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Questions tagged [entanglement]

For questions about the principle and application of quantum entanglement. It is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. (Wikipedia)

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Generalization of Bell inequality for N-partite n-level systems

There are generalizations of Bell inequalities for systems of $N$ qubits, see this work I am looking for a generalization of such inequalities when the system in question is that of N qudits, with ...
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29 views

Tests of entanglement between one and many qubits

I have a 5-qubit state $|\psi \rangle$, which has a physical interpretation that the middle qubit is the "impurity" with spin $s_{imp} = 1/2$. The rest 4 qubits highlight the presence of ...
4 votes
1 answer
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Is purity convex in time?

Is the purity $\mathrm{Tr}[\rho(t)^2]$ of a quantum state $\rho(t)$ that evolves according to a time-independent Lindbladian $\partial_t \rho = \mathcal{L}[\rho]$ convex in time $t$? I suspect the the ...
1 vote
1 answer
30 views

CHSH game sharing more general states

In the CHSH game, when the players share EPR states they can achieve best the winning rate of approximately 85% which can be proved through the Tsirelson's bound. I wonder what the best winning rate ...
7 votes
1 answer
139 views

What is the stabilizer rank of the W state?

The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal $r$ such that \begin{equation} |{\psi}\rangle = \...
4 votes
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90 views

Proof that quantum entanglement does not increase the asymptotic capacity of classical channel

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the ...
0 votes
2 answers
47 views

Why do we need to put the control qubit in superposition in Bell State?

I'm new to quantum computing, so I hope you don't find this question tedious. However, after watching many hours of lectures and reading online, I still don't 100% understand why we need to initialize ...
14 votes
0 answers
581 views

Relation between quantum entanglement and quantum state complexity

Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
2 votes
0 answers
61 views

List of inequalities for purity of a traced out bipartite system

I would like to know if there are inequalities related to the purity of the partial trace of a bipartite system. The purity $P$ of a density matrix $\rho$ is given by $$P(\rho) = Tr(\rho^2).$$ The ...
2 votes
1 answer
49 views

Can we perform teleported-error-correction with noisy Bell pairs?

It is well-known that in https://arxiv.org/abs/quant-ph/0312190 that error correction can be performed by teleportation on the logical level, so prepare one logical Bell pair and (logical?) Bell ...
2 votes
2 answers
90 views

Do we consider the entangled-based protocol E91 to be a device-independent protocol?

Since both rely on Bell inequalities to maintain security, does the Ekert protocol rely on trustworthiness of the devices?
1 vote
1 answer
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How to calculate the number of m-partitions of an N-partite quantum state?

I am reading the structure of multipartite entanglement from section 3.3. It is stated there that the number of possible partitions of $N$ parties into $m$ parts is given by $\frac{m^N}{m!}$. I could ...
2 votes
1 answer
39 views

What is the F12 rule for the Game of Life

This is more of a help call to find a specific rule set for the game of life. I'm currently reading the "Entanglement in the Quantum Game of Life", however they refere to the classical F12 ...
1 vote
2 answers
94 views

Can Bell states be reexpressed with respect to arbitrary local bases?

Suppose I take the Bell state $\Phi^+ = \vert 00\rangle + \vert 11\rangle$. Is it true that I can choose any basis with basis vectors $\vert b_0\rangle$ and $\vert b_1\rangle$ and reexpress the same ...
1 vote
0 answers
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How do two-way protocols allow to extract entanglement from states like Werner's?

As discussed in [Lo and Popescu 1999], it is always possible to distill entanglement from pure bipartite states using a one-way protocol. The gist of the idea, as I understand it, is Proposition 1 in ...
3 votes
3 answers
249 views

How to mathematically describe the action of CNOT on the control qubit alone?

Basically the title. From what I know, starting from the $|{+0}\rangle$ state where the reduced density matrix of the first qubit $|+\rangle$ is $\frac{1}{2}\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{...
10 votes
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130 views

Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
0 votes
1 answer
59 views

doesn't a reset on an entangled qubit collapse a superposition?

When I reset an entangled qubit then measure it looks a superposition isn't collapsed to a certain states. In my experiment, the state just before applying a reset is: $$\frac{1}{2}(|000⟩+|011⟩+|101⟩+|...
1 vote
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53 views

Prove that convex combinations of product states admit a hidden variable model

Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
6 votes
1 answer
388 views

What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?

As shown e.g. in Watrous' book (Proposition 6.6, page 314), a separable state $\rho$ can always be written as a convex combination of at most $\mathrm{rank}(\rho)^2$ pure, separable states. More ...
2 votes
0 answers
75 views

Uniqueness, absolutely maximally entangled states, and the 3 qutrit code

There is a well known $ [[3,1,2]]_3 $ qutrit stabilizer code with stabilizer generators $ XXX $ and $ ZZZ $. This code is related to a $ [[4,0,3]]_3 $ qutrit stabilizer state with stabilizer ...
5 votes
1 answer
3k views

What is the difference between "maximally entangled" and "entangled" states?

when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
1 vote
1 answer
20 views

In e91 protocol, if one of the bases combination was not chosen, what should be done to avoid division by zero?

In e91 protocol, if one of the bases combination was not chosen, what should be done in this case to avoid division by zero? One solution that comes to mind is setting the whole value to zero, but is ...
3 votes
1 answer
214 views

What are the possible gates that I can use to vary input states before CNOT?

We know that the noise of the $\text{CNOT}$ gate varies depending on the input state before it. What are the gates that I can put in the place of the 4 identity gates above to change the input state ...
0 votes
1 answer
148 views

Trouble re-creating quantum psuedo-telepathy

I am trying to replicate the results from this webpage here utilizing qiskit: http://twistedoakstudios.com/blog/Post6536_implementing-quantum-pseudo-telepathy Since the splitter gate mentioned in the ...
2 votes
2 answers
69 views

In quantum teleportation, why does measuring entanglement not destroy the whole state?

In quantum teleportation, we have three qubits. Sender, receiver and ancillary. First, we entangle the ancillary and target qubit. Next, we entangle ancillary and sender qubits. Now, the whole system ...
3 votes
1 answer
54 views

Benefits of using quantum encrypted keys

Considering, in a perfect world everyone has the capability to create a quantum key. What would the benefits of using quantum encrypted keys instead of using classically encrypted keys? Besides the ...
1 vote
1 answer
37 views

E91-Protocole the type of Bell state use in this protocol

my question is, what is the type of the Bell state used in Ekert-91 link for Bell states in question correlated or anti-correlated. And if they can use both of them , how do Alice & Bob know ...
5 votes
2 answers
251 views

$M(\rho)=\operatorname{Tr}_2[U(\rho\otimes\rho_2)U^{\dagger}]$ is unitary $\iff U=U_1\otimes U_2$, a product of $2$ unitary operators?

Let $\rho : V_1 \to V_1 $ and $\rho_2 : V_2 \to V_2 $, where $V_1$ and $V_2$ are Hilbert spaces. Suppose that $U:V_1\otimes V_2 \to V_1\otimes V_2$ is a unitary operator. Define a map $M : L(V_1, ...
2 votes
1 answer
137 views

How to analyse a quantum circuit with an uncertain gate F?

The following quantum circuit consists of two CNOT gates in the middle of the circuit. The two-qubit input quantum register $|x\rangle$ is an arbitrary quantum state and can be set by the user. The ...
1 vote
1 answer
98 views

Efficient Clifford simulation and entropy of reduced density matrices

Suppose I have a Clifford circuit $C$ and I want to estimate the entanglement entropy of a subset of two qubits, say, $\{q_0, q_1\}$, i.e. the quantity $$S(\rho_{q_0 q_1}) = - \text{Tr}[\rho_{q_0 q_1} ...
1 vote
1 answer
100 views

Entanglement-based attack on E91 protocol

My first question is if the bell pair that Alice and Bob share for the E91 protocol matters since I've seen different resources use different pairs for the explanation. My second question is say they ...
3 votes
1 answer
159 views

How to understand the idea of maximal entanglement intuitively?

I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
3 votes
1 answer
46 views

What is the general form for GHZ and W class states?

I am reading the following paper on mixed three-qubit states. It states that any three–qubit pure state can be written as (equation 1 of the paper) $|\psi_{GHZ}\rangle=\lambda_0 |000\rangle+\lambda_1 ...
4 votes
2 answers
229 views

Can a non-local unitary operator preserve separability

Consider a $2$-qubit system with Hilbert space $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$. A pure separable state in $\mathcal{H}$ is of the form $\lvert \psi_1 \rangle \otimes \lvert \...
0 votes
1 answer
73 views

Distributing entanglement using entanglement swapping

I've read papers that consider the problem of sharing entanglement between A and C with an intermediate B. A and B share an entangled state and so do B and C. Then, entanglement swapping is used to ...
3 votes
1 answer
113 views

How does quantum teleportation not lose information?

This may be a bit of an elementary question, but I think understanding it will help me understand fundamentally what makes quantum algorithms a bit magical. Alice starts with a message she wants to ...
2 votes
3 answers
445 views

Why are entanglement breaking channels, defined as $\Phi(\rho)=\sum_a \operatorname{Tr}(\mu(a)\rho)\sigma_a$, entanglement breaking?

Define an entanglement breaking channel $\Phi$ as a channel (CPTP map) of the form $$\Phi(\rho) = \sum_a \operatorname{Tr}(\mu(a)\rho) \sigma_a\tag A$$ for some POVM $\{\mu(a)\}_a$ and states $\...
0 votes
1 answer
118 views

This is a question about IBM quantum circuit used to generate the quantum cheque state

I'm learning about quantum cheque. And I read "Experimental realization of quantum cheque using a five-qubit quantum computer" which is written by Bikash K. Behera ,Anindita Banerjee and ...
0 votes
1 answer
35 views

Synthesizing quantum circuits from unitary matrices vs quantum state vectors, and determining qubit entanglement

I'm studying how to build quantum circuits and understand qubit entanglement. The following are my two confusing questions. I would greatly appreciate any assistance or insights regarding these ...
0 votes
1 answer
63 views

Maximum entanglement entropy of a random circuit

Consider the random quantum circuit below where the gates are randomly taken from SU(4) accordingly with the Haar measure. I am looking to determine an upper bound on the entanglement entropy between ...
1 vote
1 answer
197 views

How is phase kickback possible if qubits are unentangled?

If I have two independent (unentangled) qubits, let's say one in state |1> and the other one in some superposition state with equal amplitudes and arbitrary phases. If I measure the qubit that is ...
1 vote
1 answer
73 views

Does measurement in different bases allow for FTL communication?

Imagine for a moment that we could distinguish between arbitrary quantum states. We’ll show that this implies the ability to communicate faster than light, using entan- glement. Suppose Alice and Bob ...
3 votes
0 answers
37 views

Is entanglement trainable?

There exists a famous result from Google that the gradients of the parameters of quantum neural networks (QNN) vanish exponentially with the number of qubits in the quantum circuit. Their result ...
2 votes
0 answers
22 views

Is a state in the GHZ entanglement class iff it's true 3-partite entangled and at least one of its reduced states is mixed?

Consider 3-qubit state. In W. Dür et al. (2000), it is stated that a 3-qubit state can be 3-partite entangled in 2 different ways. We call it entanglement classes. GHZ state is a representative of one ...
3 votes
2 answers
815 views

Question about DIY Quantum Computer Prototype

I recently came across these 2 videos on Coursera which show how to build a simple quantum computer that can implement the simplest case of the Deutsch-Jozsa algorithm (which uses only 2 qubits). ...
2 votes
1 answer
114 views

Minimizing $1 - \text{Tr}(\Phi(\rho,U)^2)$

I am looking for a computationally efficient way to minimize the following function. Let $$\Phi(\rho, U) = \text{Tr}_2(U\rho U^\dagger)$$ be a reduced density matrix where $\rho = \overline{\rho}_1 \...
3 votes
1 answer
151 views

Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings. Say you ...
-2 votes
1 answer
52 views

Special entangled tripartite state

Suppose three particles a, b and c a is entangled with b, a is entangled with c, b and c are separatable Is it possible?
1 vote
1 answer
43 views

Why does Lidar define a decoherence-free subspace as "a subspace that undergoes purely unitary evolution"

In this paper from 2014, Lidar defines: "an open system which undergoes purely unitary evolution (possibly only in a subspace of its Hilbert space) is said to be decoherence-free." Why is ...

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