WORLD SOILS. By E. M. Bridges.

Rains, Bruce

doi:10.1111/j.1745-7939.1971.tb00667.x

Cited by 28 publications

(47 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1. For the benefit of subsequent discussion, we remind that SLOs-also known by the name of local filtering operations-are represented, up to normalization, by separable maps [28] …”

Section: Nonlocal Behavior From All Multipartite Entangled Statesmentioning

confidence: 99%

All entangled states display some hidden nonlocality

2012

View full text Add to dashboard Cite

A well-known manifestation of quantum entanglement is that it may lead to correlations that are inexplicable within the framework of a locally causal theory-a fact that is demonstrated by the quantum violation of Bell inequalities. The precise relationship between quantum entanglement and the violation of Bell inequalities is, however, not well understood. While it is known that entanglement is necessary for such a violation, it is not clear whether all entangled states violate a Bell inequality, even in the scenario where one allows joint operations on multiple copies of the state and local filtering operations before the Bell experiment. In this paper we show that all entangled states, or more precisely, all not-fully-separable states of arbitrary Hilbert space dimension and arbitrary number of parties, violate a Bell inequality when combined with another state which on its own cannot violate the same Bell inequality. This result shows that quantum entanglement and quantum nonlocality are in some sense equivalent, thus giving an affirmative answer to the aforementioned open question. It follows from our result that two entangled states that are apparently useless in demonstrating quantum nonlocality via a specific Bell inequality can be combined to give a Bell violation of the same inequality. Explicit examples of such activation phenomenon are provided.

show abstract

“…1. For the benefit of subsequent discussion, we remind that SLOs-also known by the name of local filtering operations-are represented, up to normalization, by separable maps [28] …”

Section: Nonlocal Behavior From All Multipartite Entangled Statesmentioning

confidence: 99%

All entangled states display some hidden nonlocality

2012

View full text Add to dashboard Cite

show abstract

“…31 This subsection is devoted to show Proposition 7 If R satisfies Eq. (9) then there exists a sequence of subcodes of stabilizer codes whose rates are greater than or equal to R and whose fidelity converges to 1 as n → ∞.…”

Section: B Average Of the Fidelity Over All The Stabilizer Codesmentioning

confidence: 99%

“…In this subsection we shall prove that the average fidelity of the subcodes of all [[n, ⌊Rn⌋]] stabilizer codes converges to 1 as n → ∞ under the conditions (8) and (9). The proof is proceeded as follows:…”

Section: B Average Of the Fidelity Over All The Stabilizer Codesmentioning

confidence: 99%

Lower bound for the quantum capacity of a discrete memoryless quantum channel

Matsumoto

Uyematsu

2002

Journal of Mathematical Physics

View full text Add to dashboard Cite

We generalize the random coding argument of stabilizer codes and derive a lower bound on the quantum capacity of an arbitrary discrete memoryless quantum channel. For the depolarizing channel, our lower bound coincides with that obtained by Bennett et al. We also slightly improve the quantum Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue of the quantum GilbertVarshamov bound for linear stabilizer codes. Our proof is restricted to the binary quantum channels, but its extension of to l-adic channels is straightforward.

show abstract

“…Several such quantities have recently been proposed and analyzed [12,[30][31][32][33][34][35][36][37][38][39][40], and none of them can be considered as the unique, canonical measure. However, the quantity called entanglement of formation [12] plays an important role due to a simple interpretation: it gives a minimal amount of entanglement necessary to create a given density matrix.…”

Section: B Entanglement Of Formationmentioning

confidence: 99%

Volume of the set of separable states. II

1999

View full text Add to dashboard Cite

The problem of how many entangled or, respectively, separable states there are in the set of all quantum states is investigated. We study to what extent the choice of a measure in the space of density matrices ̺ describing N -dimensional quantum systems affects the results obtained. We demonstrate that the link between the purity of the mixed states and the probability of entanglement is not sensitive to the measure chosen. Since the criterion of partial transposition is not sufficient to distinguish all separable states for N ≥ 8, we develop an efficient algorithm to calculate numerically the entanglement of formation of a given mixed quantum state, which allows us to compute the volume of separable states for N = 8 and to estimate the volume of the bound entangled states in this case. 03.65.Bz, 42.50.Dv, 89.70.+c

show abstract

WORLD SOILS. By E. M. Bridges.

Cited by 28 publications

References 0 publications

All entangled states display some hidden nonlocality

All entangled states display some hidden nonlocality

Lower bound for the quantum capacity of a discrete memoryless quantum channel

Volume of the set of separable states. II

Contact Info

Product

Resources

About