Constructive feedback of non-Markovianity on resources in random quantum states

Gupta, Rivu; Gupta, Shashank; Mal, Shiladitya; De, Aditi Sen

doi:10.1103/physreva.105.012424

Cited by 10 publications

(1 citation statement)

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“…In particular, it was demonstrated that most of the typical states become highly multiparty entangled with an increase of the number of parties. Moreover, these states have also been used to disprove the additivity of minimal output entropy [41], to obtain the maximal purity in k-uniform states with N parties [42], in showing constructive feedback in presence of a non-Markovian noisy environment [43], putting restriction on classical correlation [44], and analysing power of teleportation and densecodability of bipartite channels [45]. For our purpose, we are interested in bipartite pure states of arbitrary dimensions chosen at random with respect to the uniform measure, called Haar measure, on the unit sphere in a finitedimensional Hilbert space that is invariant under all unitary transformations.…”

Section: Introductionmentioning

confidence: 99%

Statistics of Entanglement Transformation with Hierarchies among Catalysts

Gupta,

Maity,

Mal

et al. 2022

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The distribution of typical bipartite pure states is studied within the framework of state transformation via local operation and classical communication (LOCC). We report the statistics of comparable and incomparable states in different dimensions for single-and multi-copy regimes and establish a connection between state transformation and the difference between the entanglement contents of the initial and the target states. From the analysis of catalyst resources, required to further otherwise impossible LOCC transformations between pairs, we demonstrate a universal pattern in the average and minimum entanglement of the randomly generated catalysts. Furthermore, we introduce a concept of hierarchy between different kinds of catalysts and show how they can not only aid in the conversion of incomparable states but can also act as a less costly resource towards this goal. We confirm the existence of catalysts, referred to as strong catalysts, which can activate LOCC transformation between pairs at the single-copy level, when it is initially impossible even with multiple copies.

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