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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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How do I show that a two-qubit state is an entangled state?

The Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle )$ is an entangled state. But why is that the case? How do I mathematically prove that?
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24 votes
3 answers
2k views

Is entanglement transitive?

Is entanglement transitive, in a mathematical sense? More concretely, my question is this: Consider 3 qubits $q_1, q_2$ and $q_3$. Assume that $q_1$ and $q_2$ are entangled, and that $q_2$ and $q_3$...
Peter's user avatar
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19 votes
3 answers
11k views

What does it mean for two qubits to be entangled?

I have done some sort of online research on qubits and the factors making them infamous i.e allowing qubits to hold 1 and 0 at the same time and another is that qubits can be entangled somehow so that ...
Arshdeep Singh's user avatar
18 votes
2 answers
10k views

How to implement the 4 Bell states on the IBM Q (composer)?

I would like to simulate the 4 "Bell States" on the IBM composer? How can I best implement those 4 Bell states using the existing set of gates ? Here below you see the definition of the 4 Bell ...
JanVdA's user avatar
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17 votes
1 answer
1k views

Is entanglement necessary for quantum computation?

Entanglement is often discussed as being one of the essential components that makes quantum different from classical. But is entanglement really necessary to achieve a speed-up in quantum computation?
DaftWullie's user avatar
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15 votes
4 answers
5k views

General construction of $W_n$-state

Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|...
nippon's user avatar
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15 votes
2 answers
2k views

Is it true to say that one qubit in an entangled state can instantaneously affect all others?

When a qubit is measured, there is a ‘collapse of the wave-function’ as a result is randomly chosen. If the qubit is entangled with others, this collapse will also effect them. And the way it affects ...
James Wootton's user avatar
15 votes
2 answers
573 views

Does higher channel fidelity imply higher entanglement fidelity?

Consider two noisy quantum channels (CPTP maps), $\Phi_1^A$ and $\Phi_2^A$, acting on a system $A$. Suppose that for any pure state $\left|\psi\right>\in \mathcal H_A$, $$ F\big(\psi, \Phi_1^A(\psi)...
UncertainTea's user avatar
14 votes
2 answers
2k views

Why is an entangled qubit shown at the origin of a Bloch sphere?

I'm unclear why the Bloch sphere representation of a maximally entangled qubit shows the state of the bit as being at the origin of the sphere. For example, this illustration shows the effect of ...
orome's user avatar
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14 votes
1 answer
3k views

Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?

Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake. Based on Wikipedia ...
u185619's user avatar
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14 votes
1 answer
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What does "bipartite" mean?

This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ...
CFRedDemon's user avatar
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 ...
XXDD's user avatar
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13 votes
2 answers
2k views

Does quantum computing already possess the level of abstraction to be explicable even without knowledge of physics?

Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only ...
Tetragrammaton's user avatar
13 votes
1 answer
701 views

What are min and max overlaps of a maximally entangled state with a separable state?

Let $A,B$ be Hilbert spaces of dimension $d$. Let $\rho$ be some separable quantum state of the composite system $AB$. Given a maximally entangled state: $$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=...
Jules's user avatar
  • 133
13 votes
2 answers
344 views

Using a fractional number of classical bits within quantum teleportation

Recently, I heard that there can be transfer of rational classical bits (for example 1.5 cbits) from one party to another via quantum teleportation. In the Standard Teleportation Protocol, 2 classical ...
Vijeth Aradhya's user avatar
13 votes
2 answers
613 views

What are the possible non-entangling two-qubit gates?

The non-entangling gates in $ SU_4 $ contains the entire group of gates of the form $$ SU_2 \otimes SU_2. $$ It also contains $$ \zeta_8 SWAP= \zeta_8 \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &...
Ian Gershon Teixeira's user avatar
13 votes
3 answers
869 views

What are the possible ways to visualise large, entangled states?

What are the prominent visualizations used to depict large, entangled states and in what context are they most commonly applied? What are their advantages and disadvantages?
SLesslyTall's user avatar
  • 1,646
12 votes
3 answers
2k views

Why do we have to uncompute rather than simply set registers to zero?

In implementing a quantum subroutine it is important to uncompute temporary registers after use, to ensure the output state of the subroutine is not entangled with them (which would affect its ...
Sideshow Bob's user avatar
12 votes
3 answers
1k views

When was the first use of the word Entanglement?

Schrödinger wrote a letter to Einstein after the 1935 EPR paper, and in that letter Schrödinger used the German word "Verschränkung" which translates into "entanglement", but when was the word first ...
user1271772 No more free time's user avatar
12 votes
1 answer
748 views

Where exactly does entanglement appear in Shor's algorithm?

One deals with the notion of superposition when studying Shor's algorithm, but how about entanglement? Where exactly does it appear in this particular circuit? I assume it is not yet present in the ...
wondering's user avatar
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11 votes
5 answers
918 views

What is quantum entanglement, and what role does it play in quantum error correction?

I want to understand what quantum entanglement is and what role does it play in quantum error correction. NOTE: As per the suggestions of @JamesWootton and @NielDeBeaudrap, I have asked a separate ...
Chinni's user avatar
  • 251
11 votes
2 answers
772 views

What is the complexity of determining if a state is entangled?

I have been looking around for an answer to this question but can't really come up with anything. Given some oracle, $U$, that maps $| 0 \rangle$ to $| \psi \rangle$, is there some algorithm that ...
Loic Stoic's user avatar
11 votes
0 answers
203 views

Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
Paul B. Slater's user avatar
10 votes
2 answers
3k views

How does evolving a two-qubit state through a CNOT gate entangle them?

Reading into CNOT gate I understand that, mathematically, such a gate entangles the control qubit and the target. (the resulting state is $\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$) However, looking ...
ItamarG3's user avatar
  • 705
10 votes
3 answers
721 views

Does the Quantum Fourier Transform (QFT) preserve entanglement?

It is well known that entanglement in a quantum state is not affected when you perform a combination of 1-qubit unitary transformations. I have seen that the QFT can be decomposed into product of 1-...
Hùng Phạm's user avatar
10 votes
2 answers
1k views

How to show whether a bipartite high-dimensional system is entangled?

"How do I show that a two-qubit state is an entangled state?" includes an answer which references the Peres–Horodecki criterion. This works for $2\times 2$ and $2\times3$ dimensional cases; however, ...
user820789's user avatar
  • 3,312
10 votes
1 answer
725 views

What happens if two separately entangled qubits are passed through a C-NOT gate?

Suppose I transform a state as follows: I start with the state $\lvert 0\rangle \otimes \lvert0\rangle \otimes \lvert0\rangle \otimes \lvert 0 \rangle$. I entangle the 1st and 2nd qubits (with an H ...
Midhun XDA's user avatar
10 votes
2 answers
3k views

CNOT Gate on Entangled Qubits

I was trying to generate Greenberger-Horne-Zeilinger (GHZ) state for $N$ states using quantum computing, starting with $|000...000\rangle$ (N times) The proposed solution is to first apply Hadamard ...
Satvik Golechha's user avatar
10 votes
1 answer
649 views

Are there connections between long-range entanglement and topological quantum computation?

Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot ...
Yupan Liu's user avatar
  • 488
10 votes
1 answer
278 views

Understanding the $M$ upper bound in the paper: "Multipartite entanglement and high-precision metrology"

This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) ...
narip's user avatar
  • 2,999
10 votes
1 answer
458 views

How to keep track of entanglements when emulating quantum computation?

I am trying to build a quantum computation library as my university project. I am still learning all the aspects of the Quantum Computing field. I know there are efficient libraries already for ...
Midhun XDA's user avatar
10 votes
0 answers
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 ...
glS's user avatar
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10 votes
0 answers
102 views

Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
Josu Etxezarreta Martinez's user avatar
10 votes
0 answers
213 views

Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ...
agaitaarino's user avatar
  • 3,827
9 votes
4 answers
1k views

How can one imagine entanglement in a non-mathematical way?

I understand the theoretical concept of an entanglement and what it means for our computation to have two entangled qubits, but what does it really mean when two qubits are entangled? How are they ...
Blubsiwubsi's user avatar
9 votes
2 answers
742 views

What is the maximum separation between two entangled qubits that has been achieved experimentally?

Considering two entangled flying qubits, as far as I know, there is no physical limit for separating them without losing quantum information. See: Is there any theoretical limit to the distance at ...
SalvaCardona's user avatar
9 votes
2 answers
887 views

What is the role of entanglement in quantum-computational speed-up?

The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is ...
Ognyan Tsvetkov's user avatar
9 votes
1 answer
231 views

What is the applicability of quantum network coding?

As the title suggests, I want to know what the applicability of quantum network coding is, besides the EPR pair construction between distant pairs of 'Users-Targets'. Can quantum network coding be ...
Ivanovitch's user avatar
9 votes
1 answer
336 views

Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in ...
SLesslyTall's user avatar
  • 1,646
9 votes
1 answer
262 views

Decoherence of spin-entangled triplet-pair states in the solid state: local vs delocalized vibrations

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ...
agaitaarino's user avatar
  • 3,827
8 votes
3 answers
7k 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 =...
Bekaso's user avatar
  • 285
8 votes
3 answers
830 views

Unentangling a qubit from a system: can we convert $\alpha|000\rangle+\beta|111\rangle$ into $\alpha|00\rangle+\beta|11\rangle$?

Let's say I start with the following arbitrary qubits: $$ \color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\ \color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \...
M. Al Jumaily's user avatar
8 votes
3 answers
1k views

Is quantum computer without entanglement no better than anything classically achievable?

Today I saw a tweet by Tom Wong which writes: "Did you know? Without quantum entanglement, quantum computers would be no better than traditional computers." But I remember I came up with ...
user777's user avatar
  • 377
8 votes
3 answers
2k views

How to prepare mixed states on a quantum computer?

I am a little bit confused by density matrix notation in quantum algorithms. While I am pretty confident with working with pure states, I never had the need to work with algorithm using density ...
Nicholas Sathripa's user avatar
8 votes
2 answers
924 views

What is a separable decomposition for the Werner state?

Consider the two-qubit Werner state, defined as $$\rho_z = z |\Psi_-\rangle\!\langle \Psi_-| + \frac{1-z}{4}I, \quad |\Psi_-\rangle\equiv\frac{1}{\sqrt2}(|00\rangle-|11\rangle),$$ for $z\ge0$. Using ...
glS's user avatar
  • 25.5k
8 votes
2 answers
921 views

Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere

The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection $\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia: Quantum ...
Sanchayan Dutta's user avatar
8 votes
1 answer
729 views

Parametrization of a two-qubit state

A single-qubit state can be parametrized with real $\theta$ and $\phi$ as follows: $$|\psi(\theta, \phi)\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i \phi} \sin\frac{\theta}{2}|1\rangle.$$ I would ...
MonteNero's user avatar
  • 2,684
8 votes
1 answer
156 views

Is LOCC equivalence the same as LU equivalence?

I'm currently learning on LOCC transformations. In the Dur, 2000 paper, there is a statement that (...) two pure states $|\psi\rangle$ and $|\phi\rangle$ can be obtained with certainty from each ...
Steve J.'s user avatar
  • 173
8 votes
1 answer
574 views

How does the conditional min-entropy $H_{\rm min}(A|B)_\rho$ relate to the conditional entropy $H(X|Y)_\rho$?

Suppose we have a classical quantum state $\sum_x |x\rangle \langle x|\otimes \rho_x$, one can define the smooth-min entropy $H_\min(A|B)_\rho$ as the best probability of guessing outcome $x$ given $\...
john_smith's user avatar
8 votes
1 answer
435 views

Can two states with the same entanglement be transformed into each other using local unitaries?

Take two pure bi-partite states $\psi$ and $\phi$ that have the same amount of entanglement in them as quantified by concurrence (does the measure make a difference?). Can any such states be ...
user120404's user avatar

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