2,717 research outputs found
Quantum replication at the Heisenberg limit
No process in nature can perfectly clone an arbitrary quantum state. But is
it possible to engineer processes that replicate quantum information with
vanishingly small error? Here we demonstrate the possibility of probabilistic
super-replication phenomena where N equally prepared quantum clocks are
transformed into a much larger number of M nearly perfect replicas, with an
error that rapidly vanishes whenever M is small compared to the square of N.
The quadratic replication rate is the ultimate limit imposed by Quantum
Mechanics to the proliferation of information and is fundamentally linked with
the Heisenberg limit of quantum metrology.Comment: 9 + 16 pages, 2 figures, published versio
Credible, Truthful, and Two-Round (Optimal) Auctions via Cryptographic Commitments
We consider the sale of a single item to multiple buyers by a
revenue-maximizing seller. Recent work of Akbarpour and Li formalizes
\emph{credibility} as an auction desideratum, and prove that the only optimal,
credible, strategyproof auction is the ascending price auction with reserves
(Akbarpour and Li, 2019).
In contrast, when buyers' valuations are MHR, we show that the mild
additional assumption of a cryptographically secure commitment scheme suffices
for a simple \emph{two-round} auction which is optimal, strategyproof, and
credible (even when the number of bidders is only known by the auctioneer).
We extend our analysis to the case when buyer valuations are
-strongly regular for any , up to arbitrary
in credibility. Interestingly, we also prove that this construction cannot be
extended to regular distributions, nor can the be removed with
multiple bidders
Lower bounds to randomized algorithms for graph properties
AbstractFor any property P on n-vertex graphs, let C(P) be the minimum number of edges needed to be examined by any decision tree algorithm for determining P. In 1975 Rivest and Vuillemin settled the Aanderra-Rosenberg Conjecture, proving that C(P)=Ω(n2) for every nontrivial monotone graph property P. An intriguing open question is whether the theorem remains true when randomized algorithms are allowed. In this paper we show that Ω(n(log n)112 edges need to be examined by any randomized algorithm for determining any nontrivial monotone graph property
Finite Speed of Quantum Scrambling with Long Range Interactions
In a locally interacting many-body system, two isolated qubits, separated by a large distance r, become correlated and entangled with each other at a time tâ„r/v. This finite speed v of quantum information scrambling limits quantum information processing, thermalization, and even equilibrium correlations. Yet most experimental systems contain long range power-law interactionsâqubits separated by r have potential energy V(r)âr^(âα). Examples include the long range Coulomb interactions in plasma (α=1) and dipolar interactions between spins (α=3). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large α. This result parametrically improves previous bounds, compares favorably with recent numerical simulations, and can be realized in quantum simulators with dipolar interactions. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems, and improve bounds on environmental decoherence in experimental quantum information processors
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