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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36 views

How do you mix two pure states to obtain a mixed state?

If we have the following two states \begin{equation} |\psi\rangle_1 = \frac{1}{\sqrt{2}}|0\rangle_A|0\rangle_B + \frac{1}{\sqrt{2}} |1\rangle_A |1\rangle_B \end{equation} \begin{equation} |\psi\...
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Can someone elaborate how to use Qutrits to do teleportation? And the unitary operation Bob needs to do? [duplicate]

I can understand doing teleportation by using qubits, however, I am stuck there when it comes to qutrits and the operation Bob needs to perform. Suppose Alice and Bob are sharing the most entangled ...
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2answers
81 views

What gate combinations create entangled two-qubit states?

I know that in order to make a two quit entangled state, this quantum circuit is used: But I was wondering if there are any other gate combinations which also create entangled two quit states. If ...
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1answer
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How to get a qubit into superposition?

I have a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ so if i give values $\alpha_1 + i\alpha_2 = 1 + 4i$ and $\beta_1 + i\...
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1answer
42 views

Show algebraically that $U|0\rangle\otimes |0\rangle+U|1\rangle\otimes|1\rangle=|0\rangle\otimes U^T|0\rangle+|1\rangle\otimes U^T|1\rangle$

Suppose that Alice applies a unitary operator $U$ with real entries to her qubit in an EPR pair $|\beta\rangle=\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$. Is this the same as having Bob apply $U^T$ to ...
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1answer
29 views

In VQE, what ansatz would be best used for a maximally entangled $n$-qubit $H$?

What ansatz would be best used for a maximally entangled n qubit H? I came across this question in the Qiskit textbook and I really don't know how I would answer it.
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What is the best book or resource to start Learning about Quantum Computing? [duplicate]

What is the best book or resource to start Learning about Quantum Computing ?
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Reduced Density Matrix as Tensor

I have just started learning tensor networks. I was referring to these Lecture notes. Slide no. 32. What I understood is that reduced density matrix over first qubit $s_1$ of a two qubit state $\psi$ ...
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1answer
51 views

Does $\mathrm{tr}(A \otimes B) = \mathrm{tr} (A) \otimes \mathrm{tr}(B)$ hold for partial trace?

I was reading this question from this site answered by DaftWullie. I would like to request you to read the question there. The answer says However, in this particular case, the calculation is much ...
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1answer
171 views

Condition that a tripartite/multipartite qubit state does/does not admit a Schmidt decomposition?

I saw answers such as this and this which provide examples of tripartite system that don't take a Schmidt decomposition, but I wonder if there's an explicit condition that can tell whether a state is ...
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Clarification of a theorem mentioned in a paper on RED

I am reading a paper "A study of Teleportation and Super Dense Coding capacity in Remote Entangled Distribution" (arXiv:1210.1312). In this paper Relations on two-qubit pure states are ...
3
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1answer
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How to limit the error probability in large scale quantum computers

I am quite stumped by the fact that the roadmaps for quantum computers as given by IBM, Google, IonQ, etc. seem to imply a linear/exponential growth in the size of their quantum computers. Naively, I ...
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Any suggestions on Software to implement Remote Entangled Distribution

I am studying a paper "Remote Preparation and Distribution of Bipartite Entangled States" and trying to implement it using a software. https://arxiv.org/abs/quant-ph/0410016 This paper talks ...
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1answer
58 views

Do states get entangled in Grover’s algorithm?

I am new to QC and right now trying to understand Grover’s algorithm. In Qiskit documents, in the section about solving Sudoku using Grover’s, the first step is explained to be creating three register:...
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1answer
32 views

How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?

How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?
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1answer
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What is the logarithmic Negativity of the Werner state? [closed]

What is the Logarithmic Negativity of the Werner state $$\rho_w = p|\Psi^-\rangle\langle\Psi^-|+\frac{1-p}{4}I_4$$ where $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|10\rangle-|01\rangle)$?
2
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1answer
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EPR pair and individual operations [closed]

I have created an EPR pair. Let's suppose it's $(|00\rangle + |11\rangle)/\sqrt{2}$. We both of our halves and then we move into our places. If I ask you how does your half look like (mathematical ...
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1answer
74 views

In quantum teleportation, does Bob's qubit depend on Alice's $\alpha$ and $\beta$ coefficients?

Does applying an operation to one half of an entangled pair affect the other? As in the case of quantum teleportation when Alice applies CNOT to her half of the pair and the qubit she wants to send ($\...
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What is the difference between “entanglement distillation” and “entanglement purification”?

To my understanding, entanglement distillations is transformation of several copies of weakly entangled states into fewer copies of more strongly entangled states using local operations and classical ...
3
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1answer
73 views

How do I calculate Logarithmic Negativity for the given bipartite state?

How can I calculate Logarithmic Negativity for the given state? $\rho = \frac{1}{2} |0\rangle \langle0| \otimes |+\rangle \langle+| +\frac{1}{2} |+\rangle \langle+| \otimes |1\rangle \langle1| $
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1answer
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How do I determine if a given pure two-qubit state is separable?

I'm trying to self-study some topics about quantum computing and I came across a topic of state separability. Talking about that, I wanted to determine separability on the following state (from Qiskit ...
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1answer
55 views

Entanglement Witnesses close to GHZ states

Consider page 2 of Toth's paper 'Entanglement detection in the stabilizer formalism (2005)'. To detect entanglement close to GHZ states, they construct entanglement witnesses of the form $$\mathcal{W} ...
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1answer
120 views

How do I arrange these two-qubit states based on their entanglement?

How can I arrange the following states in decreasing order based on their entanglement? i) $\rho_1 = \frac{1}{2}|0\rangle \langle0|\otimes |+\rangle \langle+| +\frac{1}{2}|+\rangle \langle+|\otimes |...
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0answers
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How are inputs during the quantum communication between Alice and Bob placed in the Galois Field?

I have to write a report on "Classical Interaction Cannot Replace a Quantum Message" by Gavinsky (arxiv link). The author gave a lecture, and at 14:55 explains that a communication problem ...
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49 views

Modified CHSH game - Does entanglement help?

I'm thinking about a modified version of the CHSH game and I'm trying to convince myself that in this case, entanglement cannot be used to gain an advantage or else it would imply signalling is ...
2
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1answer
49 views

$\rho_{SE}(0)=\rho_S(0)\otimes\rho_E(0)$: No coupling or no entanglement?

We know that the entangled states cannot be expressed like product state, e.g. $|\omega\rangle = |\psi\rangle\otimes|\phi\rangle$. In the density matrix describing the correlations between system $S$ ...
4
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3answers
177 views

Prove that $a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle$ is separable iff $ad-bc=0$

I am having trouble rigorously proving that a two qubit state $|\psi\rangle=a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle$ is unentangled/separable if $ad-bc=0$ I currently have fairly little ...
3
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1answer
57 views

Cirq: n-qubit GHZ state

I am trying to write $n$ party GHZ state but at the end of the day, it seems like bi partite state. I am missing a detail. Here is my code ...
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0answers
50 views

What is the relation between fidelity and concurrence for a two qubit maximally mixed state?

I am trying to understand the relation between Fidelity and Concurrence for a two qubit maximally mixed state. When I calculate the Fidelity and Concurrence, I observe that Concurrence is zero whereas ...
2
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2answers
70 views

If Alice and Bob share only classical communication resources, is shared entanglement always equivalent to shared randomness?

If Alice and Bob share only classical communication resources such as noisy or perfect classical channels, is shared entanglement always equivalent to shared randomness? In other words, must there be ...
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1answer
55 views

Probability on measuring bell state in x-basis with pauli operator sigma x [duplicate]

I am confused about how to calculate the probabilities of getting a certain result when measuring a Pauli observable on a Bell state. When you measure an observable the state is projected onto an ...
2
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1answer
78 views

Quantum teleportaion seems to occuring without entanglement in circuit (what's wrong)

Please, pardon the caption. No intention of making new theories. I am a bit confused about the quantum teleportation. I missed a hadamard gate before CNOT gate for creating the EPR pair. But the ...
9
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5answers
949 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 ...
3
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1answer
52 views

How can measuring a particle in a GHZ state leave behind a maximally entangled pair?

I am trying to understand the section on the Wikipedia page for GHZ states entitled "Pairwise entanglement". In this section, it is claimed that measuring the third particle in a GHZ state ...
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1answer
81 views

Trouble understanding the EPR Experiment

I fail to understand the EPR experiment. From Wikipedia: Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, ...
2
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1answer
60 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 ...
4
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1answer
73 views

Unitary over bipartite states that can turn a non-product state into a product state

Consider a bipartite quantum state $\rho_{AB}$ over a product of finite-dimensional Hilbert spaces $\mathcal{H}_A \otimes \mathcal{H}_B$. Does there exists a unitary $U$ over $\mathcal{H}_A \otimes \...
2
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0answers
123 views

Three qubit identity

Problem: I'm having trouble seeing how this paper claims the following identity to be true for a three qubit system (labelled by $A$, $B$, and $C$) under a pure state $|\psi \rangle$ with real ...
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0answers
64 views

A question in classical and quantum information

Let $\rho, \sigma \in \mathfrak{D}(A)$ with $\operatorname{supp}(\rho) \subseteq \operatorname{supp}(\sigma),$ and spectral decomposition $$ \rho=\sum_{x} p_{x}\left|\psi_{x}\right\rangle\left\langle\...
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1answer
217 views

How do I prove that $P_\pm=\frac12(1\pm U)$ if $U^2=I$?

Suppose I have an $n$-qubit Hermitian operator $U$ such that $U^2=I$. The projection operators with eigenvalue $+1$ and $−1$ are $P_+$ and $P_-$. How can I prove that $P_+=\frac{1}{2}(1+U)$ and $P_-=\...
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1answer
94 views

In a bipartite system $AB$, why does the entanglement negativity $\mathcal{N}(\rho^{T_A})$ measure the entanglement between $A$ and $B$?

Consider a system composed of two subsystems $A$ and $B$ living in $\mathcal{H}=\mathcal{H}_A \otimes \mathcal{H}_B$. The density matrix of the system $AB$ is defined to be $\rho$. The entanglement ...
4
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1answer
92 views

Role of convexity in proof of Monogamy of Bell correlations

In this paper, the authors give a proof of the monogamy principle in quantum physics. I'm having trouble understanding the convexity argument in the proof of Lemma 2 (penultimate paragraph, page 2). I ...
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3answers
81 views

How can I get $|00\rangle |01\rangle |10\rangle |11\rangle$ entangled on IBMQ experience?

How can I get this situation entangled on IBMQ experience? $$|00\rangle:\\ |01\rangle:\\ |10\rangle:\\ |11\rangle: $$
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1answer
65 views

Pauli Matrix tolerant and encoding

I'm stumped by these questions in Chuang's book. If I have a state $|ψ\rangle=1/2\sqrt2(1+M_0)(1+M_1)(1+M_2)|0\rangle_7$, where $$M_0=X_0X_4X_5X_6; M_1=X_1X_3X_5X_6; M_2=X_2X_3X_4X_6$$ I rewrite its ...
2
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1answer
41 views

Two qubit state + Depolarizing channel = Bell diagonal state?

In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...
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1answer
64 views

What is the meaning of measuring a Bell state with Pauli operators?

There will be a certain value of getting the probability when measuring any Bell's state with Pauli operators such as observable X, Y, or Z. What is the meaning behind all this measurement? the result ...
2
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2answers
99 views

What are the possible results of measuring $X$ and $Z$ on the state $|01\rangle+|10\rangle$?

When calculating the probability of getting +1 on X-basis on the first qubit of Bell's state $|01\rangle+|10\rangle$, the result is 1/2 with the state after measurement |++⟩ while the probability of ...
4
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2answers
71 views

Can the following Bell states have probability amplitudes other than 1/2 and still be entangled?

From my understanding, a qubit is entangled when the state of one qubit depends on the other, and vice versa. Can the following bell states have probability amplitudes other than 1/2 and still be ...
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1answer
62 views

Is there a way to entangle to a dirty qubit?

Let's say I do something to a qubit, and I want to entangle it to a 2nd one, like this: ...
2
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1answer
57 views

Positive conditional quantum entropy for entangled state

The quantum conditional entropy $S(A|B)\equiv S(AB)-S(A)$, where $S(AB)=S(\rho_{\rm AB})$ and $S(B)=S(\rho_{\rm B})$ is known to be non-negative for separable states. For entangled states, it is known ...

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