The asymptotic entanglement cost of preparing a quantum state

By Patrick M. Hayden, Michal Horodecki, Barbara M. Terhal. 2000

292 citations recorded by the source corpus.

We give a detailed proof of the conjecture that the asymptotic entanglement cost of preparing a state ρ is equal to limn→∞ Ef (ρ ⊗n )/n where Ef is the entanglement of formation.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/a09d9fc186cea435716abe5328b818e145689c8c

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement certification from theory to experiment (2018, background): “[67] Patrick M.”
The role of relative entropy in quantum information theory (2001, background): “W0 = I⊗ I W0 I ⊗ I, (48) W1 = σ1 ⊗ I W0 σ1 ⊗ I, (49) W2 = σ2 ⊗ I W0 σ2 ⊗ I, (50) W3 = σ3 ⊗ I W0 σ3 ⊗ I.”
Fundamentals of quantum information theory (2002, methodology): “For pure states we have discussed beside distillation the “dilution” of entanglement and we can use, similar to ED, the asymptotic rate with which bipartite systems in a given state can be prepared out of maximally entangled singlets [78].”
Geometry of Quantum States: Index (2007, background): “Moreover, entanglement cost was shown [421] to be equal to the regularised entanglement of formation, EC(ρ) = limn→∞ EF(ρ⊗n)/n.”
Multiboundary wormholes and holographic entanglement (2014, background): “A stringent operational definition of entanglement is to ask for the maximum rate at which nearperfect Bell pairs can be extracted from many copies of a given state using only LOCC, a quantity known as the distillable entanglement, ED [50].”
Entanglement of assistance and multipartite state distillation (2005, background): “In the limit of many copies we have to substitute the entanglement cost E C ( ψ AB ) [16].”
Entanglement of purification through holographic duality (2017, background): “E#(Φ + d ) = log d) which satisfies (c) and (d), the regularization E∞ # (ρ) = limn→∞E#(ρ ⊗n)/n is always bounded from below by the entanglement distillation ED(ρAB) [33] and from above by the entanglement cost EC(ρAB) [34, 35]:”
Equivalence of Additivity Questions in Quantum Information Theory (2003, background): “has been proven to give the entanglement cost of a quantum state [7].”
Entanglement of two-mode Gaussian states: characterization and experimental production and manipulation (2005, unknown): “The asymptotic regularization of the entanglement of formation is equal to the entanglement cost EC(̺), defined as the minimum number of singlets (maximally entangled antisymmetric two-qubit states) which is needed to prepare the state ̺ through local operations and classical communication [37].”
Aspects of Generic Entanglement (2004, background): “The number of EPR pairs needed per copy of σ created is defined to be the entanglement cost [21], Ec(σAB) = limn→∞ 1 nEf (σ ⊗n AB), where Ef (σAB) = min ∑”