147 research outputs found
The general structure of quantum resource theories
In recent years it was recognized that properties of physical systems such as
entanglement, athermality, and asymmetry, can be viewed as resources for
important tasks in quantum information, thermodynamics, and other areas of
physics. This recognition followed by the development of specific quantum
resource theories (QRTs), such as entanglement theory, determining how quantum
states that cannot be prepared under certain restrictions may be manipulated
and used to circumvent the restrictions. Here we discuss the general structure
of QRTs, and show that under a few assumptions (such as convexity of the set of
free states), a QRT is asymptotically reversible if its set of allowed
operations is maximal; that is, if the allowed operations are the set of all
operations that do not generate (asymptotically) a resource. In this case, the
asymptotic conversion rate is given in terms of the regularized relative
entropy of a resource which is the unique measure/quantifier of the resource in
the asymptotic limit of many copies of the state. This measure also equals the
smoothed version of the logarithmic robustness of the resource.Comment: 5 pages, no figures, few references added, published versio
Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions
We provide quantitative bounds on the characterisation of multiparticle
separable states by states that have locally symmetric extensions. The bounds
are derived from two-particle bounds and relate to recent studies on quantum
versions of de Finetti's theorem. We discuss algorithmic applications of our
results, in particular a quasipolynomial-time algorithm to decide whether a
multiparticle quantum state is separable or entangled (for constant number of
particles and constant error in the LOCC or Frobenius norm). Our results
provide a theoretical justification for the use of the Search for Symmetric
Extensions as a practical test for multiparticle entanglement.Comment: 5 pages, 1 figur
When does noise increase the quantum capacity?
Superactivation is the property that two channels with zero quantum capacity
can be used together to yield positive capacity. Here we demonstrate that this
effect exists for a wide class of inequivalent channels, none of which can
simulate each other. We also consider the case where one of two zero capacity
channels are applied, but the sender is ignorant of which one is applied. We
find examples where the greater the entropy of mixing of the channels, the
greater the lower bound for the capacity. Finally, we show that the effect of
superactivation is rather generic by providing example of superactivation using
the depolarizing channel.Comment: Corrected minor typo
Witnessed Entanglement
We present a new measure of entanglement for mixed states. It can be
approximately computable for every state and can be used to quantify all
different types of multipartite entanglement. We show that it satisfies the
usual properties of a good entanglement quantifier and derive relations between
it and other entanglement measures.Comment: Revised version. 7 pages and one figur
Toy model of boundary states with spurious topological entanglement entropy
Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminate topological entanglement entropy. We show that, if the state at the boundary of a subregion is a stabilizer state, then it has a nonzero spurious contribution to the region if and only if the state is in a nontrivial one-dimensional G₁×G₂ symmetry-protected-topological (SPT) phase under an on-site symmetry. However, we provide a candidate of a boundary state that has a nonzero spurious contribution but does not belong to any such SPT phase
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