"""
Entanglement Analysis Tools for PsiAnimator-MCP
Implements the calculate_entanglement MCP tool for computing various entanglement measures
and visualizing quantum correlations in multi-particle systems.
"""
import asyncio
import json
import logging
from typing import Dict, List, Optional, Union, Any, Tuple
import numpy as np
import qutip as qt
from ..quantum.state_manager import QuantumStateManager
from ..quantum.validation import validate_quantum_state
from ..server.config import MCPConfig
from ..server.exceptions import (
QuantumMeasurementError,
ValidationError,
QuantumStateError,
DimensionError
)
from .quantum_state_tools import get_state_manager
logger = logging.getLogger(__name__)
async def calculate_entanglement(arguments: Dict[str, Any], config: MCPConfig) -> Dict[str, Any]:
"""
Calculate various entanglement measures for quantum states.
Parameters
----------
arguments : dict
Tool arguments containing:
- state_id: str - ID of the quantum state to analyze
- measure_type: str - Type of entanglement measure
- subsystem_partition: list - How to partition the system
- visualize_correlations: bool - Whether to generate correlation visualization
- detect_entanglement: bool - Whether to perform entanglement detection
- witnesses: list - Entanglement witnesses to evaluate
config : MCPConfig
Server configuration
Returns
-------
dict
Entanglement analysis results with measures and correlations
"""
try:
logger.info(f"Calculating entanglement with arguments: {arguments}")
# Validate required arguments
required_args = ['state_id', 'measure_type']
for arg in required_args:
if arg not in arguments:
raise ValidationError(f"{arg} is required", field=arg)
state_id = arguments['state_id']
measure_type = arguments['measure_type']
subsystem_partition = arguments.get('subsystem_partition', None)
visualize_correlations = arguments.get('visualize_correlations', False)
detect_entanglement = arguments.get('detect_entanglement', True)
witnesses = arguments.get('witnesses', [])
# Validate measure type
valid_measures = ['von_neumann', 'linear_entropy', 'concurrence', 'negativity', 'mutual_information']
if measure_type not in valid_measures:
raise ValidationError(
f"Invalid measure_type: {measure_type}",
field="measure_type",
expected_type=f"one of: {', '.join(valid_measures)}"
)
# Get quantum state
state_manager = get_state_manager(config)
if state_id not in state_manager.list_states():
raise QuantumStateError(f"State with ID '{state_id}' not found")
quantum_state = state_manager.get_state(state_id)
quantum_state = validate_quantum_state(quantum_state)
# Convert to density matrix if needed
if quantum_state.type == 'ket':
rho = quantum_state * quantum_state.dag()
else:
rho = quantum_state
# Determine system structure
system_info = analyze_system_structure(rho, subsystem_partition)
# Calculate requested entanglement measure
if measure_type == 'von_neumann':
result = await calculate_von_neumann_entropy(rho, system_info)
elif measure_type == 'linear_entropy':
result = await calculate_linear_entropy(rho, system_info)
elif measure_type == 'concurrence':
result = await calculate_concurrence(rho, system_info)
elif measure_type == 'negativity':
result = await calculate_negativity(rho, system_info)
elif measure_type == 'mutual_information':
result = await calculate_mutual_information(rho, system_info)
# Perform entanglement detection if requested
if detect_entanglement:
detection_results = await perform_entanglement_detection(rho, system_info)
result['entanglement_detection'] = detection_results
# Evaluate entanglement witnesses if provided
if witnesses:
witness_results = await evaluate_entanglement_witnesses(rho, witnesses)
result['witness_evaluation'] = witness_results
# Generate correlation analysis
correlation_analysis = await analyze_quantum_correlations(rho, system_info)
result['correlation_analysis'] = correlation_analysis
# Visualization data if requested
if visualize_correlations:
visualization_data = generate_correlation_visualization_data(rho, system_info, result)
result['visualization_data'] = visualization_data
# Prepare final result
entanglement_result = {
'success': True,
'state_id': state_id,
'measure_type': measure_type,
'system_info': system_info,
'entanglement_analysis': result,
'quantum_state_properties': {
'type': quantum_state.type,
'dimensions': quantum_state.dims,
'hilbert_space_dim': quantum_state.shape[0],
'is_pure': quantum_state.type == 'ket' or abs((rho * rho).tr() - 1.0) < 1e-10
},
'message': f"Successfully calculated {measure_type} entanglement measure for state {state_id}"
}
logger.info(f"Successfully calculated entanglement for state {state_id}")
return entanglement_result
except (ValidationError, QuantumMeasurementError, QuantumStateError, DimensionError) as e:
logger.error(f"Entanglement calculation failed: {e}")
return {
'success': False,
'error': e.__class__.__name__,
'message': str(e),
'details': e.details if hasattr(e, 'details') else {}
}
except Exception as e:
logger.error(f"Unexpected error in calculate_entanglement: {e}")
return {
'success': False,
'error': 'UnexpectedError',
'message': f"An unexpected error occurred: {str(e)}",
'details': {}
}
def analyze_system_structure(rho: qt.Qobj, subsystem_partition: Optional[List[List[int]]]) -> Dict[str, Any]:
"""
Analyze the structure of the quantum system.
Parameters
----------
rho : qt.Qobj
Density matrix of the system
subsystem_partition : list of list of int, optional
How to partition the system into subsystems
Returns
-------
dict
System structure information
"""
try:
total_dim = rho.shape[0]
# Try to determine if this is a multi-qubit system
if total_dim > 1 and (total_dim & (total_dim - 1)) == 0: # Power of 2
n_qubits = int(np.log2(total_dim))
is_qubit_system = True
subsystem_dims = [2] * n_qubits
else:
# General multi-level system
is_qubit_system = False
n_qubits = 0
# Try to factorize dimension
subsystem_dims = factorize_dimension(total_dim)
# Use provided partition or default bipartition
if subsystem_partition is None:
if is_qubit_system and n_qubits >= 2:
# Default: split in half
partition_a = list(range(n_qubits // 2))
partition_b = list(range(n_qubits // 2, n_qubits))
subsystem_partition = [partition_a, partition_b]
elif len(subsystem_dims) >= 2:
# For general systems, partition by subsystem index
partition_a = [0]
partition_b = list(range(1, len(subsystem_dims)))
subsystem_partition = [partition_a, partition_b]
else:
# Single subsystem - no entanglement possible
subsystem_partition = [[0]]
return {
'total_dimension': total_dim,
'is_qubit_system': is_qubit_system,
'n_qubits': n_qubits,
'subsystem_dimensions': subsystem_dims,
'subsystem_partition': subsystem_partition,
'n_partitions': len(subsystem_partition),
'is_bipartite': len(subsystem_partition) == 2
}
except Exception as e:
logger.warning(f"System structure analysis failed: {e}")
return {
'total_dimension': rho.shape[0],
'is_qubit_system': False,
'n_qubits': 0,
'subsystem_dimensions': [rho.shape[0]],
'subsystem_partition': [[0]],
'n_partitions': 1,
'is_bipartite': False,
'error': str(e)
}
def factorize_dimension(dim: int) -> List[int]:
"""
Factorize Hilbert space dimension into subsystem dimensions.
Parameters
----------
dim : int
Total Hilbert space dimension
Returns
-------
list of int
List of subsystem dimensions
"""
factors = []
d = dim
# Try small primes first
for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]:
while d % p == 0:
factors.append(p)
d = d // p
if d == 1:
break
# If not fully factorized, add remaining factor
if d > 1:
factors.append(d)
return factors if factors else [dim]
async def calculate_von_neumann_entropy(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Calculate von Neumann entropy for entanglement quantification.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Von Neumann entropy results
"""
try:
results = {
'measure_type': 'von_neumann',
'entanglement_values': {},
'subsystem_entropies': {},
'interpretation': {}
}
if not system_info['is_bipartite'] or len(system_info['subsystem_partition']) < 2:
return {
'measure_type': 'von_neumann',
'error': 'Von Neumann entropy requires bipartite system',
'entanglement_values': {},
'subsystem_entropies': {}
}
partition = system_info['subsystem_partition']
# Calculate reduced density matrices and their entropies
for i, subsystem in enumerate(partition):
try:
rho_reduced = rho.ptrace(subsystem)
eigenvals = rho_reduced.eigenenergies()
# Calculate von Neumann entropy
entropy = -np.sum(eigenvals * np.log2(eigenvals + 1e-16))
results['subsystem_entropies'][f'subsystem_{i}'] = {
'entropy': float(np.real(entropy)),
'eigenvalues': [float(np.real(val)) for val in eigenvals],
'subsystem_indices': subsystem,
'reduced_dimension': rho_reduced.shape[0]
}
except Exception as e:
logger.warning(f"Could not calculate entropy for subsystem {i}: {e}")
results['subsystem_entropies'][f'subsystem_{i}'] = {'error': str(e)}
# For bipartite systems, entanglement entropy is the entropy of either subsystem
if len(results['subsystem_entropies']) >= 2:
entropies = [info.get('entropy', 0) for info in results['subsystem_entropies'].values()
if 'entropy' in info]
if entropies:
entanglement_entropy = entropies[0] # Should be same for both subsystems in pure states
results['entanglement_values']['entanglement_entropy'] = entanglement_entropy
# Interpretation
if entanglement_entropy < 0.01:
interpretation = "Separable (no entanglement)"
elif entanglement_entropy < 1.0:
interpretation = "Weakly entangled"
elif entanglement_entropy < 2.0:
interpretation = "Moderately entangled"
else:
interpretation = "Highly entangled"
results['interpretation']['entanglement_level'] = interpretation
results['interpretation']['max_possible_entropy'] = np.log2(min(
results['subsystem_entropies']['subsystem_0'].get('reduced_dimension', 1),
results['subsystem_entropies']['subsystem_1'].get('reduced_dimension', 1)
))
return results
except Exception as e:
raise QuantumMeasurementError(
f"Failed to calculate von Neumann entropy: {str(e)}",
measurement_type="von_neumann"
)
async def calculate_linear_entropy(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Calculate linear entropy (1 - Tr(ρ²)) for entanglement quantification.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Linear entropy results
"""
try:
results = {
'measure_type': 'linear_entropy',
'entanglement_values': {},
'subsystem_entropies': {},
'interpretation': {}
}
if not system_info['is_bipartite'] or len(system_info['subsystem_partition']) < 2:
# Calculate global linear entropy
purity = np.real((rho * rho).tr())
linear_entropy = 1 - purity
results['entanglement_values']['global_linear_entropy'] = float(linear_entropy)
results['interpretation']['purity'] = float(purity)
return results
partition = system_info['subsystem_partition']
# Calculate linear entropy for each subsystem
for i, subsystem in enumerate(partition):
try:
rho_reduced = rho.ptrace(subsystem)
purity = np.real((rho_reduced * rho_reduced).tr())
linear_entropy = 1 - purity
results['subsystem_entropies'][f'subsystem_{i}'] = {
'linear_entropy': float(linear_entropy),
'purity': float(purity),
'subsystem_indices': subsystem,
'reduced_dimension': rho_reduced.shape[0]
}
except Exception as e:
logger.warning(f"Could not calculate linear entropy for subsystem {i}: {e}")
results['subsystem_entropies'][f'subsystem_{i}'] = {'error': str(e)}
# Entanglement measure based on average subsystem linear entropy
if len(results['subsystem_entropies']) >= 2:
linear_entropies = [info.get('linear_entropy', 0) for info in results['subsystem_entropies'].values()
if 'linear_entropy' in info]
if linear_entropies:
avg_linear_entropy = np.mean(linear_entropies)
results['entanglement_values']['average_subsystem_linear_entropy'] = float(avg_linear_entropy)
# Interpretation
if avg_linear_entropy < 0.01:
interpretation = "Separable (no entanglement)"
elif avg_linear_entropy < 0.3:
interpretation = "Weakly entangled"
elif avg_linear_entropy < 0.7:
interpretation = "Moderately entangled"
else:
interpretation = "Highly entangled"
results['interpretation']['entanglement_level'] = interpretation
return results
except Exception as e:
raise QuantumMeasurementError(
f"Failed to calculate linear entropy: {str(e)}",
measurement_type="linear_entropy"
)
async def calculate_concurrence(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Calculate concurrence for two-qubit entanglement quantification.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Concurrence results
"""
try:
results = {
'measure_type': 'concurrence',
'entanglement_values': {},
'interpretation': {}
}
# Concurrence is defined for two-qubit systems
if not (system_info['is_qubit_system'] and system_info['n_qubits'] == 2):
return {
'measure_type': 'concurrence',
'error': 'Concurrence is only defined for two-qubit systems',
'entanglement_values': {}
}
# Calculate concurrence using Wootters formula
# C(ρ) = max(0, λ₁ - λ₂ - λ₃ - λ₄)
# where λᵢ are square roots of eigenvalues of ρ * ρ̃ in decreasing order
# ρ̃ = (σy ⊗ σy) ρ* (σy ⊗ σy)
sigma_y = qt.sigmay()
flip_op = qt.tensor(sigma_y, sigma_y)
# Complex conjugate of density matrix
rho_conj = qt.Qobj(np.conj(rho.full()))
# Flipped density matrix
rho_tilde = flip_op * rho_conj * flip_op
# Calculate eigenvalues of ρ * ρ̃
R = rho * rho_tilde
eigenvals = R.eigenenergies()
# Take square roots and sort in decreasing order
sqrt_eigenvals = np.sqrt(np.maximum(0, np.real(eigenvals)))
sqrt_eigenvals = np.sort(sqrt_eigenvals)[::-1]
# Calculate concurrence
if len(sqrt_eigenvals) >= 4:
concurrence = max(0, sqrt_eigenvals[0] - sqrt_eigenvals[1] - sqrt_eigenvals[2] - sqrt_eigenvals[3])
else:
concurrence = 0
results['entanglement_values']['concurrence'] = float(concurrence)
results['entanglement_values']['sqrt_eigenvalues'] = [float(val) for val in sqrt_eigenvals]
# Calculate entanglement of formation from concurrence
if concurrence > 0:
x = (1 + np.sqrt(1 - concurrence**2)) / 2
if x > 0:
entanglement_of_formation = -x * np.log2(x) - (1-x) * np.log2(1-x + 1e-16)
else:
entanglement_of_formation = 0
else:
entanglement_of_formation = 0
results['entanglement_values']['entanglement_of_formation'] = float(entanglement_of_formation)
# Interpretation
if concurrence < 0.01:
interpretation = "Separable (no entanglement)"
elif concurrence < 0.3:
interpretation = "Weakly entangled"
elif concurrence < 0.7:
interpretation = "Moderately entangled"
else:
interpretation = "Highly entangled"
results['interpretation']['entanglement_level'] = interpretation
results['interpretation']['max_concurrence'] = 1.0
return results
except Exception as e:
raise QuantumMeasurementError(
f"Failed to calculate concurrence: {str(e)}",
measurement_type="concurrence"
)
async def calculate_negativity(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Calculate negativity for entanglement quantification.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Negativity results
"""
try:
results = {
'measure_type': 'negativity',
'entanglement_values': {},
'interpretation': {}
}
if not system_info['is_bipartite'] or len(system_info['subsystem_partition']) < 2:
return {
'measure_type': 'negativity',
'error': 'Negativity requires bipartite system',
'entanglement_values': {}
}
partition = system_info['subsystem_partition']
# Calculate partial transpose and its eigenvalues
# For simplicity, assume we're doing partial transpose with respect to first subsystem
try:
rho_pt = rho.ptrace(partition[0]).dag() * rho.ptrace(partition[1]) # Simplified - needs proper partial transpose
# Actual partial transpose calculation for qubits
if system_info['is_qubit_system']:
# For 2-qubit system, partial transpose is straightforward
if system_info['n_qubits'] == 2:
rho_matrix = rho.full()
# Partial transpose with respect to second qubit
rho_pt_matrix = np.array([
[rho_matrix[0,0], rho_matrix[0,2], rho_matrix[2,0], rho_matrix[2,2]],
[rho_matrix[0,1], rho_matrix[0,3], rho_matrix[2,1], rho_matrix[2,3]],
[rho_matrix[1,0], rho_matrix[1,2], rho_matrix[3,0], rho_matrix[3,2]],
[rho_matrix[1,1], rho_matrix[1,3], rho_matrix[3,1], rho_matrix[3,3]]
])
rho_pt = qt.Qobj(rho_pt_matrix)
eigenvals = rho_pt.eigenenergies()
# Negativity is sum of absolute values of negative eigenvalues
negative_eigenvals = eigenvals[eigenvals < 0]
negativity = np.sum(np.abs(negative_eigenvals))
# Logarithmic negativity
log_negativity = np.log2(2 * negativity + 1) if negativity > 0 else 0
results['entanglement_values']['negativity'] = float(negativity)
results['entanglement_values']['logarithmic_negativity'] = float(log_negativity)
results['entanglement_values']['eigenvalues_pt'] = [float(np.real(val)) for val in eigenvals]
results['entanglement_values']['negative_eigenvalues'] = [float(val) for val in negative_eigenvals]
# Interpretation
if negativity < 0.01:
interpretation = "Separable (no entanglement)"
elif negativity < 0.1:
interpretation = "Weakly entangled"
elif negativity < 0.3:
interpretation = "Moderately entangled"
else:
interpretation = "Highly entangled"
results['interpretation']['entanglement_level'] = interpretation
results['interpretation']['ppt_criterion'] = negativity > 0.01 # PPT = Positive Partial Transpose
else:
results['error'] = f"Partial transpose not implemented for {system_info['n_qubits']}-qubit systems"
else:
results['error'] = "Partial transpose not implemented for general multi-level systems"
except Exception as e:
results['error'] = f"Partial transpose calculation failed: {str(e)}"
return results
except Exception as e:
raise QuantumMeasurementError(
f"Failed to calculate negativity: {str(e)}",
measurement_type="negativity"
)
async def calculate_mutual_information(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Calculate quantum mutual information.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Mutual information results
"""
try:
results = {
'measure_type': 'mutual_information',
'entanglement_values': {},
'subsystem_entropies': {},
'interpretation': {}
}
if not system_info['is_bipartite'] or len(system_info['subsystem_partition']) < 2:
return {
'measure_type': 'mutual_information',
'error': 'Mutual information requires bipartite system',
'entanglement_values': {}
}
partition = system_info['subsystem_partition']
# Calculate entropies: S(A), S(B), S(AB)
# Mutual information I(A:B) = S(A) + S(B) - S(AB)
# Total system entropy
eigenvals_total = rho.eigenenergies()
S_total = -np.sum(eigenvals_total * np.log2(eigenvals_total + 1e-16))
subsystem_entropies = []
# Calculate subsystem entropies
for i, subsystem in enumerate(partition):
try:
rho_reduced = rho.ptrace(subsystem)
eigenvals = rho_reduced.eigenenergies()
entropy = -np.sum(eigenvals * np.log2(eigenvals + 1e-16))
subsystem_entropies.append(entropy)
results['subsystem_entropies'][f'subsystem_{i}'] = {
'entropy': float(np.real(entropy)),
'eigenvalues': [float(np.real(val)) for val in eigenvals],
'subsystem_indices': subsystem
}
except Exception as e:
logger.warning(f"Could not calculate entropy for subsystem {i}: {e}")
subsystem_entropies.append(0)
results['subsystem_entropies'][f'subsystem_{i}'] = {'error': str(e)}
# Calculate mutual information
if len(subsystem_entropies) >= 2:
S_A, S_B = subsystem_entropies[0], subsystem_entropies[1]
mutual_information = S_A + S_B - S_total
results['entanglement_values']['mutual_information'] = float(np.real(mutual_information))
results['entanglement_values']['total_entropy'] = float(np.real(S_total))
results['entanglement_values']['subsystem_A_entropy'] = float(np.real(S_A))
results['entanglement_values']['subsystem_B_entropy'] = float(np.real(S_B))
# Interpretation
if mutual_information < 0.01:
interpretation = "No quantum correlations"
elif mutual_information < 0.5:
interpretation = "Weak quantum correlations"
elif mutual_information < 1.5:
interpretation = "Moderate quantum correlations"
else:
interpretation = "Strong quantum correlations"
results['interpretation']['correlation_level'] = interpretation
results['interpretation']['max_possible_mutual_information'] = float(np.real(min(S_A, S_B)))
return results
except Exception as e:
raise QuantumMeasurementError(
f"Failed to calculate mutual information: {str(e)}",
measurement_type="mutual_information"
)
async def perform_entanglement_detection(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Perform various entanglement detection tests.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Entanglement detection results
"""
try:
detection_results = {
'tests_performed': [],
'entanglement_detected': False,
'separability_tests': {}
}
# PPT (Positive Partial Transpose) test for 2-qubit systems
if system_info['is_qubit_system'] and system_info['n_qubits'] == 2:
try:
# Simple PPT test
rho_matrix = rho.full()
rho_pt_matrix = np.array([
[rho_matrix[0,0], rho_matrix[0,2], rho_matrix[2,0], rho_matrix[2,2]],
[rho_matrix[0,1], rho_matrix[0,3], rho_matrix[2,1], rho_matrix[2,3]],
[rho_matrix[1,0], rho_matrix[1,2], rho_matrix[3,0], rho_matrix[3,2]],
[rho_matrix[1,1], rho_matrix[1,3], rho_matrix[3,1], rho_matrix[3,3]]
])
eigenvals_pt = np.linalg.eigvals(rho_pt_matrix)
has_negative_eigenvals = np.any(np.real(eigenvals_pt) < -1e-10)
detection_results['separability_tests']['ppt_test'] = {
'test_name': 'Positive Partial Transpose',
'entanglement_detected': has_negative_eigenvals,
'min_eigenvalue': float(np.min(np.real(eigenvals_pt))),
'interpretation': 'Entangled' if has_negative_eigenvals else 'PPT (possibly separable)'
}
detection_results['tests_performed'].append('ppt_test')
if has_negative_eigenvals:
detection_results['entanglement_detected'] = True
except Exception as e:
detection_results['separability_tests']['ppt_test'] = {'error': str(e)}
# Realignment criterion (for comparison)
try:
# Simplified realignment test
# This would require more sophisticated implementation for full accuracy
purity = np.real((rho * rho).tr())
detection_results['separability_tests']['purity_test'] = {
'test_name': 'Purity Check',
'purity': float(purity),
'interpretation': 'Pure state' if purity > 0.99 else 'Mixed state'
}
detection_results['tests_performed'].append('purity_test')
except Exception as e:
detection_results['separability_tests']['purity_test'] = {'error': str(e)}
# Schmidt decomposition for pure states
if abs((rho * rho).tr() - 1.0) < 1e-10: # Pure state
try:
# For pure bipartite states, entanglement can be detected via Schmidt rank
if system_info['is_bipartite'] and len(system_info['subsystem_partition']) == 2:
partition_a = system_info['subsystem_partition'][0]
rho_a = rho.ptrace(partition_a)
eigenvals_a = rho_a.eigenenergies()
# Schmidt rank is number of non-zero eigenvalues
schmidt_rank = np.sum(eigenvals_a > 1e-10)
detection_results['separability_tests']['schmidt_decomposition'] = {
'test_name': 'Schmidt Decomposition',
'schmidt_rank': int(schmidt_rank),
'entanglement_detected': schmidt_rank > 1,
'interpretation': 'Entangled' if schmidt_rank > 1 else 'Separable (product state)'
}
detection_results['tests_performed'].append('schmidt_decomposition')
if schmidt_rank > 1:
detection_results['entanglement_detected'] = True
except Exception as e:
detection_results['separability_tests']['schmidt_decomposition'] = {'error': str(e)}
return detection_results
except Exception as e:
logger.warning(f"Entanglement detection failed: {e}")
return {'error': str(e)}
async def evaluate_entanglement_witnesses(rho: qt.Qobj, witnesses: List[Dict[str, Any]]) -> Dict[str, Any]:
"""
Evaluate entanglement witnesses on the quantum state.
Parameters
----------
rho : qt.Qobj
Density matrix
witnesses : list
List of witness specifications
Returns
-------
dict
Witness evaluation results
"""
try:
witness_results = {
'witnesses_evaluated': [],
'entanglement_detected': False,
'witness_values': {}
}
for i, witness_spec in enumerate(witnesses):
try:
witness_name = witness_spec.get('name', f'witness_{i}')
witness_matrix = witness_spec.get('matrix', None)
if witness_matrix is None:
witness_results['witness_values'][witness_name] = {
'error': 'No witness matrix provided'
}
continue
# Create witness operator
W = qt.Qobj(np.array(witness_matrix, dtype=complex))
# Calculate expectation value
witness_value = np.real((W * rho).tr())
# Witness detects entanglement if expectation value is negative
entanglement_detected = witness_value < 0
witness_results['witness_values'][witness_name] = {
'expectation_value': float(witness_value),
'entanglement_detected': entanglement_detected,
'interpretation': 'Entangled' if entanglement_detected else 'Witness inconclusive'
}
witness_results['witnesses_evaluated'].append(witness_name)
if entanglement_detected:
witness_results['entanglement_detected'] = True
except Exception as e:
witness_results['witness_values'][f'witness_{i}'] = {'error': str(e)}
return witness_results
except Exception as e:
logger.warning(f"Witness evaluation failed: {e}")
return {'error': str(e)}
async def analyze_quantum_correlations(rho: qt.Qobj, system_info: Dict[str, Any]) -> Dict[str, Any]:
"""
Analyze various types of quantum correlations.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
Returns
-------
dict
Correlation analysis results
"""
try:
correlation_analysis = {
'correlation_types': {},
'classical_correlations': {},
'quantum_correlations': {}
}
if system_info['is_bipartite'] and len(system_info['subsystem_partition']) == 2:
# For bipartite systems, analyze different correlation measures
# Total correlations (mutual information)
partition = system_info['subsystem_partition']
# Calculate subsystem entropies
S_A = 0
S_B = 0
try:
rho_A = rho.ptrace(partition[0])
eigenvals_A = rho_A.eigenenergies()
S_A = -np.sum(eigenvals_A * np.log2(eigenvals_A + 1e-16))
rho_B = rho.ptrace(partition[1])
eigenvals_B = rho_B.eigenenergies()
S_B = -np.sum(eigenvals_B * np.log2(eigenvals_B + 1e-16))
# Total system entropy
eigenvals_total = rho.eigenenergies()
S_total = -np.sum(eigenvals_total * np.log2(eigenvals_total + 1e-16))
# Total correlations (mutual information)
total_correlations = S_A + S_B - S_total
correlation_analysis['correlation_types']['total_correlations'] = {
'mutual_information': float(np.real(total_correlations)),
'interpretation': 'Measures all correlations (classical + quantum)'
}
# Quantum discord (simplified estimation)
# This is a simplified calculation - full quantum discord requires optimization
discord_estimate = S_A - S_total # Simplified approximation
correlation_analysis['quantum_correlations']['discord_estimate'] = {
'value': float(np.real(discord_estimate)),
'interpretation': 'Approximate quantum discord (requires optimization for exact value)'
}
except Exception as e:
correlation_analysis['error'] = f"Correlation calculation failed: {str(e)}"
return correlation_analysis
except Exception as e:
logger.warning(f"Correlation analysis failed: {e}")
return {'error': str(e)}
def generate_correlation_visualization_data(rho: qt.Qobj, system_info: Dict[str, Any],
results: Dict[str, Any]) -> Dict[str, Any]:
"""
Generate data for correlation visualization.
Parameters
----------
rho : qt.Qobj
Density matrix
system_info : dict
System structure information
results : dict
Entanglement analysis results
Returns
-------
dict
Visualization data
"""
try:
viz_data = {
'visualization_type': 'correlation_matrix',
'data': {}
}
if system_info['is_qubit_system'] and system_info['n_qubits'] <= 3:
# For small qubit systems, create correlation matrix visualization
# Calculate Pauli correlation matrix
pauli_ops = [qt.qeye(2), qt.sigmax(), qt.sigmay(), qt.sigmaz()]
pauli_names = ['I', 'X', 'Y', 'Z']
n_qubits = system_info['n_qubits']
if n_qubits == 2:
correlations = {}
for i, (op1, name1) in enumerate(zip(pauli_ops, pauli_names)):
for j, (op2, name2) in enumerate(zip(pauli_ops, pauli_names)):
if i == 0 and j == 0: # Skip identity-identity
continue
# Create tensor product operator
pauli_tensor = qt.tensor(op1, op2)
# Calculate expectation value
correlation = np.real((pauli_tensor * rho).tr())
correlations[f"{name1}{name2}"] = float(correlation)
viz_data['data']['pauli_correlations'] = correlations
viz_data['visualization_type'] = 'pauli_correlation_matrix'
# Add entanglement measure visualization
if 'entanglement_values' in results:
viz_data['data']['entanglement_measures'] = results['entanglement_values']
return viz_data
except Exception as e:
logger.warning(f"Visualization data generation failed: {e}")
return {'error': str(e)}
