No-cloning theorem

In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park,[1] in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by William Wootters and Wojciech H. Zurek[2] as well as Dennis Dieks[3] the same year). The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. The no-cloning theorem (as generally understood) concerns only pure states whereas the generalized statement regarding mixed states is known as the no-broadcast theorem.

The no-cloning theorem has a time-reversed dual, the no-deleting theorem. Together, these underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger compact category.[4][5] This formulation, known as categorical quantum mechanics, allows, in turn, a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in the same sense that intuitionistic logic arises from Cartesian closed categories).

  1. ^ Park, James (1970). "The concept of transition in quantum mechanics". Foundations of Physics. 1 (1): 23–33. Bibcode:1970FoPh....1...23P. CiteSeerX 10.1.1.623.5267. doi:10.1007/BF00708652. S2CID 55890485.
  2. ^ Wootters, William; Zurek, Wojciech (1982). "A Single Quantum Cannot be Cloned". Nature. 299 (5886): 802–803. Bibcode:1982Natur.299..802W. doi:10.1038/299802a0. S2CID 4339227.
  3. ^ Dieks, Dennis (1982). "Communication by EPR devices". Physics Letters A. 92 (6): 271–272. Bibcode:1982PhLA...92..271D. CiteSeerX 10.1.1.654.7183. doi:10.1016/0375-9601(82)90084-6. hdl:1874/16932.
  4. ^ Baez, John; Stay, Mike (2010). "Physics, Topology, Logic and Computation: A Rosetta Stone" (PDF). New Structures for Physics. Berlin: Springer. pp. 95–172. ISBN 978-3-642-12821-9.
  5. ^ Coecke, Bob (2009). "Quantum Picturalism". Contemporary Physics. 51: 59–83. arXiv:0908.1787. doi:10.1080/00107510903257624. S2CID 752173.