scholarly journals Quantum solution to a three player Kolkata restaurant problem using entangled qutrits

2014 ◽  
Vol 14 (3&4) ◽  
pp. 295-305
Author(s):  
Puya Sharif ◽  
Hoshang Heydari
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Solution ◽  
Quantum States ◽  
Minority Game ◽  
Initial State ◽  
Quantum Solution ◽  
Better Than

Three player quantum Kolkata restaurant problem is modelled using three entangled qutrits. This first use of three level quantum states in this context is a step towards a $N$-choice generalization of the $N$-player quantum minority game. It is shown that a better than classical payoff is achieved by a Nash equilibrium solution where the space of available strategies is spanned by subsets of SU(3) and the players share a tripartite entangled initial state.

Adversarial Risk Analysis for Auctions Using Mirror Equilibrium and Bayes Nash Equilibrium

2021 ◽  
Author(s):  
Muhammad Ejaz ◽  
Stephen Joe ◽  
Chaitanya Joshi
Keyword(s):  
Nash Equilibrium ◽  
Risk Analysis ◽  
Equilibrium Solution ◽  
Risk Averse ◽  
Prior Work ◽  
Reserve Price ◽  
Solution Concepts ◽  
Risk Seeking ◽  
Sealed Bid ◽  
Sealed Bid Auctions

In this paper, we use the adversarial risk analysis (ARA) methodology to model first-price sealed-bid auctions under quite realistic assumptions. We extend prior work to find ARA solutions for mirror equilibrium and Bayes Nash equilibrium solution concepts, not only for risk-neutral but also for risk-averse and risk-seeking bidders. We also consider bidders having different wealth and assume that the auctioned item has a reserve price.

Quantum circuits for calculating the squared sum of the inner product of quantum states and its application

2019 ◽  
Vol 17 (05) ◽  
pp. 1950043
Author(s):  
Panchi Li ◽  
Jiahui Guo ◽  
Bing Wang ◽  
Mengqi Hao
Keyword(s):  
Quantum Circuit ◽  
Quantum States ◽  
Experimental Results ◽  
Quantum Circuits ◽  
Inner Product ◽  
Superposition State ◽  
Initial State ◽  
Control Rules ◽  
Control Qubit ◽  
Classical Computer

In this paper, we propose a quantum circuit for calculating the squared sum of the inner product of quantum states. The circuit is designed by the multi-qubits controlled-swapping gates, in which the initial state of each control qubit is [Formula: see text] and they are in the equilibrium superposition state after passing through some Hadamard gates. Then, according to the control rules, each basis state in the superposition state controls the corresponding quantum states pair to swap. Finally, the Hadamard gates are applied to the control qubits again, and the squared sum of the inner product of many pairs of quantum states can be obtained simultaneously by measuring only one control qubit. We investigate the application of this method in quantum images matching on a classical computer, and the experimental results verify the correctness of the proposed method.

PHASE TRANSITION IN A TOY MARKET

2000 ◽  
Vol 03 (03) ◽  
pp. 451-454 ◽  
Author(s):  
DAMIEN CHALLET ◽  
MATTEO MARSILI ◽  
RICCARDO ZECCHINA
Keyword(s):  
Phase Transition ◽  
Nash Equilibrium ◽  
Stationary State ◽  
The Other ◽  
Minority Game ◽  
Learning Dynamics ◽  
Analytical Results ◽  
Other Hand ◽  
Exactly Solvable ◽  
Available Information

We review recent exact analytical results on Minority Game — a binary exactly solvable El Farol's bar problem. Inductive agents minimize the available information, not their losses, thus the stationary state differs from a Nash equilibrium. On the other hand, the same learning dynamics leads to a Nash equilibrium when agents take into account their impact on the market.

scholarly journals All macroscopic quantum states are fragile and hard to prepare

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 118
Author(s):  
Andrea López-Incera ◽  
Pavel Sekatski ◽  
Wolfgang Dür
Keyword(s):  
Quantum State ◽  
Quantum Fisher Information ◽  
System Size ◽  
Quantum States ◽  
Initial State ◽  
Macroscopic Quantum ◽  
Effective System ◽  
Local Observables ◽  
The One ◽  
Arbitrary Quantum

We study the effect of local decoherence on arbitrary quantum states. Adapting techniques developed in quantum metrology, we show that the action of generic local noise processes --though arbitrarily small-- always yields a state whose Quantum Fisher Information (QFI) with respect to local observables is linear in system size N, independent of the initial state. This implies that all macroscopic quantum states, which are characterized by a QFI that is quadratic in N, are fragile under decoherence, and cannot be maintained if the system is not perfectly isolated. We also provide analytical bounds on the effective system size, and show that the effective system size scales as the inverse of the noise parameter p for small p for all the noise channels considered, making it increasingly difficult to generate macroscopic or even mesoscopic quantum states. In turn, we also show that the preparation of a macroscopic quantum state, with respect to a conserved quantity, requires a device whose QFI is already at least as large as the one of the desired state. Given that the preparation device itself is classical and not a perfectly isolated macroscopic quantum state, the preparation device needs to be quadratically bigger than the macroscopic target state.

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