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Quantum Entanglement Calculator

Calculate quantum entanglement measures including concurrence, von Neumann entropy, tangle, and Bell state fidelity.

Inputs

Results

Concurrence

1

Entanglement Entropy

1 bits

Tangle

1

Entanglement of Formation1
Bell State Fidelity100%
P(|00⟩)50%
How to Use This Calculator
  1. Enter the four two-qubit state amplitudes: |00⟩, |01⟩, |10⟩, and |11⟩. A Bell state (max entanglement) uses |00⟩ = |11⟩ = 1/√2 ≈ 0.707.
  2. The amplitudes must be normalized: the sum of squares should equal 1. Adjust until the Inner Product is ~1.
  3. Read Concurrence (0–1): 0 means separable (unentangled), 1 means maximally entangled.
  4. Entanglement Entropy (bits) gives the von Neumann entropy: 0 for separable, 1 bit for a Bell state.
  5. Use Bell State Fidelity (%) to check how close your state is to a canonical Bell state.

How the result changes with |00⟩ Amplitude

|00⟩ AmplitudeConcurrenceEntanglement EntropyTangle
-0.80.99240.9891 bits0.9849
-0.30.71920.6163 bits0.5172
0.30.71920.6163 bits0.5172
0.80.99240.9891 bits0.9849

What each input means

|00⟩ Amplitude
Amplitude of the |00⟩ component
|11⟩ Amplitude
Amplitude of the |11⟩ component
|01⟩ Amplitude
Amplitude of the |01⟩ component
|10⟩ Amplitude
Amplitude of the |10⟩ component

How this is calculated

Formula

C = 2|a₀₀·a₁₁ - a₀₁·a₁₀|

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    |00⟩ Amplitude = 0.707, |11⟩ Amplitude = 0.707, |01⟩ Amplitude = 0, |10⟩ Amplitude = 0 = 4 input(s) provided
  2. Calculate Concurrence
    Concurrence
    1 = 1
  3. Calculate Entanglement Entropy
    Entanglement Entropy
    1 = 1
  4. Calculate Tangle
    Tangle
    1 = 1
  5. Calculate Entanglement of Formation
    Entanglement of Formation
    1 = 1
  6. Calculate Bell State Fidelity
    Bell State Fidelity
    100 = 100%

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators.

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