defmodule Object.QuantumEntanglement do
  @moduledoc """
  Real-time quantum entanglement simulation with WebRTC-style hooks for Elixir/OTP.
  
  This module provides a complete quantum mechanical simulation framework with:
  - Complex number support for quantum amplitudes
  - Bell state generation and entanglement correlation
  - Real-time measurement synchronization across distributed systems
  - Phoenix LiveView integration for interactive quantum visualization
  
  Based on quantum mechanical principles:
  - Quantum superposition: |ψ⟩ = α|0⟩ + β|1⟩ where |α|² + |β|² = 1
  - Entanglement: |Ψ⟩ = (1/√2)(|00⟩ + |11⟩) - inseparable quantum correlations
  - Measurement collapse: probabilistic projection onto measurement basis
  - No-communication theorem: entanglement cannot transmit information faster than light
  """

  defmodule Complex do
    @moduledoc "Complex number representation for quantum amplitudes"
    
    defstruct real: 0.0, imag: 0.0
    
    @type t :: %__MODULE__{real: float(), imag: float()}
    
    def new(real, imag \\ 0.0) do
      %__MODULE__{real: real, imag: imag}
    end
    
    def magnitude(%__MODULE__{real: r, imag: i}) do
      :math.sqrt(r * r + i * i)
    end
    
    def phase(%__MODULE__{real: r, imag: i}) do
      :math.atan2(i, r)
    end
    
    def conjugate(%__MODULE__{real: r, imag: i}) do
      %__MODULE__{real: r, imag: -i}
    end
    
    def add(%__MODULE__{real: r1, imag: i1}, %__MODULE__{real: r2, imag: i2}) do
      %__MODULE__{real: r1 + r2, imag: i1 + i2}
    end
    
    def multiply(%__MODULE__{real: r1, imag: i1}, %__MODULE__{real: r2, imag: i2}) do
      %__MODULE__{
        real: r1 * r2 - i1 * i2,
        imag: r1 * i2 + i1 * r2
      }
    end
    
    def scale(%__MODULE__{real: r, imag: i}, factor) do
      %__MODULE__{real: r * factor, imag: i * factor}
    end
  end

  defmodule QubitState do
    @moduledoc "Single qubit quantum state representation"
    
    defstruct amplitude_0: nil, amplitude_1: nil, measured: false, measurement_result: nil
    
    @type t :: %__MODULE__{
      amplitude_0: Complex.t(),
      amplitude_1: Complex.t(),
      measured: boolean(),
      measurement_result: 0 | 1 | nil
    }
    
    def new(amp_0 \\ Complex.new(1.0), amp_1 \\ Complex.new(0.0)) do
      # Normalize amplitudes to ensure |α|² + |β|² = 1
      norm = :math.sqrt(
        Complex.magnitude(amp_0) * Complex.magnitude(amp_0) +
        Complex.magnitude(amp_1) * Complex.magnitude(amp_1)
      )
      
      %__MODULE__{
        amplitude_0: Complex.scale(amp_0, 1.0 / norm),
        amplitude_1: Complex.scale(amp_1, 1.0 / norm),
        measured: false,
        measurement_result: nil
      }
    end
    
    def probability_0(%__MODULE__{amplitude_0: amp_0}) do
      Complex.magnitude(amp_0) |> then(&(&1 * &1))
    end
    
    def probability_1(%__MODULE__{amplitude_1: amp_1}) do
      Complex.magnitude(amp_1) |> then(&(&1 * &1))
    end
    
    def is_superposition(%__MODULE__{amplitude_0: amp_0, amplitude_1: amp_1}) do
      p0 = Complex.magnitude(amp_0) |> then(&(&1 * &1))
      p1 = Complex.magnitude(amp_1) |> then(&(&1 * &1))
      p0 > 0.001 and p1 > 0.001
    end
  end

  defmodule EntangledPair do
    @moduledoc "Two-qubit entangled quantum state"
    
    defstruct [
      :amplitude_00, :amplitude_01, :amplitude_10, :amplitude_11,
      :entanglement_id, :creation_time, :measured_qubits, :correlation_stats
    ]
    
    @type t :: %__MODULE__{
      amplitude_00: Complex.t(),
      amplitude_01: Complex.t(), 
      amplitude_10: Complex.t(),
      amplitude_11: Complex.t(),
      entanglement_id: String.t(),
      creation_time: DateTime.t(),
      measured_qubits: MapSet.t(),
      correlation_stats: map()
    }
    
    # Helper function to generate unique IDs
    defp generate_id do
      :crypto.strong_rand_bytes(16) |> Base.encode16(case: :lower)
    end
    
    def bell_state_phi_plus() do
      # |Φ⁺⟩ = (1/√2)(|00⟩ + |11⟩) - Maximum entanglement
      inv_sqrt2 = 1.0 / :math.sqrt(2)
      
      %__MODULE__{
        amplitude_00: Complex.new(inv_sqrt2),
        amplitude_01: Complex.new(0.0),
        amplitude_10: Complex.new(0.0),
        amplitude_11: Complex.new(inv_sqrt2),
        entanglement_id: generate_id(),
        creation_time: DateTime.utc_now(),
        measured_qubits: MapSet.new(),
        correlation_stats: %{measurements: 0, correlations: []}
      }
    end
    
    def bell_state_phi_minus() do
      # |Φ⁻⟩ = (1/√2)(|00⟩ - |11⟩)
      inv_sqrt2 = 1.0 / :math.sqrt(2)
      
      %__MODULE__{
        amplitude_00: Complex.new(inv_sqrt2),
        amplitude_01: Complex.new(0.0),
        amplitude_10: Complex.new(0.0),
        amplitude_11: Complex.new(-inv_sqrt2),
        entanglement_id: generate_id(),
        creation_time: DateTime.utc_now(),
        measured_qubits: MapSet.new(),
        correlation_stats: %{measurements: 0, correlations: []}
      }
    end
    
    def bell_state_psi_plus() do
      # |Ψ⁺⟩ = (1/√2)(|01⟩ + |10⟩)
      inv_sqrt2 = 1.0 / :math.sqrt(2)
      
      %__MODULE__{
        amplitude_00: Complex.new(0.0),
        amplitude_01: Complex.new(inv_sqrt2),
        amplitude_10: Complex.new(inv_sqrt2),
        amplitude_11: Complex.new(0.0),
        entanglement_id: generate_id(),
        creation_time: DateTime.utc_now(),
        measured_qubits: MapSet.new(),
        correlation_stats: %{measurements: 0, correlations: []}
      }
    end
    
    def bell_state_psi_minus() do
      # |Ψ⁻⟩ = (1/√2)(|01⟩ - |10⟩)
      inv_sqrt2 = 1.0 / :math.sqrt(2)
      
      %__MODULE__{
        amplitude_00: Complex.new(0.0),
        amplitude_01: Complex.new(inv_sqrt2),
        amplitude_10: Complex.new(-inv_sqrt2),
        amplitude_11: Complex.new(0.0),
        entanglement_id: generate_id(),
        creation_time: DateTime.utc_now(),
        measured_qubits: MapSet.new(),
        correlation_stats: %{measurements: 0, correlations: []}
      }
    end
    
    def entanglement_entropy(%__MODULE__{} = pair) do
      # Von Neumann entropy: S = -Tr(ρ log ρ) for reduced density matrix
      # For Bell states, entropy = 1 (maximum entanglement)
      # For product states, entropy = 0 (no entanglement)
      
      probs = [
        probability_00(pair),
        probability_01(pair),
        probability_10(pair),
        probability_11(pair)
      ]
      
      -Enum.reduce(probs, 0, fn p, acc ->
        if p > 1.0e-12 do
          acc + p * :math.log2(p)
        else
          acc
        end
      end)
    end
    
    def probability_00(%__MODULE__{amplitude_00: amp}) do
      Complex.magnitude(amp) |> then(&(&1 * &1))
    end
    
    def probability_01(%__MODULE__{amplitude_01: amp}) do
      Complex.magnitude(amp) |> then(&(&1 * &1))
    end
    
    def probability_10(%__MODULE__{amplitude_10: amp}) do
      Complex.magnitude(amp) |> then(&(&1 * &1))
    end
    
    def probability_11(%__MODULE__{amplitude_11: amp}) do
      Complex.magnitude(amp) |> then(&(&1 * &1))
    end
    
    defp generate_id do
      :crypto.strong_rand_bytes(8) |> Base.encode16() |> String.downcase()
    end
  end
end