Quantum Computing
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Von Neumann Entropy

Quantum analogue of Shannon entropy — measures the uncertainty in a quantum state.

Formula

S(ρ)=−tr(ρlog⁡2ρ)S(\rho) = -\text{tr}(\rho \log_2 \rho)

Variables

S(\rho)Von Neumann entropy (bits)
\rhoDensity matrix

Example

A maximally mixed single qubit: S = 1 bit

Did You Know?

A pure quantum state has S = 0 — zero uncertainty — while a maximally mixed n-qubit state has S = n.

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Qubit Superposition State

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General state of a single qubit as a superposition of the computational basis states.

Normalisation Constraint

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The squared amplitudes of a qubit must sum to 1, ensuring total probability is 100 %.

Hadamard Gate

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Puts a qubit into an equal superposition — the most common single-qubit gate.

Pauli-X Gate (Quantum NOT)

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Flips |0⟩ to |1⟩ and vice versa — the quantum equivalent of a classical NOT gate.

CNOT Gate

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Two-qubit gate that flips the target qubit only when the control qubit is |1⟩.

Bell State (EPR Pair)

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Maximally entangled two-qubit state — measuring one qubit instantly determines the other.