ترغب بنشر مسار تعليمي؟ اضغط هنا

All Quantum Adversary Methods are Equivalent

55   0   0.0 ( 0 )
 نشر من قبل Robert Spalek
 تاريخ النشر 2004
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Robert Spalek




اسأل ChatGPT حول البحث

The quantum adversary method is one of the most versatile lower-bound methods for quantum algorithms. We show that all known variants of this method are equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted adversary (Ambainis, 2003), strong weighted adversary (Zhang, 2005), and the Kolmogorov complexity adversary (Laplante and Magniez, 2004). We also pa few new equivalent formulations of the method. This shows that there is essentially _one_ quantum adversary method. From our approach, all known limitations of the



قيم البحث

اقرأ أيضاً

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.
45 - Robert Spalek 2007
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants upper-bound the_d ifference_ of the progress function, whereas our new variant upper-bounds the_ratio_ and that is why we coin it the multiplicative adversary. The new method generalizes to all functions the new quantum lower-bound method by Ambainis [Amb05, ASW06] based on the analysis of eigenspaces of the density matrix. We prove a strong direct product theorem for all functions that have a multiplicative adversary lower bound.
Quantum catalysis is a fascinating concept which demonstrates that certain transformations can only become possible when given access to a specific resource that has to be returned unaffected. It was first discovered in the context of entanglement th eory and since then applied in a number of resource-theoretic frameworks, including quantum thermodynamics. Although in that case the necessary (and sometimes also sufficient) conditions on the existence of a catalyst are known, almost nothing is known about the precise form of the catalyst state required by the transformation. In particular, it is not clear whether it has to have some special properties or be finely tuned to the desired transformation. In this work we describe a surprising property of multi-copy states: we show that in resource theories governed by majorization all resourceful states are catalysts for all allowed transformations. In quantum thermodynamics this means that the so-called second laws of thermodynamics do not require a fine-tuned catalyst but rather any state, given sufficiently many copies, can serve as a useful catalyst. These analytic results are accompanied by several numerical investigations that indicate that neither a multi-copy form nor a very large dimension catalyst are required to activate most allowed transformations catalytically.
Understanding the relation between the different forms of inseparability in quantum mechanics is a longstanding problem in the foundations of quantum theory and has implications for quantum information processing. Here we make progress in this direct ion by establishing a direct link between quantum teleportation and Bell nonlocality. In particular, we show that all entangled states which are useful for teleportation are nonlocal resources, i.e. lead to deterministic violation of Bells inequality. Our result exploits the phenomenon of super-activation of quantum nonlocality, recently proved by Palazuelos, and suggests that the latter might in fact be generic.
138 - Andrew M. Childs , Troy Lee 2007
The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find the exact va lue of the best possible quantum adversary lower bound for a symmetrized version of ordered search (whose query complexity differs from that of the original problem by at most 1). Thus we show that the best lower bound for ordered search that can be proved by the adversary method is (1/pi) ln n + O(1). Furthermore, we show that this remains true for the generalized adversary method allowing negative weights.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا