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
-
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
-
81P15 Quantum measurement theory
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
- Subjects
- Dates
-
Issue 35 (7 September 2001)
Received 23 November 2000
Published 24 August 2001
-
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
-
Folksonomies and clustering in the collaborative system CiteULike
Andrea Capocci and Guido Caldarelli 2008 J. Phys. A: Math. Theor. 41 224016
-
First joint search for gravitational-wave bursts in LIGO and GEO 600 data
B Abbott et al 2008 Class. Quantum Grav. 25 245008
-
A joint search for gravitational wave bursts with AURIGA and LIGO
L Baggio et al 2008 Class. Quantum Grav. 25 095004
-
Safety of pulsed electric devices
Amit J Nimunkar and John G Webster 2009 Physiol. Meas. 30 101
-
Ferroelectric catastrophe: beyond nanometre-scale optical resolution
Junji Tominaga et al 2004 Nanotechnology 15 411
-
Numerical estimation of the curvature of a light wavefront in a weak gravitational field
A San Miguel et al 2009 Class. Quantum Grav. 26 235004
-
An alternative view on quasicrystalline random tilings
Christoph Richard 1999 J. Phys. A: Math. Gen. 32 8823
-
All spacetimes with vanishing curvature invariants
V Pravda et al 2002 Class. Quantum Grav. 19 6213
-
Scale-invariance in gravity and implications for the cosmological constant
Bryan Kelleher 2004 Class. Quantum Grav. 21 2623
Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Spectral problems in open quantum chaos
- Lectures on localization and matrix models in supersymmetric Chern–Simons-matter theories
super-Yang–Mills*