z i&SrSSKJr SSKrSSKJr SSKJr SSK J r SSK J r J r JrJr SSSjjrSSS jjrSSS jjrSSS jjrSS jrSS jrSrg)zJ Quantum information measures, metrics, and related functions for states. ) annotationsN) QiskitError) Statevector) DensityMatrix) partial_traceshannon_entropy _format_state _funm_svdc[XS9n[XS9nURnURn[U[5(a{[U[5(a7[R "UR 5RU55S-nOUR 5RU5RU5nO[U[5(a/UR 5RU5RU5nOd[U[R5n[U[R5n[RRURU5SS9S-n[[R"U55$)a-Return the state fidelity between two quantum states. The state fidelity :math:`F` for density matrix input states :math:`\rho_1, \rho_2` is given by .. math:: F(\rho_1, \rho_2) = Tr[\sqrt{\sqrt{\rho_1}\rho_2\sqrt{\rho_1}}]^2. If one of the states is a pure state this simplifies to :math:`F(\rho_1, \rho_2) = \langle\psi_1|\rho_2|\psi_1\rangle`, where :math:`\rho_1 = |\psi_1\rangle\!\langle\psi_1|`. Args: state1 (Statevector or DensityMatrix): the first quantum state. state2 (Statevector or DensityMatrix): the second quantum state. validate (bool): check if the inputs are valid quantum states [Default: True] Returns: float: The state fidelity :math:`F(\rho_1, \rho_2)`. Raises: QiskitError: if ``validate=True`` and the inputs are invalid quantum states. validatenuc)ord)r data isinstancernpabsconjdotr sqrtlinalgnormfloatreal)state1state2r arr1arr2fids1sqs2sqs ]/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/states/measures.pystate_fidelityr$s 86 5F 6 5F ;;D ;;D&+&& fk * *&&./14C))+//$'++D1C FK ( (iikood#''-rww'rww'iinnTXXd^n71<  c4[XS9nUR5$)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)stater s r#r'r'Rs& % 3E <<>r%cSSKJn [USS9n[U[5(ag[ R "[ R"URUR55S5n[X1S9$)aCalculate the von-Neumann entropy of a quantum state. The entropy :math:`S` is given by .. math:: S(\rho) = - Tr[\rho \log(\rho)] Args: state (Statevector or DensityMatrix): a quantum state. base (int): the base of the logarithm [Default: 2]. Returns: float: The von-Neumann entropy S(rho). Raises: QiskitError: if the input state is not a valid QuantumState. rNTr base) scipy.linalgrr rrrmaximumreigvalsrr)r(r,laevalss r#entropyr2isT& %$ /E%%% JJrwwrzz%**56 r*r>)r-rr rrr6r5rrrrrrr'dimrrfliplrdiagrrsortr/r.maxsum)r(r0r6qargsrhoyy_matsigmaws r# concurrencerJsXJ %$ /E%%%zz| t9>GH HAwa(qcE)RWWQ!bggfSk&:":;<== yyA~IJJ   # #C YYrww~. /F GGFO   + / / 7E  5)*+A  1c"#A sAbEBFF1Qr7O+ ,,r%c[USS9n[U[5(aOUR5n[ U5S:wa [ S5eUSUS:aS/OS/n[ [X5SS9$URS:wa [ S 5e[U5nS[R"SUS-- 5-S- n[USU- /5$) aCalculate 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. Tr rr;rr4r+r<r=) r rrr6r5rr2rr?rJrrr)r(r6rEconcvals r#entanglement_of_formationrNs" %$ /E%%%zz| t9>GH HAwa(qc}U2;; yyA~IJJ u D rwwqD!G}% % *C CS> **r%c[U[5(a [U5nURU5n[R R URSS9n[R"U5nUS- S- nU$)aCalculates the negativity The mathematical expression for negativity is given by: .. math:: {\cal{N}}(\rho) = \frac{|| \rho^{T_A}|| - 1 }{2} Args: state (Statevector or DensityMatrix): a quantum state. qargs (list): The subsystems to be transposed. Returns: negv (float): Negativity value of the quantum state Raises: QiskitError: if the input state is not a valid QuantumState. F) compute_uvr4r) rrrpartial_transposerrsvdrrD)r(rEsingular_valuesr/negvs r# negativityrUsf$%%%e$  # #E *EiimmEJJ5mAOff_%G aK1 D Kr%)T)rStatevector | DensityMatrixrrVr boolreturnr)r(rVr rWrXr)r)r(rVr,intrXr)r(rVrXr)__doc__ __future__rnumpyrqiskit.exceptionsr&qiskit.quantum_info.states.statevectorr(qiskit.quantum_info.states.densitymatrixr qiskit.quantum_info.states.utilsrrr r r$r'r2r9rJrNrUr%r#rbss#)>B`d2 '21L2X\2 2j.-:]>9-x +Fr%