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Alvarez-Rodriguez U
; Sanz M
; Lamata L
; Solano E
Sci Rep
2015[Jul]; 5
(?): 11983
PMID26153134
show ga
Quantum information provides fundamentally different computational resources than
classical information. We prove that there is no unitary protocol able to add
unknown quantum states belonging to different Hilbert spaces. This is an inherent
restriction of quantum physics that is related to the impossibility of copying an
arbitrary quantum state, i.e., the no-cloning theorem. Moreover, we demonstrate
that a quantum adder, in absence of an ancillary system, is also forbidden for a
known orthonormal basis. This allows us to propose an approximate quantum adder
that could be implemented in the lab. Finally, we discuss the distinct character
of the forbidden quantum adder for quantum states and the allowed quantum adder
for density matrices.
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