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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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 ...
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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 ...
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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 ...
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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:
...
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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?
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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\...
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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 \...
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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 \...
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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:
$$1/\sqrt2 (|0⟩ ⊗ |0⟩ + 1/\sqrt 2(|1⟩ ⊗ |1⟩ + |1⟩ ⊗ |0⟩))$$...
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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 ...
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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
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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.
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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 $$\left|\phi'\right>=\frac{1}{|{\rm norm}|}\sum_{i}\left|a_i,x_i\right>,$$...
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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 ...
glS♦
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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 ...
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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 ...
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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 ...
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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 ...
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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.
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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 ...
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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 ...
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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.
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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}} \...
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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 $\rho$ ...
glS♦
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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 ...
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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:
$$...
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Can separable states have quantum mutual information larger than one?
Consider bipartite (qubit) systems. The classical mutual information between a pair of binary
registers,
$$I(X:Y)\equiv H(X)+H(Y)-H(X,Y),$$
is always lesser than $1$ (and non-negative). On the other ...
glS♦
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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?
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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}...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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What is this circuit doing?
Can anyone help me understanding what is this circuit doing ?
The circuit can be reproduced with qiskitas follows:
...
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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 ...
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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 ...
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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} = \...
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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 ...
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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}$$
Can someone help me ...
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Deutsch's algorithm makes no sense
Here are the 4 classical functions over $1$ bit we're examining, $f(x) = \{0,1\}, x \in\{0,1\}$:
identity (balanced) -> $f(x) = x$: \begin{bmatrix}1&0\\0&1\end{bmatrix}
negation (balanced) ...
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What is a "maximally mixed state"?
What is meant by maximally mixed states? Does this mean that there are partially mixed states?
For example, consider $\rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right|$ and $\rho_W =...
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Why do we use the Bell state $|00\rangle+|11\rangle$ for quantum teleportation?
In the quantum teleportation protocol we use the Bell state given by
$$\frac{1}{\sqrt{2}} \left( |00\rangle + |11\rangle\right). $$
My intuition tells me this works is because we can transform this ...
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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 ...
glS♦
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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 ...
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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'...
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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 ...
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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 ...
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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 ...
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