bie ddlmZmZddlZddlmZddlmZddl m Z ddl m Z ddl mZ d ded eeefd ed fd Zy))LiteralTupleN)kron) partial_trace)hermitian_wrap)quantum_rel_entr) Expressionrhodimssys)rctt|dk7rddt|dz}t||dk(r.ttj|dt |||}nB|dk(r.tt |||tj|d}ntd|dt |}t||| S) a  Returns (an approximation of) the quantum conditional entropy for a bipartite state, conditioning on system :math:`\texttt{sys}.` Formally, if :math:`N` is the von Neumann entropy function and :math:`\operatorname{tr}_{\texttt{sys}}` is the partial trace operator over subsystem :math:`\texttt{sys},` the returned expression represents .. math:: N(\rho) - N(\operatorname{tr}_{\texttt{sys}}(\rho)). Parameters ---------- rho : Expression A Hermitian matrix of order :math:`\texttt{dims[0]}\cdot\texttt{dims[1]}.` dims : tuple The dimensions of the two subsystems that definte :math:`\rho` as a bipartite state. sys : int The subsystem on which to condition in evaluating the conditional quantum entropy. quad_approx : Tuple[int, int] quad_approx[0] is the number of quadrature nodes and quad_approx[1] is the number of scaling points in the quadrature scheme from https://arxiv.org/abs/1705.00812. Notes ----- This function does not assume :math:`\operatorname{tr}( ho)=1,` which would be required for most uses of this function in the context of quantum information theory. See https://en.wikipedia.org/wiki/Conditional_quantum_entropy for more information. zEThis function is only defined for a tensor product of two subsystems,zbut z0 subsystems were implied from the value of dims.rr z(Argument sys must be either 0 or 1; got .)len ValueErrorrnpeyerrr)r r r quad_approxerr composite_args X/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/cvxpy/atoms/quantum_cond_entr.pyquantum_cond_entrr sF 4yA~U s4ykIJKo ax FF47O]3c:   #tS )266$q'? CC5JKK"=1M S- = ==)r)r)typingrrnumpyrcvxpy.atoms.affine.kronr cvxpy.atoms.affine.partial_tracercvxpy.atoms.affine.wrapsrcvxpy.atoms.quantum_rel_entrrcvxpy.expressions.expressionr intrrrr%sJ!(:393V\2> 2> %c3h2>6=dm2>r