mercurial.branches.decoherence module

Branch decoherence: orthogonality and decoherence rate (Definition 5.1).

class mercurial.branches.decoherence.BranchDecoherenceDynamics(decoherence_measure: DecoherenceMeasure)[source]

Bases: object

Simulates the time evolution of branch state vectors under decoherence.

Methods

`evolve_branch_state`(state, dt[, ...])	Simplified evolution: state loses coherence with environment. d\|ψ>/dt = -γ_env \|ψ> + noise.
`evolve_pair`(state_a, state_b, dt, entropy_a, ...)	Evolve two branch states with mutual decoherence.

evolve_branch_state(state: StateVector, dt: float, environment_noise: float = 0.01) → StateVector[source]: Simplified evolution: state loses coherence with environment. d|ψ>/dt = -γ_env |ψ> + noise

evolve_pair(state_a: StateVector, state_b: StateVector, dt: float, entropy_a: float, entropy_b: float) → Tuple[StateVector, StateVector][source]: Evolve two branch states with mutual decoherence. The decoherence rate between them drives them apart.

class mercurial.branches.decoherence.DecoherenceMeasure(base_rate: float = 0.1, environment_coupling: float = 0.01)[source]

Bases: object

Computes decoherence between branches and the rate of decoherence.

Key concepts: - Orthogonality: |⟨x_a, x_b⟩| ≈ 0 - Decoherence rate: γ_dec = γ_0 * (1 - |⟨x_a, x_b⟩|²)

Methods

`decoherence_rate`(state_a, state_b, ...)	γ_dec = γ_0 * (1 - \|⟨x_a, x_b⟩\|²) * f(S_a, S_b) where f(S) = exp(-(S_a + S_b)/S_crit) – higher entropy increases decoherence.
`decoherence_time`(state_a, state_b, ...)	Characteristic time for decoherence: τ_dec = 1/γ_dec.
`is_decohered`(state_a, state_b[, threshold])	Return True if branches are effectively decohered.
`orthogonality`(state_a, state_b)	Orthogonality measure: 1 - \|⟨x_a, x_b⟩\|.
`overlap`(state_a, state_b)	Compute \|⟨x_a, x_b⟩\|, the absolute value of the inner product.

__init__(base_rate: float = 0.1, environment_coupling: float = 0.01)[source]

Parameters:

base_ratefloat: γ_0 – maximum decoherence rate (per second).
environment_couplingfloat: Coupling to environmental degrees of freedom that drive decoherence.

decoherence_rate(state_a: StateVector, state_b: StateVector, entropy_a: float, entropy_b: float) → float[source]: γ_dec = γ_0 * (1 - |⟨x_a, x_b⟩|²) * f(S_a, S_b) where f(S) = exp(-(S_a + S_b)/S_crit) – higher entropy increases decoherence.

decoherence_time(state_a: StateVector, state_b: StateVector, entropy_a: float, entropy_b: float) → float[source]: Characteristic time for decoherence: τ_dec = 1/γ_dec.

is_decohered(state_a: StateVector, state_b: StateVector, threshold: float = 0.99) → bool[source]: Return True if branches are effectively decohered. threshold = 0.99 means 99% orthogonal.

orthogonality(state_a: StateVector, state_b: StateVector) → float[source]: Orthogonality measure: 1 - |⟨x_a, x_b⟩|. Fully orthogonal = 1, identical = 0.

overlap(state_a: StateVector, state_b: StateVector) → float[source]: Compute |⟨x_a, x_b⟩|, the absolute value of the inner product.