Lie algebraic invariants in passive linear optical quantum systems
Summary
This research paper presents a method for deriving conserved quantities (invariants) in quantum linear optics without post-selection. The authors provide a recipe to identify invariants in the evolution of arbitrary states through passive linear interferometers, with a key example being the spectrum of a density matrix mapped onto the Lie algebra of passive linear optical Hamiltonians. This work addresses the fundamental limitations of linear optical state preparation, which cannot produce arbitrary quantum states from given inputs without post-selection, hindering applications that require entangled resources.
Source
bskyLie algebraic invariants in passive linear optical quantum systemsquantum-journal.orgKey quotes
· 4 pulledQuantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state.
This limits its utility since some applications require entangled resources that are difficult to prepare.
In this work, we give a recipe to derive conserved quantities in the evolution of arbitrary states along any possible passive linear interferometer.
One example of such an invariant is the spectrum of a density matrix mapped onto the Lie algebra of passive linear optical Hamiltonians.
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