QuantumComputingBench · graph-grounded exercise book
Study state and channel representations, symmetry and tensor structure through primary-source-grounded problems. Planned curriculum anchors are not local Lean closure for the complete answers.
These links open the shared core's formal companion panel. Each card distinguishes admitted fixed-reference views from pending formalization. Preserve the exact core contract and split; a formal view is not another core.
Work in the cited source's finite-dimensional complex setting H=C^d, initially d>=1. Let Herm_d={X in M_d(C):X=X†}, regarded as a REAL vector space, D_d={rho in Herm_d:rho>=0, tr(rho)=1}, and A_d={X in Herm_d:tr(X)=1}. P…
primary source nl only
A mixed state can be written as a probabilistic mixture of pure states |psi_i> with weights p_i; such a list is called a realizing ensemble. Prove that a mixed state has more than one realizing ensemble by the following …
primary source nl only
Call a bipartite state a product state if it factorizes as a single tensor product of local states, and separable if it is a probabilistic mixture of product states. (a) Show that in a product state the outcomes of any t…
primary source nl only
A two-qubit state invariant under all local transformations of the form U tensor U can be written with a single real parameter x in [-1,1] as rho(x) = ((2 - x)/6) I + ((2x - 1)/6) F, where I is the identity and F is the …
primary source nl only