2022 Developer Survey is open! Take survey.

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)

Filter by
Sorted by
Tagged with
1 vote
1 answer
35 views

Why use superpositions to write states even when they are not entangled?

I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
user avatar
  • 11
2 votes
0 answers
51 views

Is there a relation between quantum entanglement and inclusion-exclusion principle?

If an entangled state is not simply the multiplication of each particle wave function: $$ |\Psi_{ABC}\rangle \neq |\Psi_{A}\rangle|\Psi_{B}\rangle|\Psi_{C}\rangle $$ then can we apply the inclusion ...
user avatar
3 votes
1 answer
54 views

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

This question is about the Magic Squares game. Links here, here and link here in which two players try to win a game. It's a cooperative game - either the team wins or the team loses. It is claimed ...
user avatar
0 votes
0 answers
27 views

what does the multiplication of Quantum state represent? [duplicate]

According to my understanding of QC/QM: A matrix is a function/operation which when applied on vectors, changes/rotates them. Ket and bra notation is used to denote quantum state. Question 1: ...
user avatar
2 votes
2 answers
354 views

Depth circuit optimization for 6-qubits GHZ state

Standard implementation of the generalized GHZ circuit has a depth that grows linearly with the number of qubits. I am looking for an optimized version in the case of 6 qubits. Is there any?
user avatar
0 votes
2 answers
57 views

Create a 2-qubit quantum circuit with given state probabilities

Let's say we are given two probability values $p_1 > 0$ and $p_2 > 0$, with $p_1+p_2 \leq 1$ but not necessarily equals to $1$. We are asked to create a 2-qubit quantum circuit with state $|01\...
user avatar
1 vote
0 answers
31 views

Entanglement across a bi-partition of a many particle system

Alice and Bob each have two qubits labelled $A', A$ and $B, B'$ respectively. The density operator of the total system is $\rho_{A'ABB' } \in \mathcal{H}^2 \otimes \mathcal{H}^2 \otimes \mathcal{H}^2 \...
user avatar
2 votes
1 answer
32 views

Show that any two product states of the same dimension are LU-equivalent

States $|Ψ \rangle$, $|Φ\rangle$ on $C_d⊗C_{d′}$ are said to be equivalent up to Local Unitarities (LU-equivalent) if there exist unitaries $U : C_d → C_d$ and $V : C_{d′} → C_{d′}$ such that: $|Ψ \...
user avatar
0 votes
2 answers
70 views

Prove whether the state $|0\rangle\otimes|0\rangle+|1\rangle\otimes|+\rangle$ is entangled

I'm trying to figure out whether or not the following state is entangling: $$|Ψ⟩ = 1/\sqrt2 (|0⟩ ⊗ |0⟩ + |1⟩ ⊗ |+⟩)$$ Expanding it out I get: $$1/\sqrt2 (|0⟩ ⊗ |0⟩ + 1/\sqrt 2(|1⟩ ⊗ |1⟩ + |1⟩ ⊗ |0⟩))$$...
user avatar
2 votes
1 answer
34 views

Calculating entanglement with CRZ Gates on non-neighbor qubits

I'm trying to prove that my quantum circuit is behaving the way I want it to, which means I want to calculate its state vector. Until entanglement, I can show it works using the bloch-sphere - after ...
user avatar
  • 147
-3 votes
1 answer
43 views

Write in seperable form [closed]

Consider the two-qubit state $$𝜌 = 1/4 \{(|00⟩ + |11⟩) (⟨00| + ⟨11|) + (|01⟩ + |10⟩) (⟨01| + ⟨10|)\}.$$ Though looks like an entangled state, it is in fact a separable one. Write it down in the ...
user avatar
1 vote
2 answers
153 views

Is there a non-deterministic protocol for entanglement generation between distant parties?

I'm aware that one can imperfectly clone entanglement that's shared between two parties (i.e. Bell pairs) using deterministic quantum cloning machines to produce two, lower fidelity entangled states. ...
user avatar
  • 95
4 votes
2 answers
145 views

Is there a way to convert a superposition $\sum_i a_i |x_i\rangle$ into $\sum_i |a_i,x_i\rangle$?

I am wondering if there is a way to convert a superposition $$\left|\phi\right>=\sum_{i}a_i\left|x_i\right>$$ into $$\left|\phi'\right>=\frac{1}{|{\rm norm}|}\sum_{i}\left|a_i,x_i\right>,$$...
user avatar
0 votes
1 answer
38 views

How does the teleportation step work in entanglement dilution?

Consider the entanglement dilution protocol for pure states, as described in Preskill's notes (Link to pdf, see around page 32). The context is that Alice and Bob share $k=n(S(\rho_A)+\delta)$ Bell ...
user avatar
  • 18.2k
0 votes
1 answer
71 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 ...
user avatar
  • 1
6 votes
0 answers
59 views

Five qubits can be entangled in how many ways?

It is well-known that there are two ways to entangle three qubits (https://arxiv.org/abs/quant-ph/0005115) and nine ways to entangle four qubits (https://arxiv.org/abs/quant-ph/0109033). I found in a ...
user avatar
  • 161
1 vote
1 answer
67 views

Why can you check for entanglement using the quantum Fourier transform?

I'm reading this paper on quantum random oracles, and I have some fundamental questions about certain statements that seem to be intuitive (but I can't seem to figure it out). My goal is to have a ...
user avatar
2 votes
1 answer
120 views

What really is Quantum Entanglement and what are its benefits? [closed]

My question is very basic. I am studying quantum gates from various books. I read that by putting a CNOT gate, the qubits are entangled. Is this correct? What exactly entanglement means and what is ...
user avatar
6 votes
0 answers
67 views

Verification of local unitary equivalence between two pure states

This might be a non-trivial and hard problem. I've been thinking about this for days but couldn't find a good answer, so I hope any of you could give me a good answer/intuition for me to move forward. ...
user avatar
1 vote
1 answer
70 views

What is the meaning of eigenvalues and eigenvectors of quantum gates?

My question is very basic but I was still unable to find its correct answer. I am studying quantum gates from various books. They calculate eigenvalues and eigenvectors with quantum gates. What is the ...
user avatar
5 votes
1 answer
112 views

What is a bipartite quantum state?

I'm very confused for the definition bipartite quantum states. If it's just quantum states defined in $H_1 \otimes H_2$, then if $H_1$ and $H_2$ both are just 1 qubit system, then the bipartite ...
user avatar
1 vote
1 answer
40 views

Efficient Protocol for Entanglement Purification

By using entanglement purification, we can produce a high-fidelity entangled state from several pieces of low-fidelity entangled states. From my study, there is a protocol proposed by Bennett et al. ...
user avatar
1 vote
1 answer
57 views

How to prove that there are only 2 classes in 3 qubits entangled state?

Given 2 non-biseparable classes of 3 qubits (more generally tripartite) entangled states : $|GHZ\rangle = \frac{1}{\sqrt{2}} \left(|000\rangle + |111\rangle\right) $ $|W\rangle = \frac{1}{\sqrt{3}} \...
user avatar
5 votes
0 answers
35 views

Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?

This question is tightly related to What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?. In there, examples were given of separable states $\rho$ ...
user avatar
  • 18.2k
2 votes
3 answers
125 views

does CNOT gate cause entanglement?

I have just started learning Quantum computing. Pairs of qubits that are “entangled,” which means the two members of a pair exist in a single quantum state. Changing the state of one of the qubits ...
user avatar
3 votes
2 answers
60 views

What justifies using tensor product of matrices for parallel gates when applying them to an entangled state?

In my university we defined tensor product of two matrices $A$, $B$ as a matrix $A \otimes B$ such that for any vectors $\left| \phi \right>$, $\left| \psi \right>$ the following is satisfied: $$...
user avatar
  • 33
3 votes
0 answers
39 views

Can separable states have quantum mutual information larger than one?

Consider bipartite (qubit) systems. The classical mutual information between a pair of binary registers, $$I(X:Y)\equiv H(X)+H(Y)-H(X,Y),$$ is always lesser than $1$ (and non-negative). On the other ...
user avatar
  • 18.2k
2 votes
3 answers
267 views

Show that trace over 1 system of GHZ state is unentangled

If I compute the trace over 1 system of the GHZ state I have a matrix with no off diagonal non-zero elements. Is this sufficient evidence that the reduced 2 qubit state is unentangled?
user avatar
  • 23
1 vote
1 answer
22 views

Does the entanglement have the conventional meaning in optical interferometers?

Let's consider a two-mode quantum state described in Fock state. A N00N state can be written as $|\psi _{{\text{NOON}}}\rangle ={\frac {|N\rangle _{a}|0\rangle _{b}+e^{{iN\theta }}|{0}\rangle _{a}|{N}...
user avatar
  • 2,408
0 votes
0 answers
68 views

Do quantum states with a single parameter give any theoretical or experimental advantage compared to multi-parameter ones?

If a quantum state is a single parameter two-qubit mixed entangled state then is there any theoretical or experimental advantage compared to a multi-parameter state? suppose, we take a single ...
user avatar
2 votes
2 answers
274 views

What is the difference between "permutationally invariant" and "symmetric" states?

In this paper: ArXiv and PRL links, the authors give the definition of two $d\times d$ qudits to be permutationally invariant states if $\varrho$ is invariant under exchanging the particles. This can ...
user avatar
  • 533
4 votes
1 answer
40 views

How can the transformation between entangled states like two Bell states be derived?

As it is stated in this post: Transforming the first Bell state into the other Bell states, one can transform the $|\phi^{+}\rangle$ state to the $|\psi ^{-}\rangle$ by applying the tensor product of ...
user avatar
  • 41
1 vote
2 answers
94 views

Creating an entangled state in Hadamard basis (Qiskit)

I am familiar with building a quantum circuit of an entangled pair providing that they are in the computational basis: |ψ⟩ = 1/√2 (|00⟩ + |11⟩) This circuit works great. I am trying to build the ...
user avatar
-1 votes
1 answer
58 views

Entanglement for Byzantine fault problem

In "Proof of Work"-Blockchains, the block is added by the member who first solves a hard problem. That's very expensive. But if all blockchain-members get an entangled dice, that randomly ...
user avatar
1 vote
1 answer
88 views

Understanding phase kickback caused by the CNOT gate

Applying the CNOT gate to the state |+-⟩ would result in the state |--⟩ as per: What has occurred is a "phase kickback". The relative negative phase from the target qubit has transferred to ...
user avatar
7 votes
2 answers
882 views

What is this circuit doing?

Can anyone help me understanding what is this circuit doing ? The circuit can be reproduced with qiskitas follows: ...
user avatar
  • 115
-2 votes
1 answer
130 views

Does this quantum algorithm to check for a permuting function make sense? [closed]

Even "Deutsch's algorithm" seems too difficult. Maybe I found an algorithm that is more appropriate for people without knowledge. Less to explain. Easy to understand. Or do you have ...
user avatar
1 vote
0 answers
25 views

What's the map from any linear classical codes to entanglement-assisted stabilizers codes

When a linear code is self-dual, its parity check matrix can be used to easily define a stabilizer code. From my understanding, thanks to entanglement-assisted stabilizer codes, it is possible to ...
user avatar
6 votes
1 answer
128 views

Schmidt decomposition for tripartite system $ABC$ with vanishing mutual information between $A$ and $C$

Suppose I have a tripartite system $ABC$ in a pure state $|\psi_{ABC}\rangle$ with mutual information $I(A:C)=0$. This implies that the reduced density matrix $\rho_{AC}$ factorizes as $\rho_{AC} = \...
user avatar
  • 353
5 votes
3 answers
80 views

What physically limits qubit connectivity in superconducting chips?

All the superconducting based quantum computers I'm familiar with have a maximum of 4 nearest neighbors per qubit. Trapped ion architectures seem to be able to drive entangling gates between all pairs ...
user avatar
  • 549
0 votes
0 answers
59 views

Probability that the measurement will give +1 as a result for entangled state

On page 28 of this paper the following calculation is made: $$P\left(\sigma_{\theta}=+1\right)=\left|\left\langle+\mid \Psi_{0}\right\rangle\right|^{2}=\cos ^{2} \frac{\theta}{2}$$ Can someone help me ...
user avatar
  • 21
3 votes
1 answer
121 views

Deutsch's algorithm makes no sense

Here are the 4 classical functions over $1$ bit we're examining, $f(x) = \{0,1\}, x \in\{0,1\}$: identity (balanced) -> $f(x) = x$: \begin{bmatrix}1&0\\0&1\end{bmatrix} negation (balanced) ...
user avatar
5 votes
3 answers
1k views

What is a "maximally mixed state"?

What is meant by maximally mixed states? Does this mean that there are partially mixed states? For example, consider $\rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right|$ and $\rho_W =...
user avatar
  • 255
5 votes
1 answer
78 views

Why do we use the Bell state $|00\rangle+|11\rangle$ for quantum teleportation?

In the quantum teleportation protocol we use the Bell state given by $$\frac{1}{\sqrt{2}} \left( |00\rangle + |11\rangle\right). $$ My intuition tells me this works is because we can transform this ...
user avatar
  • 51
5 votes
1 answer
82 views

What does equality of partial traces, ${\rm Tr}_1\rho={\rm Tr}_1\sigma$, say about a pair of states $\rho,\sigma$?

Let $\rho,\sigma$ be a pair of bipartite quantum states such that ${\rm Tr}_1\rho={\rm Tr}_1\sigma$. What does this tell us about $\rho,\sigma$? More precisely, is there a way to write more explicitly ...
user avatar
  • 18.2k
5 votes
2 answers
125 views

Relationship between entanglement and complex vector space

In the article Quantum Algorithm Implementations for Beginners I found the following sentence Entanglement makes it possible to create a complete $2^n$ dimensional complex vector space to do our ...
user avatar
2 votes
1 answer
57 views

Kind of errors on entangled states

I see on this chapter that, when noise applies to an even number of entangled qubits, such noise can be considered as operating only on half of those qubits. This is interesting, but I'm not sure if I'...
user avatar
2 votes
1 answer
57 views

Why von Neumann entropy requires diagonalization and linear entropy doesn't?

The linear entropy for a state $\rho$ is defined as $S_L = 1 - Tr[\rho^2]$, while as von Neumann entropy as $S_{N} = -Tr[\rho \ln \rho]$. According to quantiki, the computation of $S_{N}$ requires ...
user avatar
  • 476
3 votes
0 answers
76 views

Relation between geometric and discrete circuit complexity

Geometric complexity of a unitary, as introduced for example here https://arxiv.org/abs/quant-ph/0502070, measures the length of a geodesic connecting the identity matrix and a given unitary in the ...
user avatar
2 votes
0 answers
43 views

What it means to say that SWAP gate has maximum operator entanglement entropy?

In this (freely available) article, just below equation 14, it says The SWAP operator has the maximum operator entanglement entropy... The operator entanglement entropy, denoted by $E(U)$ for an ...
user avatar
  • 476

1
2 3 4 5
12