1,240 research outputs found
Optimal two-object auctions with synergies.
We design the revenue-maximizing auction for two goods when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the goods inefficiently with respect to an environ-ment with no synergies. In particular, if the synergy is large then it may occur that a buyerâs valuations for the goods weakly dominate the valuations of another buyer and the latter one receives the bundle. We link this fact, which contrasts with the results for a setting without synergies, to "non-regular" one-good models.Multiple-unit Auctions; Multi-dimensional Screening; Bundling
Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States
A long-standing open question about Gaussian continuous-variable cluster
states is whether they enable fault-tolerant measurement-based quantum
computation. The answer is yes. Initial squeezing in the cluster above a
threshold value of 20.5 dB ensures that errors from finite squeezing acting on
encoded qubits are below the fault-tolerance threshold of known qubit-based
error-correcting codes. By concatenating with one of these codes and using
ancilla-based error correction, fault-tolerant measurement-based quantum
computation of theoretically indefinite length is possible with finitely
squeezed cluster states.Comment: (v3) consistent with published version, more accessible for general
audience; (v2) condensed presentation, added references on GKP state
generation and a comparison of currently achievable squeezing to the
threshold; (v1) 13 pages, a few figure
Passive interferometric symmetries of multimode Gaussian pure states
As large-scale multimode Gaussian states begin to become accessible in the
laboratory, their representation and analysis become a useful topic of research
in their own right. The graphical calculus for Gaussian pure states provides
powerful tools for their representation, while this work presents a useful tool
for their analysis: passive interferometric (i.e., number-conserving)
symmetries. Here we show that these symmetries of multimode Gaussian states
simplify calculations in measurement-based quantum computing and provide
constructive tools for engineering large-scale harmonic systems with specific
physical properties, and we provide a general mathematical framework for
deriving them. Such symmetries are generated by linear combinations of
operators expressed in the Schwinger representation of U(2), called nullifiers
because the Gaussian state in question is a zero eigenstate of them. This
general framework is shown to have applications in the noise analysis of
continuous-various cluster states and is expected to have additional
applications in future work with large-scale multimode Gaussian states.Comment: v3: shorter, included additional applications, 11 pages, 7 figures.
v2: minor content revisions, additional figures and explanation, 23 pages, 18
figures. v1: 22 pages, 16 figure
A note on information revelation in procurement auctions
This paper is about a procurement auction setting, introduced in Gal-Or, Gal-Or and Dukes (2007), in which suppliers offer differentiated products and the buyer needs to decide whether to reveal or not to the suppliers the own preferences for the various products. We provide some technical remarks and complements to the analysis of Gal-Or, Gal-Or and Dukes (2007), and an extension to the case of risk averse suppliers.Information Revelation, Logconcavity, Risk Aversion
Revenue Comparison in Asymmetric Auctions with Discrete Valuations
We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. We prove that in this context the second price auction yields a higher expected revenue than the first price auction for a broad set of parameter values, although the opposite result is common in the literature on asymmetric auctions. For instance, the second price auction is superior both when a bidderâs valuation is more uncertain that the valuation of the other bidder, and in case of a not too large distribution shift or rescaling. In addition, we show that in some cases the revenue in the first price auction decreases when all the valuations increase [in doing so, we correct a claim in Maskin and Riley (1985), and we derive the biddersâ preferences between the two auctions.Asymmetric auctions, First price auctions, Second price auctions.
Temporal-mode continuous-variable cluster states using linear optics
I present an extensible experimental design for optical continuous-variable
cluster states of arbitrary size using four offline (vacuum) squeezers and six
beamsplitters. This method has all the advantages of a temporal-mode encoding
[Phys. Rev. Lett. 104, 250503], including finite requirements for coherence and
stability even as the computation length increases indefinitely, with none of
the difficulty of inline squeezing. The extensibility stems from a construction
based on Gaussian projected entangled pair states (GPEPS). The potential for
use of this design within a fully fault tolerant model is discussed.Comment: 9 pages, 19 color figure
Information revelation in procurement auctions with two-sided asymmetric information
A buyer needs to procure a good from either of two potential suppliers offering differentiated products and with privately observed costs. The buyer privately observes the own valuations for the products and (ex ante) decides how much of this information should be revealed to suppliers before they play a first score auction. We show that the more significant is each supplierâs private information on the own cost, the less information the buyer should reveal. Part of our analysis is linked to the comparison between a first and a second price auction in an asymmetric setup with a distribution shift.Asymmetric auctions
Sound clocks and sonic relativity
Sound propagation within certain non-relativistic condensed matter models
obeys a relativistic wave equation despite such systems admitting entirely
non-relativistic descriptions. A natural question that arises upon
consideration of this is, "do devices exist that will experience the relativity
in these systems?" We describe a thought experiment in which 'acoustic
observers' possess devices called sound clocks that can be connected to form
chains. Careful investigation shows that appropriately constructed chains of
stationary and moving sound clocks are perceived by observers on the other
chain as undergoing the relativistic phenomena of length contraction and time
dilation by the Lorentz factor, with c the speed of sound. Sound clocks within
moving chains actually tick less frequently than stationary ones and must be
separated by a shorter distance than when stationary to satisfy simultaneity
conditions. Stationary sound clocks appear to be length contracted and time
dilated to moving observers due to their misunderstanding of their own state of
motion with respect to the laboratory. Observers restricted to using sound
clocks describe a universe kinematically consistent with the theory of special
relativity, despite the preferred frame of their universe in the laboratory.
Such devices show promise in further probing analogue relativity models, for
example in investigating phenomena that require careful consideration of the
proper time elapsed for observers.Comment: (v2) consistent with published version; (v1) 15 pages, 9 figure
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