g&dZddlmZddlZddlmZddlmZddl m Z ddl m Z m Z mZmZ dddZdddZdddZdddZd dZd dZdZdS)!zJ Quantum information measures, metrics, and related functions for states. ) annotationsN) QiskitError) Statevector) DensityMatrix) partial_traceshannon_entropy _format_state _funm_svdTstate1Statevector | DensityMatrixstate2validateboolreturnfloatc^t||}t||}|j}|j}t|trt|tr=t j||dz}n|||}nt|tr;|||}nkt|tj }t|tj }tj ||ddz}tt j |S)aqReturn the state fidelity between two quantum states. The state fidelity :math:`F` for density matrix input states :math:`\rho_1, \rho_2` is given by .. math:: F(\rho_1, \rho_2) = Tr[\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}]^2. If one of the states is a pure state this simplifies to :math:`F(\rho_1, \rho_2) = \langle\psi_1|\rho_2|\psi_1\rangle`, where :math:`\rho_1 = |\psi_1\rangle\!\langle\psi_1|`. Args: state1 (Statevector or DensityMatrix): the first quantum state. state2 (Statevector or DensityMatrix): the second quantum state. validate (bool): check if the inputs are valid quantum states [Default: True] Returns: float: The state fidelity :math:`F(\rho_1, \rho_2)`. Raises: QiskitError: if ``validate=True`` and the inputs are invalid quantum states. rnuc)ord)r data isinstancernpabsconjdotr sqrtlinalgnormrreal)r r rarr1arr2fids1sqs2sqs Y/granary/edev/quantum/lib/python3.11/site-packages/qiskit/quantum_info/states/measures.pystate_fidelityr'sL86H 5 5 5F 6H 5 5 5F ;D ;D&+&&= fk * * 2&..//14CC))++//$''++D11CC FK ( (=iikkood##''--rw''rw''innTXXd^^n771<   statecLt||}|S)aCalculate the purity of a quantum state. The purity of a density matrix :math:`\rho` is .. math:: \text{Purity}(\rho) = Tr[\rho^2] Args: state (Statevector or DensityMatrix): a quantum state. validate (bool): check if input state is valid [Default: True] Returns: float: the purity :math:`Tr[\rho^2]`. Raises: QiskitError: if the input isn't a valid quantum state. r)r purity)r)rs r&r+r+Rs$& %( 3 3 3E <<>>r(rbaseintcddlm}t|d}t|trdSt jt j||j d}t||S)aCalculate the von-Neumann entropy of a quantum state. The entropy :math:`S` is given by .. math:: S(\rho) = - Tr[\rho \log(\rho)] Args: state (Statevector or DensityMatrix): a quantum state. base (int): the base of the logarithm [Default: 2]. Returns: float: The von-Neumann entropy S(rho). Raises: QiskitError: if the input state is not a valid QuantumState. rNTrr,) scipy.linalgrr rrrmaximumr eigvalsrr)r)r,laevalss r&entropyr6is{& %$ / / /E%%%q Jrwrzz%*5566 < zz|| t99>>GHH HAwa((qcE5))RWQ!bgfSkk&:&:":;<<=== yA~~IJJJ    #C Yrw~~~.. / /F GGFOO   + + / / 7 7E  5))**++A  1c""##A sAbEBF1QrT7OO+ , ,,r(ct|d}t|trm|}t |dkrt d|d|dkrdgndg}t t||dS|jdkrt d t|}dtj d|dzz zdz }t|d|z gS) a Calculate the entanglement of formation of quantum state. The input quantum state must be either a bipartite state vector, or a 2-qubit density matrix. Args: state (Statevector or DensityMatrix): a 2-qubit quantum state. Returns: float: The entanglement of formation. Raises: QiskitError: if the input state is not a valid QuantumState. QiskitError: if input is not a bipartite QuantumState. QiskitError: if density matrix input is not a 2-qubit state. Trrr?rr8r0r@rA) r rrr:r9rr6rrCrNrrr)r)r:rIconcvals r&entanglement_of_formationrRs" %$ / / /E%%%<zz|| t99>>GHH HAwa((qc}UE22;;;; yA~~IJJJ u  D rwqD!G}%% % *C CS> * **r(ct|trt|}||}tj|jd}t j|}|dz dz }|S)aCalculates the negativity The mathematical expression for negativity is given by: .. math:: {\cal{N}}(\rho) = \frac{|| \rho^{T_A}|| - 1 }{2} Args: state (Statevector or DensityMatrix): a quantum state. qargs (list): The subsystems to be transposed. Returns: negv (float): Negativity value of the quantum state Raises: QiskitError: if the input state is not a valid QuantumState. F) compute_uvr8r) rrrpartial_transposerrsvdrrH)r)rIsingular_valuesr3negvs r& negativityrYsq$%%%%e$$  # #E * *EimmEJ5mAAOf_%%G aK1 D Kr()T)r r r r rrrr)r)r rrrr)r)r)r r,r-rr)r)r rr)__doc__ __future__rnumpyrqiskit.exceptionsr&qiskit.quantum_info.states.statevectorr(qiskit.quantum_info.states.densitymatrixr qiskit.quantum_info.states.utilsrrr r r'r+r6r=rNrRrYr(r&rbsU#"""""))))))>>>>>>BBBBBB`d22222j.-----:]]]]]>9-9-9-9-x + + + +Fr(