The Forbidden Quantum Adder

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 impo...

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Detalles Bibliográficos
Autores: Álvarez Rodríguez, Unai, Sanz Ruiz, Mikel, Lamata Manuel, Lucas, Solano Villanueva, Enrique Leónidas
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/16131
Acceso en línea:http://hdl.handle.net/10810/16131
Access Level:acceso abierto
Palabra clave:information theory and computation
quantum information
MULTIDISCIPLINARY SCIENCES
Descripción
Sumario: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.