M A Nielsen 2001 J. Phys. A: Math. Gen. 34 6987 doi:10.1088/0305-4470/34/35/324
On the units of bipartite entanglement: is sixteen ounces of entanglement always equal to one pound?
M A Nielsen
Show affiliationsIn a good physical theory dimensionless quantities, such as the ratio mp/me of the mass of the proton to the mass of the electron, do not depend on the system of units being used. This paper demonstrates that one widely used method for defining measures of entanglement violates this principle. Specifically, in this approach dimensionless ratios E(ρ)/E(σ) of entanglement measures may depend on what state is chosen as the basic unit of entanglement. This observation leads us to suggest three novel approaches to the quantification of entanglement. These approaches lead to unit-free definitions for the entanglement of formation and the distillable entanglement, and suggest natural measures of entanglement for multipartite systems. We also show that the behaviour of one of these novel measures, the entanglement of computation, is related to some open problems in computational complexity.
- PACS
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03.67.Lx Quantum computation architectures and implementations
03.67.Mn Entanglement measures, witnesses, and other characterizations
03.65.Ta Foundations of quantum mechanics; measurement theory
- MSC
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81P15 Quantum measurement theory
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
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Issue 35 (7 September 2001)
Received 23 November 2000
Published 24 August 2001
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On the units of bipartite entanglement: is sixteen ounces of entanglement always equal to one pound?
M A Nielsen 2001 J. Phys. A: Math. Gen. 34 6987
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