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 after breaking the entanglement does the phase disk in the second qbit not match the result?
I am new in IBM composer quantum and I have a doubt.
I have the next circuit
After reinitializing q0 and reading it. (breaking entanglement) The phase disk for qubit q1 says that 100% is 0, but the ...
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General Proof of the Statement that You Need $1$ Ebit and $2$ Bits to Teleport $1$ Qubit?
I understand from the standard teleportation protocol that 1 ebit is used up in teleporting 1 qubit and thus, cannot be used again -- and thus, we need 1 fresh ebit of shared entanglement between ...
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In a state $\alpha \vert HL \rangle + \beta \vert VR \rangle$ can a particle be measured in the $\{|L\rangle,|R\rangle\}$ basis?
Given a pair of entangled particles:
$\alpha \vert HL \rangle + \beta \vert VR \rangle$
where:
$\alpha^2 + \beta^2=1$
$H$ and $V$ are orthonormal vectors.
$L$ and $R$ are orthogonal vectors (but not ...
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How to check if a statevector is made of product of EPR pairs in Qiskit?
I have a statevector of 10 qubits. I want to check if the qubits 0,1 and 2,3 are EPR pairs/Bell pairs. The other qubits (4,5,6,7,8,9) have been measured.
There are four possible 2-qubit states that ...
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A doubt regarding Mach-Zehnder Interferometer functioning
I am tying to understand the working of Mach-Zehnder Interferometer in the physical sense (how it behaves and why it does so etc.). The source I am referring to is this: (https://www.cs.princeton.edu/...
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A doubt regarding probabilities of a entangled states?
Given an state of entangled particle pair in Horizontal-Vertical basis ($H,V$):
$ \psi_{hybrid}= (1/\sqrt2) (HH+VV)$
Let us define a new Right-Left basis ($R,L$) as follows:
$L=(1/\sqrt2)(H-iV)$
$R=(...
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Implementing quantum swap operation such that $|x\rangle|f(x)\rangle$ changes to $|x\rangle|f(x+1)\rangle$
Suppose that a quantum state $|\psi\rangle$ in question is $|\psi\rangle \propto \sum_x |x\rangle|f(x)\rangle$.
I want to implement a quantum swap operation such that computational basis $|x\rangle|f(...
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Why can two atoms can be entangled?
As a qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in ...
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How to know if a given 2-qubit gate is separable into two single-qubit gates?
This question seems fairly trivial but I'm struggling to find an elegant way to determine such. Suppose that you have a unitary matrix $U$ (not necessarily a density matrix) and you want to know if $U=...
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Can EPR pairs be established with only classical communication?
EPR pairs are used in superdense coding and quantum teleportation, but these protocols assume that Alice & Bob "share" half of an entangled quantum state.
How does this "sharing&...
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How to check if a $n$-qubit unitary is the tensor product of single-qubit unitaries
Let's assume I give you the expression of a unitary matrix acting on two qubits that is:
$$U=\sum_{i} A_i \otimes B_i$$
for some operators $A_i$ and $B_i$.
Is there a simple criterion allowing you to ...
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What is the difference between $|\Phi^+\rangle=\frac1{\sqrt2}(|0,0\rangle+|1,1\rangle)$ and a mixture of $|00\rangle$ and $|11\rangle$?
I struggle to see the difference between $|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B + |1\rangle_A \otimes |1\rangle_B)$ and the mixed state defined with probabilities {0.5, ...
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How to convert tableau representation of random clifford gate into its matrix representation using stim?
I am currently trying to benchmark my code with a Haar circuit and I require to sample clifford gates in matrix form. I know a function "stim.Tableau.random(n)" which does that and gives me ...
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How does a Hadamard gate impact the initial/previous values of a Qubit? [closed]
I've been studying Quantum Computing and one thing that intrigued me is:
given a qubit q1 with an initial value x, when I apply a Hadamard gate on it, then it goes to superposition, so the probability ...
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Do unitary matrices acting on entangled states always give a quantum state?
I'm trying to understand what happens when Alice(Bob) apply a unitary to her(his) part of an entangled state. Let us consider the following unitary transformations:
$$U_1 = \frac{1}{\sqrt{2}}
\...
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Understanding Controlled Operation
while reading an article on phase kickback, I came across this paragraph.
When you apply a controlled operation on a target qubit that is in an eigenstate of the unitary, what’s essentially happening ...
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Must two separable states that are $\epsilon$-close in trace distance admit close separable decompositions?
$\newcommand{\complex}{\mathbb{C}}$ Let $n$ and $m$ be positive integers. Does there exist a continuous function $f: [0,1] \rightarrow [0,1]$ such that $f(0)=0$, and whenever two separable density ...
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What is the maximally entangled state in Choi matrix?
For a quantum channel $\mathcal{E}$, Choi matrix is defined as follows:
$C(\mathcal{E}) = (\mathcal{E} \otimes I) (\sum_{i}\lvert ii\rangle \sum_j \langle jj\lvert) $, where $\sum_{i}\lvert ii\rangle$ ...
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How to tell if a state is entangled?
I've read that to tell if a 2 qubit state is not entangled e.g. $$αγ|00⟩+αλ|01⟩+βγ|10⟩+βλ|11⟩$$ then multiplying the coefficients of $|00\rangle$ and $|11\rangle$ should equal the same as multiplying ...
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Entanglement test in Pauli Representation
A 2-qubit state's density matrix can be written in Pauli representation as:
$$
\rho = \frac{1}{4} \sum_{i, j = 0}^{3} c_{i, j}\; \sigma_i \otimes \sigma_j
$$
For a given $\rho$, to compute the ...
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What is the difference between "maximally entangled" and "entangled" states?
when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
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Optimising Tomography on logical computation
I already got part of the answer in thread. Which says that if I want to perform a state tomography on a known state, the estimation can be simplified.
In the case of "GHZ-class", citing ...
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How to get to the formula for the entanglement of formation of two-qubit states?
An explicit formula for the entanglement of formation $E(\rho)$ for an arbitrary two-qubit state $\rho$ was given by Wooters in Entanglement of Formation of an Arbitrary State of Two Qubits. The ...
glS♦
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Why does $\sigma_y$ seem to have a special role in the two-qubit concurrence?
The concurrence of a two-qubit state $\rho$ can be written as
$$\mathcal C(\rho) = \max(0, \lambda_1-\lambda_2-\lambda_3-\lambda_4),$$
where $\lambda_i$ are the eigenvalues of $|\sqrt\rho\sqrt{\tilde\...
glS♦
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Optimising state tomography for fully entangled states
As tomography methods are usually inefficient, it's interesting to find good approximation.
I was wondering the following:
Assume one wants to estimate a state $\rho$ on $n$-qubits.
Given a basis of ...
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Why use superpositions to write states even when they are not entangled?
I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
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Is there a relation between quantum entanglement and inclusion-exclusion principle?
If an entangled state is not simply the multiplication of each particle wave function:
$$ |\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?
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 ...
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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