object

defmodule Object.QuantumCorrelationEngine do
  @moduledoc """
  Real-time entanglement correlation engine using GenServer.
  
  Manages distributed quantum state synchronization across multiple processes/nodes:
  - Maintains registry of entangled pairs
  - Coordinates instantaneous measurement correlations 
  - Provides WebRTC-style hooks for real-time quantum interactions
  - Implements non-locality protocols for distributed quantum systems
  """

  use GenServer
  require Logger
  
  alias Object.QuantumEntanglement.{EntangledPair}
  alias Object.QuantumMeasurement.{MeasurementResult}
  
  defmodule CorrelationState do
    defstruct [
      :entangled_pairs,      # %{pair_id => EntangledPair}
      :active_sessions,      # %{session_id => %{pid, pairs, measurements}}
      :measurement_history,  # List of all measurements for analysis
      :correlation_stats,    # Real-time correlation statistics
      :subscribers,          # Pids subscribed to correlation events
      :bell_test_sessions    # Active Bell inequality test sessions
    ]
  end

  # Client API

  def start_link(opts \\ []) do
    GenServer.start_link(__MODULE__, opts, name: __MODULE__)
  end

  @doc "Create new entangled pair and register it"
  def create_entangled_pair(type \\ :bell_phi_plus) do
    GenServer.call(__MODULE__, {:create_pair, type})
  end

  @doc "Register a session that will interact with quantum pairs"
  def register_session(session_id, options \\ %{}) do
    GenServer.call(__MODULE__, {:register_session, session_id, options})
  end

  @doc "Subscribe to real-time correlation events"
  def subscribe_correlations(subscriber_pid \\ self()) do
    GenServer.call(__MODULE__, {:subscribe, subscriber_pid})
  end

  @doc "Perform correlated measurement on entangled pair"
  def measure_correlated(pair_id, qubit_index, basis, session_id) do
    GenServer.call(__MODULE__, {:measure_correlated, pair_id, qubit_index, basis, session_id})
  end

  @doc "Get real-time correlation statistics"
  def get_correlation_stats() do
    GenServer.call(__MODULE__, :get_stats)
  end

  @doc "Start Bell inequality test session"
  def start_bell_test(session_id, measurement_count \\ 1000) do
    GenServer.call(__MODULE__, {:start_bell_test, session_id, measurement_count})
  end

  @doc "Get current entanglement registry"
  def list_entangled_pairs() do
    GenServer.call(__MODULE__, :list_pairs)
  end

  # Server Implementation

  @impl true
  def init(_opts) do
    :ets.new(:quantum_correlations, [:named_table, :public, :set])
    
    state = %CorrelationState{
      entangled_pairs: %{},
      active_sessions: %{},
      measurement_history: [],
      correlation_stats: init_correlation_stats(),
      subscribers: MapSet.new(),
      bell_test_sessions: %{}
    }
    
    # Schedule periodic correlation analysis
    schedule_correlation_analysis()
    
    Logger.info("QuantumCorrelationEngine started - ready for entanglement operations")
    {:ok, state}
  end

  @impl true
  def handle_call({:create_pair, type}, _from, state) do
    pair = case type do
      :bell_phi_plus -> EntangledPair.bell_state_phi_plus()
      :bell_phi_minus -> EntangledPair.bell_state_phi_minus()
      :bell_psi_plus -> EntangledPair.bell_state_psi_plus()
      :bell_psi_minus -> EntangledPair.bell_state_psi_minus()
      _ -> EntangledPair.bell_state_phi_plus()
    end
    
    pair_id = pair.entanglement_id
    updated_pairs = Map.put(state.entangled_pairs, pair_id, pair)
    
    # Store in ETS for fast lookup
    :ets.insert(:quantum_correlations, {pair_id, pair})
    
    # Notify subscribers of new entanglement
    broadcast_event({:entanglement_created, pair_id, type}, state.subscribers)
    
    Logger.info("Created entangled pair: #{pair_id} (#{type})")
    
    {:reply, {:ok, pair_id}, %{state | entangled_pairs: updated_pairs}}
  end

  @impl true
  def handle_call({:register_session, session_id, options}, {pid, _}, state) do
    Process.monitor(pid)
    
    session_info = %{
      pid: pid,
      pairs: [],
      measurements: [],
      options: options,
      started_at: DateTime.utc_now()
    }
    
    updated_sessions = Map.put(state.active_sessions, session_id, session_info)
    
    Logger.info("Registered quantum session: #{session_id}")
    {:reply, :ok, %{state | active_sessions: updated_sessions}}
  end

  @impl true 
  def handle_call({:subscribe, subscriber_pid}, _from, state) do
    Process.monitor(subscriber_pid)
    updated_subscribers = MapSet.put(state.subscribers, subscriber_pid)
    
    {:reply, :ok, %{state | subscribers: updated_subscribers}}
  end

  @impl true
  def handle_call({:measure_correlated, pair_id, qubit_index, basis, session_id}, _from, state) do
    case Map.get(state.entangled_pairs, pair_id) do
      nil ->
        {:reply, {:error, :pair_not_found}, state}
        
      pair ->
        case Object.QuantumMeasurement.measure_entangled_pair(pair, qubit_index, basis) do
          {:error, reason} ->
            {:reply, {:error, reason}, state}
            
          {local_result, partner_result, collapsed_pair} ->
            # Update the collapsed pair state
            updated_pairs = Map.put(state.entangled_pairs, pair_id, collapsed_pair)
            :ets.insert(:quantum_correlations, {pair_id, collapsed_pair})
            
            # Record measurements
            measurement_event = %{
              pair_id: pair_id,
              session_id: session_id,
              local_result: local_result,
              partner_result: partner_result,
              timestamp: DateTime.utc_now(),
              correlation_strength: calculate_correlation_strength(local_result, partner_result)
            }
            
            updated_history = [measurement_event | state.measurement_history]
            
            # Update correlation statistics
            updated_stats = update_correlation_stats(state.correlation_stats, measurement_event)
            
            # Update session measurements
            updated_sessions = update_session_measurements(state.active_sessions, session_id, measurement_event)
            
            # Broadcast correlation event to all subscribers
            correlation_data = %{
              pair_id: pair_id,
              local_outcome: local_result.outcome,
              partner_outcome: partner_result.outcome,
              correlation_id: local_result.correlation_id,
              basis: basis,
              timestamp: local_result.timestamp,
              instantaneous: true  # Emphasize non-local correlation
            }
            
            broadcast_event({:quantum_correlation, correlation_data}, state.subscribers)
            
            Logger.info("Quantum measurement correlation: #{pair_id} -> #{local_result.outcome}|#{partner_result.outcome}")
            
            response = %{
              local_result: local_result,
              partner_result: partner_result,
              correlation_data: correlation_data,
              entanglement_entropy: EntangledPair.entanglement_entropy(collapsed_pair)
            }
            
            updated_state = %{state |
              entangled_pairs: updated_pairs,
              measurement_history: updated_history,
              correlation_stats: updated_stats,
              active_sessions: updated_sessions
            }
            
            {:reply, {:ok, response}, updated_state}
        end
    end
  end

  @impl true
  def handle_call(:get_stats, _from, state) do
    current_stats = %{
      total_pairs: map_size(state.entangled_pairs),
      active_sessions: map_size(state.active_sessions),
      total_measurements: length(state.measurement_history),
      correlation_stats: state.correlation_stats,
      bell_test_sessions: map_size(state.bell_test_sessions),
      average_correlation_strength: calculate_average_correlation(state.measurement_history),
      subscribers: MapSet.size(state.subscribers)
    }
    
    {:reply, current_stats, state}
  end

  @impl true
  def handle_call({:start_bell_test, session_id, measurement_count}, _from, state) do
    # Create multiple entangled pairs for Bell inequality testing
    test_pairs = Enum.map(1..div(measurement_count, 4), fn _ ->
      EntangledPair.bell_state_phi_plus()
    end)
    
    pair_ids = Enum.map(test_pairs, & &1.entanglement_id)
    
    # Add pairs to registry
    updated_pairs = Enum.reduce(test_pairs, state.entangled_pairs, fn pair, acc ->
      Map.put(acc, pair.entanglement_id, pair)
    end)
    
    # Create Bell test session
    bell_session = %{
      session_id: session_id,
      pair_ids: pair_ids,
      target_measurements: measurement_count,
      completed_measurements: 0,
      started_at: DateTime.utc_now(),
      measurement_bases: [:z, :x],  # Standard Bell test bases
      results: []
    }
    
    updated_bell_sessions = Map.put(state.bell_test_sessions, session_id, bell_session)
    
    broadcast_event({:bell_test_started, session_id, measurement_count}, state.subscribers)
    
    {:reply, {:ok, pair_ids}, %{state | 
      entangled_pairs: updated_pairs,
      bell_test_sessions: updated_bell_sessions
    }}
  end

  @impl true
  def handle_call(:list_pairs, _from, state) do
    pair_summary = state.entangled_pairs
    |> Enum.map(fn {id, pair} ->
      %{
        id: id,
        type: detect_bell_state_type(pair),
        entropy: EntangledPair.entanglement_entropy(pair),
        measured_qubits: MapSet.to_list(pair.measured_qubits),
        creation_time: pair.creation_time,
        measurement_count: pair.correlation_stats.measurements
      }
    end)
    
    {:reply, pair_summary, state}
  end

  @impl true
  def handle_info(:correlation_analysis, state) do
    # Perform periodic correlation analysis
    if length(state.measurement_history) > 10 do
      analysis = analyze_correlations(state.measurement_history)
      broadcast_event({:correlation_analysis, analysis}, state.subscribers)
    end
    
    schedule_correlation_analysis()
    {:noreply, state}
  end

  @impl true
  def handle_info({:DOWN, _ref, :process, pid, _reason}, state) do
    # Clean up when monitored processes die
    updated_subscribers = MapSet.delete(state.subscribers, pid)
    
    updated_sessions = state.active_sessions
    |> Enum.reject(fn {_id, info} -> info.pid == pid end)
    |> Map.new()
    
    {:noreply, %{state | 
      subscribers: updated_subscribers,
      active_sessions: updated_sessions
    }}
  end

  # Private helper functions

  defp init_correlation_stats() do
    %{
      total_correlations: 0,
      perfect_correlations: 0,
      anti_correlations: 0,
      bell_violations: 0,
      average_correlation_strength: 0.0,
      quantum_advantage_ratio: 0.0
    }
  end

  defp schedule_correlation_analysis() do
    Process.send_after(self(), :correlation_analysis, 5_000)  # Every 5 seconds
  end

  defp broadcast_event(event, subscribers) do
    Enum.each(subscribers, fn pid ->
      send(pid, {:quantum_event, event})
    end)
  end

  defp calculate_correlation_strength(local_result, partner_result) do
    # Convert 0,1 to -1,+1 for correlation calculation
    local_val = if local_result.outcome == 0, do: -1, else: 1
    partner_val = if partner_result.outcome == 0, do: -1, else: 1
    local_val * partner_val
  end

  defp update_correlation_stats(stats, measurement_event) do
    correlation = measurement_event.correlation_strength
    new_total = stats.total_correlations + 1
    
    updated_perfect = if abs(correlation) == 1, do: stats.perfect_correlations + 1, else: stats.perfect_correlations
    updated_anti = if correlation == -1, do: stats.anti_correlations + 1, else: stats.anti_correlations
    
    # Update running average
    current_avg = stats.average_correlation_strength
    new_avg = (current_avg * (new_total - 1) + correlation) / new_total
    
    %{stats |
      total_correlations: new_total,
      perfect_correlations: updated_perfect,
      anti_correlations: updated_anti,
      average_correlation_strength: new_avg
    }
  end

  defp update_session_measurements(sessions, session_id, measurement_event) do
    case Map.get(sessions, session_id) do
      nil -> sessions
      session_info ->
        updated_measurements = [measurement_event | session_info.measurements]
        updated_session = %{session_info | measurements: updated_measurements}
        Map.put(sessions, session_id, updated_session)
    end
  end

  defp calculate_average_correlation(history) when length(history) == 0, do: 0.0
  defp calculate_average_correlation(history) do
    total = Enum.reduce(history, 0.0, fn event, acc -> 
      acc + event.correlation_strength 
    end)
    total / length(history)
  end

  defp analyze_correlations(history) do
    correlations = Enum.map(history, & &1.correlation_strength)
    
    %{
      sample_size: length(correlations),
      mean_correlation: Enum.sum(correlations) / length(correlations),
      perfect_correlations: Enum.count(correlations, &(abs(&1) == 1)),
      correlation_variance: calculate_variance(correlations),
      temporal_patterns: detect_temporal_patterns(history),
      bell_parameter_estimate: estimate_bell_parameter(correlations)
    }
  end

  defp calculate_variance(values) when length(values) < 2, do: 0.0
  defp calculate_variance(values) do
    mean = Enum.sum(values) / length(values)
    sum_squares = Enum.reduce(values, 0, fn x, acc -> acc + :math.pow(x - mean, 2) end)
    sum_squares / (length(values) - 1)
  end

  defp detect_temporal_patterns(history) do
    # Simple pattern detection - could be much more sophisticated
    recent_hour = history
    |> Enum.take(100)  # Last 100 measurements
    |> Enum.map(& &1.correlation_strength)
    
    %{
      recent_trend: if(length(recent_hour) > 10, do: trend_direction(recent_hour), else: :insufficient_data),
      periodicity: detect_periodicity(recent_hour)
    }
  end

  defp trend_direction(values) when length(values) < 5, do: :stable
  defp trend_direction(values) do
    first_half = Enum.take(values, div(length(values), 2))
    second_half = Enum.drop(values, div(length(values), 2))
    
    avg_first = Enum.sum(first_half) / length(first_half)
    avg_second = Enum.sum(second_half) / length(second_half)
    
    cond do
      avg_second > avg_first + 0.1 -> :increasing
      avg_second < avg_first - 0.1 -> :decreasing
      true -> :stable
    end
  end

  defp detect_periodicity(_values) do
    # Placeholder for more sophisticated periodicity detection
    :none_detected
  end

  defp estimate_bell_parameter(correlations) when length(correlations) < 4, do: 0.0
  defp estimate_bell_parameter(correlations) do
    # Simplified Bell parameter estimation
    abs(Enum.sum(correlations) / length(correlations)) * 4
  end

  defp detect_bell_state_type(%EntangledPair{} = pair) do
    # Heuristic to detect Bell state type based on amplitudes
    cond do
      abs(Object.QuantumEntanglement.Complex.magnitude(pair.amplitude_00) - 1/:math.sqrt(2)) < 0.01 and
      abs(Object.QuantumEntanglement.Complex.magnitude(pair.amplitude_11) - 1/:math.sqrt(2)) < 0.01 ->
        if pair.amplitude_11.real > 0, do: :phi_plus, else: :phi_minus
      
      abs(Object.QuantumEntanglement.Complex.magnitude(pair.amplitude_01) - 1/:math.sqrt(2)) < 0.01 and
      abs(Object.QuantumEntanglement.Complex.magnitude(pair.amplitude_10) - 1/:math.sqrt(2)) < 0.01 ->
        if pair.amplitude_10.real > 0, do: :psi_plus, else: :psi_minus
      
      true -> :custom
    end
  end
end