbundance ratio of element X to Y relative to solar — abundance ratio
[\text{Z/Y}]variableAbundance ratio of element Z to Y relative to solar — abundance ratio
avariableSlope of the correlation — dimensionless
bvariableIntercept of the correlation — dimensionless
[{n/fe}]\approx-0.5[{o/fe}]+{const} · 2607.05509v1
$$I(A;B) = S(A) + S(B) - S(A \cup B)$$
Mutual information quantifies shared information between two subsystems.
What is in the formula
I(A;B)variableMutual information between subsystems A and B — mutual information bit
S(A)variableEntropy of subsystem A — entropy bit
S(B)variableEntropy of subsystem B — entropy bit
S(A ∪ B)variableEntropy of the combined system A and B — entropy bit
∪operatorCombines the two subsystems into one joint system — set union
s_d=s(a)+s(b)-s(a\cupb)-s(a\capb) · 2606.25653
$$C(t) = \frac{\langle A(t) A(0) \rangle}{\langle A(0)^2 \rangle}$$
Measures how a system's state correlates with its initial state over time.
What is in the formula
C(t)variableNormalized autocorrelation function of observable A — correlation function
A(t)variableValue of observable A at time t — observable varies
A(0)variableValue of observable A at initial time — observable varies
⟨...⟩operatorAverages the product over a statistical ensemble of initial conditions — ensemble average
c_{γ}(t)=\frac{\langle\hat{n}_{γ}(t)\hat{n}_{γ}(0)\rangle}{\langle\hat{n}_{γ}(0)^2\rangle} · 2606.31185
$$S = \int d^4x \sqrt{-g} \left[ f(\phi,R) - \frac{1}{2}(\partial\phi)^2 \right]$$
General action for scalar-tensor gravity with non-minimal coupling.
What is in the formula
SvariableAction of the theory — action joule second
gvariableDeterminant of the spacetime metric tensor — metric determinant
φvariableScalar field non-minimally coupled to gravity — scalar field
RvariableRicci scalar curvature — ricci scalar per metre squared
∂φvariableGradient of the scalar field — field gradient per metre
∫ d⁴xoperatorIntegration over four-dimensional spacetime — four dimensional integral
√(-g)operatorVolume element factor for curved spacetime — sqrt negative metric determinant
(∂φ)²operatorKinetic term of the scalar field, contraction of its gradient with itself — kinetic term
s=\intd^4x\sqrt{-g}[j(r/φ^2)φ^4-\frac{1}{2}(\partialφ)^2] · 2606.31472

Related articles · 13

Quantum Dance Without a Shared Stage
Two dancers on the same stage mirror each other's moves even when a curtain separates them. In the quantum world, such pairs are called entangled, and physicists have spent half a century probing how far this connection reaches. Until now, all tests with massive particles concerned their internal properties, such as spin, but not their motion itself.
Quantum Coherence Microscope: Seeing the Phase of Atoms in a Lattice
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.
The Bell of Noncommutativity: How Twisted Statistics Violate Bell Inequalities
Two observers, Alice and Bob, sit at opposite ends of the same lab. Between them is a source that fires off two pulses in turn. Each pulse gives birth to a wave packet flying toward its own detector. So far, this looks like an ordinary experiment with quantum particles.
Quantum Physics2026-07-101 minarXiv:2607.09875express
Quantum Dance of Entanglement and Magic
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 Physics2026-06-191 minarXiv:2606.21768express
Quantum Twins and the Secret of the Common Cause
Twins enter a room from different doors. Each gets a box with a button, and each time they press it, either a red or a green light flashes. If the twins are perfectly identical, you'd expect their lights to follow the same internal rules. But what if the rules differ even though the twins are exact copies? That's precisely the scenario the authors explored.
Quantum Entanglement as Geometry: Extra Time Instead of Instantaneous Communication
Two particles separated by kilometers change their states in concert, as if there were no distance between them. This is called quantum entanglement, and since its discovery it has baffled physicists: no known carrier can travel faster than light, yet correlations appear instantaneously.
Quantum Gases2026-05-281 minarXiv:2605.30540express
Acoustic Black Holes Get Entangled Differently
An acoustic black hole is a fluid flow faster than sound, so sound waves can't escape. The boundary, the surface where the flow speed reaches the speed of sound, spawns pairs of phonons: sound quanta, one flying away, the other plunging inward.
Quantum Physics2026-05-131 minarXiv:2605.13154express
Quantum Debate: What Are Particles Hiding?
Two particles behave like a pair of unusual dice: thrown at opposite ends of the universe, they always land on the same face. Physicist John Stewart Bell calculated: if the dice had hidden rules, the frequency of matches would have a strict limit.
Quantum Physics2026-05-012 minarXiv:2605.00981express
Quantum Triangle with No Buttons
Three people sit in three corners of a room. Each receives a sealed envelope from an invisible courier, but the couriers do not coordinate and have never met. The people open the envelopes and see a note with one word: "yes" or "no." They choose nothing themselves: they just read.
Quantum Physics2026-03-261 minarXiv:2603.24909express
A loophole for light: how quanta fool the clocks
Two coins are flipped in different cities, but they always land the same way. Physicists call this entanglement: particles behave as if an invisible thread connects them. But what if the thread isn't instantaneous, just very fast — still not faster than light? Then some signal could slip between measurements, and the coincidences would be explained without any magic.
Quantum Physics2026-03-171 minarXiv:2603.17030express
Comparing Scents: A New Type of Bell Inequalities
Comparing two scents is easy even without knowing their ingredients, just tell if they're alike. This everyday principle became the foundation for a new class of Bell inequalities, reimagining tests of the spooky connection between particles. Previously, you had to measure precise properties, like spin direction, but the authors showed that simply comparing outcomes is enough.
Death and Rebirth of Quantum Echo: A Hierarchy of Temporal Correlations in a Qubit
Strike a gong and the sound fades in layers: the low hum lingers longer, the high overtones vanish first, leaving silence behind. So too a qubit, living its quantum life, leaves not one but three echoes of its own past.
A Telegraph Through a Hidden Tunnel in Time
Two couriers leave the same city in opposite directions. An hour later, each opens an envelope: one contains a slip marked “plus,” the other “minus.” How did they know who would get which?