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quant-ph2019★ 6 cited
A variational lower bound on the ground state of a many-body system and the squaring parametrization of density matrices
F. Uskov, O. Lychkovskiy
A variational upper bound on the ground state energy of a quantum system, , is well-known (here is the Hamiltonian of t…
quant-ph2018
Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries
E. Shpagina, F. Uskov, N. Il'in +1
The stationary Schrödinger equation can be cast in the form , where is the system's Hamiltonian and is the system's density matrix. We explore the merits of this…
quant-ph2017
Squaring parametrization of constrained and unconstrained sets of quantum states
N. Il'in, E. Shpagina, F. Uskov +1
A mixed quantum state is represented by a Hermitian positive semi-definite operator with unit trace. The positivity requirement is responsible for a highly nontrivial geometry…