The Resource Theory of Entanglement

Shähandeh, Farid

doi:10.1007/978-3-030-24120-9_2

Cited by 5 publications

(2 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Quantification of quantum resources and the construction of the resource theory is very important and interesting direction of research [13]. Few examples of different resource theories are (i) the resource theory of entanglement [13,14], (ii) the resource theory of coherence [15,16], (iii) the resource theory of incompatibility [17], (iv) the resource theory of quantum channels [18], (v) the resource theory of quantum thermodynamics [19,20] etc. We do not claim we construct the complete resource theory here.…”

Section: An Attempt To Construct the Resource Theory Of The Sharpness...mentioning

confidence: 99%

Quantifying unsharpness of observables in an outcome-independent way

Mitra¹

2022

Preprint

View full text Add to dashboard Cite

Recently, a very beautiful measure of the unsharpness (fuzziness) of the observables is discussed in the paper [Phys. Rev. A 104, 052227 (2021)]. The measure which is defined in this paper is constructed via uncertainty and does not depend on the values of the outcomes. There exist several properties of a set of observables (e.g., incompatibility, non-disturbance) that do not depend on the values of the outcomes. Therefore, the approach in the above-said paper is consistent with the above-mentioned fact and is able to measure the intrinsic unsharpness of the observables. In this work, we also quantify the unsharpness of observables in an outcome-independent way. But our approach is different than the approach of the above-said paper. In this work, at first, we construct two Luder's instrument-based unsharpness measures and provide the tight upper bounds of those measures. Then we prove the monotonicity of the above-said measures under a class of fuzzifying processes (processes that make the observables more fuzzy). This is consistent with the resourcetheoretic framework. Then we relate our approach to the approach of the above-said paper. Next, we try to construct two instrument-independent unsharpness measures. In particular, we define two instrument-independent unsharpness measures and provide the tight upper bounds of those measures and then we derive the condition for the monotonicity of those measures under a class of fuzzifying processes and prove the monotonicity for dichotomic qubit observables. Then we show that for an unknown measurement, the values of all of these measures can be determined experimentally. Finally, we present the idea of the resource theory of the sharpness of the observables.

show abstract

Section: An Attempt To Construct the Resource Theory Of The Sharpness...mentioning

confidence: 99%

Quantifying unsharpness of observables in an outcome-independent way

Mitra¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Since not all forms of entanglement are relevant for distinct information processing applications, the determination of resource states for specific information processing tasks is of paramount importance. This, along with any characteristic protection or resilience against noise and decoherence provided by a resource state, forms the underlying principle of quantum resource theories [37][38][39][40]. In the latter pursuit, decoherence-free subspaces provide a natural solution and associated resources to produce quantum resource-states that are not easily decohered [41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Can We Entangle Entanglement?

Majumdar¹

2021

Topics on Quantum Information Science

View full text Add to dashboard Cite

In this chapter, nested multilevel entanglement is formulated and discussed in terms of Matryoshka states. The generation of such states that contain nested patterns of entanglement, based on an anisotropic XY model has been proposed. Two classes of multilevel-entanglement- the Matryoshka Q-GHZ states and Matryoshka generalised GHZ states, are studied. Potential applications of such resource states, such as for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are proposed and discussed, in terms of a Matryoshka state over seven qubits. We also discuss fractal network protocols, surface codes and graph states as well as generation of arbitrary entangled states at remote locations in this chapter.

show abstract

Quantifying Unsharpness of Observables in an Outcome-Independent way

Mitra

2022

Int J Theor Phys

View full text Add to dashboard Cite

The Resource Theory of Entanglement

Cited by 5 publications

References 61 publications

Quantifying unsharpness of observables in an outcome-independent way

Quantifying unsharpness of observables in an outcome-independent way

Can We Entangle Entanglement?

Quantifying Unsharpness of Observables in an Outcome-Independent way

Contact Info

Product

Resources

About