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What exactly are Quantum XOR Games?

Quantum xor games are a method of greatly simplifying the ideas behind Bell's theorem, which states that no physical theory of local hidden variables can ever reproduce all of the predictions of ...
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8 votes

Optimal strategy to a quantum state game

We simply translate the binary result of a qubit measurement to our guess whether it's the first state or the second, calculate the probability of success for every possible measurement of the qubit, ...
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8 votes

Algorithm-based game project to introduce quantum computing

This is definitely doable, but the tasks seem quite simple and they only introduce single-qubit measurement and the X gate, while quantum state preparation usually involves some superposition and ...
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7 votes
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Are correlations stronger than those allowed by quantum mechanics possible?

Yes, it is possible to conceive theories with "stronger correlations" than those given by quantum mechanics. One way to make this statement precise is to consider some kind of "measurement apparatus" ...
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6 votes
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In which paper was the CHSH game first presented?

As far as I have been researching from the intrenet about the CHSH game, the first experimental realization seems to be the one published by Aspect in Experimental Realization of Einstein-Podolsky-...
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6 votes
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How can quantum computing win 97% of times in coin flipping experiment?

We translate this game into conventional QC terminology as follows: The coin is a single qbit state $|\psi\rangle=\begin{bmatrix}\alpha \\ \beta\end{bmatrix}$ where $\alpha, \beta \in \mathbb{C}$ and ...
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6 votes

Proof of optimality for CHSH game classical strategy

I would argue that this is the critical issue to understand for Bell inequalities. Finding a violation of a Bell inequality tells you that the system is not classical (note: it does not prove that it ...
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5 votes
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Is Connes' Embedding Problem akin the word problem for finitely presented groups?

There are a number of equivalent formulations to CEP. One of them is Tsirelson's problem from quantum information theory, which asks whether the infinite dimensional commuting operator correlations ...
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5 votes

How could a quantum computer perform nimber arithmetic?

Nonlocal games such as the CHSH game are not impartial games in the sense of Sprague-Grundy. Alice and Bob are thought to be cooperating rather than competing, and randomness is central to the study ...
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4 votes

Has anyone analyzed multi-round nonlocal games?

It seems that using more rounds will not be such helpful for us to get something more powerful from complexity perspectives. There are a few comments about the number of rounds and the number of ...
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  • 478
4 votes

Proof of optimality for CHSH game classical strategy

One way to go about proving this is to characterise the set of all possible strategies that Alice & Bob can adopt. By "strategy" here I mean a possible relation between inputs and outputs, encoded ...
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3 votes

What is the quantum strategy required to win the Magic Squares game

Instead of $0$s and $1$s, suppose the labels of the column/rows are $+1$ and $-1$ respectively. Then if the rows are labelled $(1,1,1)$ (instead of $(0,0,0)$) and the columns are labelled $(1,1,-1)$ (...
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3 votes
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How are nonlocal games used in device-independent quantum cryptography?

Imagine you're playing a CHSH game with someone, although you don't know what quantum system it is that you're playing with, or even what measurements it is that you're doing on the system. You just ...
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3 votes

Algorithm-based game project to introduce quantum computing

They certainly seem doable. I'd suggest the first one, as it is a little more complex. For added complexity you could also include constraints on the allowed gates, such as not allowing X or Y on ...
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2 votes
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Using XOR games to benchmark quantum computers

If you look at the literature for blind quantum computation, there is the concept of a "trap state". Basically, something that isn't part of the main computation that is supposed to give specific ...
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2 votes

Algorithm-based game project to introduce quantum computing

Consider the task on one qubit. You are given a state that is either $H|0\rangle$ or $H|1\rangle$ and your task before the measurement is to get it to be either more probably $|0\rangle$ or $|1\rangle$...
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2 votes

How could a quantum computer perform nimber arithmetic?

It is relevant to consider the following research paper from Mashiko Fukiyama on Nim Game on Graph to come up with an algorithmic approach . At first, to set a starting position of the game, we fix ...
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2 votes

Proof of optimality for CHSH game classical strategy

In the CHSH game we have 2 players Alice and Bob. Can we proof in the form of a noncommunication pair of TMs which takes as input independant random bits x and y plus an arbitrary shared bitstring, ...
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2 votes
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Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?

I do understand that the sum of these three probabilities is greater than one because there are some constraints already involved; like if we uncover all three coins at least two have to be the ...
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2 votes

Using Qiskit with Blender

import sys sys.exec_prefix will show the path of python used by blender. Rename this python folder to something else. Now ...
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2 votes
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How does a classical computer simulate nonclassical correlations?

How then, would one be able to simulate say CHSH, which produces fundamentally quantum probabilities that cannot be explained locally/classically? Am I misinterpreting the meaning of simulate? ...
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2 votes

How does a classical computer simulate nonclassical correlations?

There are two definitions of simulation that are commonly used in this context. We consider a quantum computation to be: 1. loading an input 2. performing some processing 3. doing a measurement This ...
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2 votes

Problems in understanding the solution for "Mermin–Peres Magic Square Game"

Not an answer yet, but to long for comment: Alice and Bob share two entangled pairs. Now look only at Alice's. The last line gives the state that only one of'em has: $$\frac1{\sqrt 2}(|00〉+|11〉) =\...
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1 vote

How can one show that Alice's and Bob's answers agree at the intersection cells of Mermin-Peres' "magic square"?

Even though Alice and Bob use the "same" observable, it acts on different systems. To avoid confusion it's better to denote observables as $D_{ij}^A, D_{ij}^B$ and $D_{ij} = D_{ij}^A \otimes ...
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1 vote

How can one show that Alice's and Bob's answers agree at the intersection cells of Mermin-Peres' "magic square"?

General setup Suppose you have a bipartite state $\rho$, and a collection of measurements $\newcommand{\bs}[1]{\boldsymbol{#1}}\{\bs\mu^{(j)}\}_j$. Each $\bs\mu^{(j)}$ represents a way to measure the ...
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1 vote

How are Franson Interferometers used to prove security in Photonic QKD Experiments?

What a Franson interferometer does is to superpose two-photon wavepackets generated at different times (within the coherence time of the pump, supposing we are generating a pair of entangled photons ...
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1 vote
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MS Quantum Katas - Measurements Task 2.3 - problems in understanding the solution

Von Neumann measurement is a measurement that corresponds to an orthonormal basis, not necessary standard. Though it's related to the standard by a unitary transformation. As for the solution, at ...
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1 vote

Using Qiskit with Blender

Are you using Qiskit from within a conda virtual environment? If Blender isn't launched from within the same venv they may not be able to communicate (or share libraries).
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1 vote

Optimal strategy to a quantum state game

The key is in the optimal strategy for distinguishing two non-orthogonal states. This is something called the Helstrom measurement, which I described here.
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