Questions tagged [non-locality]
For questions about the phenomena related to correlations among distant observers. For example, this tag should be used for questions about Bell or CHSH inequalities, or for questions about quantum steering.
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Why are randomized strategies convex mixtures of deterministic ones?
I am looking for a proof of this fact regarding randomized strategies of the CHSH game:
"... allowing randomized strategies can not help them to get a better success probability. This is because ...
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Why can't separable pure states violate some Bell inequality?
In ch 4 of Preskill's lecture notes on quantum information, he tells us that any entangled pure state of two qubits violate some Bell inequality, whereas no such violation occurs for separable pure ...
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Parallel repetition to amplify the gap for nonlocal games
Suppose for an one-round nonlocal game $G$ with question size $n$, answer size $2$ (i.e the answer is yes or no), a verifier and two provers Alice and Bob sharing $\text{Poly}(n)$ entangled-qubits. If ...
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Why not just use Bell state entanglement in the CHSH game?
In the CHSH game, both Alice and Bob receive random bits $x$ and $y$ from a referee Charlie. Based on the bit values and a strategy discussed between Alice and Bob beforehand they will respond with ...
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Non-local $CNOT$ By means of Ising gates
Consider the circuit below.
This is almost the same as the standard protocol to perform a non-local $CNOT_{0,3}$. The only difference is that I decomposed the upper local $CNOT_{0,1}$ into one Ising ...
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Why only one of the qubits is rotated in the CHSH circuit?
When reading various tutorials on how to calculate CHSH, there is only a single qubit which is rotated inside of the quantum circuit, it is also only ever rotated around a single axis.
I would like to ...
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In the CHSH game, why do $a,b$ need to be the same unless $x=y=1$?
In this lecture, in the CHSH game section, it is claimed that a and b must be the same unless x and y are both 1. Can someone explain why? I see it the other way around.
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Choosing operators for maximal Bell-CHSH violation for an arbitrary state
If I have the density matrix $\rho$ for a bipartite system (each system is two-dimensional), what set of observables should I choose so that I obtain the maximum possible violation of the Bell-CHSH ...
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Expectation values of non-local operators in Qiskit
Is there a convenient way in Qiskit to calculate the expectation value for a non-local operator, i.e. I would like to calculate:
$$ \langle \Psi|O|\Psi \rangle $$
More precisely, I would like to ...
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Local operation to change the maximally mixed 2 qubit state to $\frac{1}{2}(|01\rangle \langle01|+|10\rangle \langle10|)$?
A paper I read talked about local interactions on only a single subsystem, leaving the state of that subsystem invariant, and the observation of this requiring the whole state.
Here is the paper
Now ...
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What type of "local hidden variable" is ruled out when discussing (non)contextuality?
While reading about noncontextuality and the Peres-Mermin square, I encountered the statement that noncontextuality is tightly related to nonlocality à la Bell. For example, (Kleinmann et al. 2011) ...
glS♦
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Is there a way to compute how many hidden variables are needed to describe a given local state?
Consider a bipartite state $\rho$ that is local. By local I mean here that there is a local hidden variable model explaining the correlations resulting from measuring $\rho$. In other words, $\rho$ ...
glS♦
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Density matrix after measuring Bell state in CHSH game
In these notes, the author says the following about the CHSH game
Does Alice and Bob’s ability to succeed more than 75% of the time mean
that they are communicating? Well, we know it’s not possible ...
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What is a non-local state?
The notion of entangled states is very neat, it simply means non-separability of the states. Another important class of states that one often hears is the non-local state. But when do we say that a ...
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Is the boundary of the set of quantum behaviours a polytope?
Consider the standard 2-2 Bell scenario, with two parties each one choosing between two measurement settings, with each measurement setting leading to one of two possible measurement outcomes.
...
glS♦
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What are the vertices of the no-signalling set $\mathcal{NS}$?
Consider the standard 2-2 Bell scenario, with two parties each one choosing between two measurement settings, with each measurement setting leading to one of two possible measurement outcomes.
...
glS♦
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What is the no-signaling set and how can it be related to other types of correlations?
The paper Bell nonlocality by Brunner et. al includes a striking diagram on page 7:
This is fascinating to me because it suggests a framework of categorizing correlations that encompasses classical, ...
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How to show that Werner states produce correlations explainable via local hidden variable models?
Werner states can be written as
$$\rho_W=
p\frac{\Pi_+}{\binom{n+1}{2}}
+(1-p)\frac{\Pi_-}{\binom{n}{2}},
$$
with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...
glS♦
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Why is the quantum discord of $\rho$ zero iff $\rho=\sum_j p_j \pi_j\otimes \rho_j$ for mutually orthogonal projections $\pi_j$?
In (Wiseman 2012), the author mentions (equation (4), page 6), that a state $\rho$ has zero quantum discord (more precisely, zero Alice-discord) if and only if it can be written in the form
$$\rho = \...
glS♦
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Who first studied nonlocal games with probabilistic predicate?
For some background, a nonlocal game consists of questions $x,y\in X,Y$ and answers $a,b \in A,B$; the pair of questions $x,y$ is asked with probability $\mu(x,y)$, and a referee accepts the pair of ...
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Is the No-Cloning Theorem Violated in $C^\ast$-Circuit Models?
In Cleve, et al., the authors discuss self-embezzlement of a catalyst state $\psi$, making the statement on page 2,
[B]y local operations, state $\psi\otimes(\vert 0 \rangle \otimes \vert 0 \rangle)$
...
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What is an example of an entangled state whose correlations are describable with a local hidden variable model?
When talks about CHSH inequality, we always say that the states that violate the inequality are entangled, while some states that do not violate the inequality can also be entangled.
For the latter ...
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How to prove that EPR outcomes have equal probability no matter the basis?
Recently in class, we learned about the EPR state. I know that no matter what basis the first qubit is measured in, the two outcomes have an equal probability. However, how does one prove this? I ...
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Bell's experiment: checking the probabilities
I have some doubts on the calculations behind Bell's experiment, which goes as follows: a pair of entangled photons is shared between two scientists, Alice and Bob, who possess a bunch of polarizers ...
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In Bell's inequalities, what is the meaning of assuming that the physical properties $P_Q,P_R,P_S,P_T$ have definite values?
Two assumptions behind Bell inequalities (Page 117 Nielsen Chuang)
(1) The assumption that the physical properties $P_{Q}$, $P_{R}$, $P_{S}$, $P_{T}$ have definite values
$Q$,$R$, $S$, $T$ which exist ...
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Formal proof of Bell's inequality in CHSH form
I have a sketch of the proof of Bell's theorem that goes as follows: Alice measures an observable $A$ along a direction $\vec a$ with possible outcomes $\pm 1$, and Bob does the same for an observable ...
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Modified CHSH game - Does entanglement help?
I'm thinking about a modified version of the CHSH game and I'm trying to convince myself that in this case, entanglement cannot be used to gain an advantage or else it would imply signalling is ...
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Three qubit identity
Problem:
I'm having trouble seeing how this paper claims the following identity to be true for a three qubit system (labelled by $A$, $B$, and $C$) under a pure state $|\psi \rangle$ with real ...
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Understanding the EPR argument with a simple description using Pauli matrices
Can someone explain the EPR argument with a simple description using Pauli matrices?
Two non-commuting physical quantity are being discussed philosophically whether there is an element of reality ...
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Role of convexity in proof of Monogamy of Bell correlations
In this paper, the authors give a proof of the monogamy principle in quantum physics. I'm having trouble understanding the convexity argument in the proof of Lemma 2 (penultimate paragraph, page 2). I ...
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Difference between Bell's inequality and CHSH
In this section of the Scholarpedia article on Bell's theorem, the first paragraph comments that Bell's original inequality is not ideal for experimental verification because it requires perfect anti-...
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How do I fix the UnboundLocalError?
I have read about the global and nonlocal variable and I know they may solve the problem, but as I'm still naive at this I couldn't figure out how to implement them to solve the UnboundLocalError. ...
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What is the difference between no signaling and non locality at operational and ontological level?
I understand the basic definitions. Locality means Alice's measurements do not affect Bob's and system and that no-signalling means a party can't send information faster than light. I also know that ...
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Where does $xy = a + b \pmod 2$ come from in the context of CHSH inequalities?
I have been looking into the great! video lecture of "CSHS Inequality" by Prof. Umesh V. Vazirani.
There are a few things I have to clarify, hope someone will answer me.
Suppose Alice and ...
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Are separable, orthogonal states LOCC distinguishable?
Consider two states $\sigma_0,\sigma_1\in\text{L}(\mathcal{H}_{AB})$, and suppose $\sigma_0,\sigma_1$ are separable and orthogonal. Is it possible to distinguish between $\sigma_0,\sigma_1$ through ...
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Are Bell states distinguishable through LOCC?
Define $|\psi^{00}\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and $|\psi^{01}\rangle = \frac{1}{\sqrt2}(|00\rangle - |11\rangle)$, and consider the state
$$ |0\rangle\langle 0|^C\otimes |\psi^...
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Understanding Hardy's proof of "nonlocality without inequalities"
I'm reading the proof of "nonlocality without inequality" presented in (Hardy 1992).
In this protocol, we consider two particles (say, an electron and a positron) evolving almost independently: they ...
glS♦
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How does a classical computer simulate nonclassical correlations?
This may be a dumb question, if so please forgive me, it is late at night.
I have learned that a classical computer can simulate a quantum computer in exponential time and space, but classical ...
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What would the CHSH inequality be equal to if the two qubits were separable?
I am writing an Excel spreadsheet to work through the matrix algebra for a simple Bell's game with the following parameters.
$$\newcommand{\bra}[1]{\langle #1|}\newcommand{\ket}[1]{|#1\rangle}A_\pm = ...
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Why is the CHSH inequality defined with a minus sign?
CHSH inequality is defined in the following way. Let $Q, R, S, T$ be two outcomes $\{\pm 1\}$ measurements. The measurements are chosen in a certain way, but that is not our concern right now. We know ...
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What is the number of local deterministic behaviours in a Bell scenario?
Consider a Bell scenario: Alice and Bob perform measurements on a shared system, and each of them has a "measurement box" with a bunch of inputs (corresponding to different measurement settings) and ...
glS♦
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Does the CHSH inequality fully characterise the local polytope?
Consider the standard two-party CHSH scenario. Each party can perform one of two measurements (denoted with $x,y\in\{0,1\}$) and observe one of two outcomes (denoted with $a,b\in\{0,1\}$).
Let $P(ab|...
glS♦
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Are there Bell-like violations that can be observed without collecting statistics?
Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally ...
glS♦
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Understanding the idea of "local hidden state model"
In Cavalcanti and Skrzypczyk (2017), section IIA, pag. 3, while introducing the idea of quantum steering, the authors introduce the idea of Local Hidden State model as following (emphasis mine):
A ...
glS♦
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Is quantum complexity basis-invariant?
Quantum computing refers (occasionally implicitly) to a "computational basis".
Some texts posit that such a basis may arise from a physically "natural" choice.
Both mathematics and physics require ...
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Are inseparable states with positive partial transpose nonlocal?
In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, ...
glS♦
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Non maximally entangled states for QKD
Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
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EPR states with permuted qubits
Suppose I prepare following state consisting of (for example) three EPR pairs:
$$\lvert\Psi\rangle = \frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}\otimes\frac{\lvert00\rangle+\lvert11\rangle}{\...
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How is Bell’s Inequality converted to the CHSH inequality?
Bell’s inequality is $$S = P(a,b)-P(a,d)+P(c,b)+P(c,d) \leq 2,$$ which is calculated as $$S = ab – ad + cb + cd \leq 2.$$
The CHSH version is:
$$E = \frac{N_{11} + N_{00} - N_{10} -N_{01}} {N_{11} + ...
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Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?
Context:
Three coins on the table. Each is either heads or tails. You can
uncover any one of the three coins, revealing whether it is heads or
tails but then you choose two the other two coins ...
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