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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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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94 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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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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69 views

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 $|\Psi^-\rangle = \frac{1}{\sqrt{2}}(|10\rangle-|01\rangle)$?
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1answer
50 views

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
93 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 ...
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1answer
116 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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159 views

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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82 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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124 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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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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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 ...
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60 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 $S$ ...
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3answers
241 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 ...
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90 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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114 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 ...
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2answers
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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
256 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 ...
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1answer
89 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 ...
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4answers
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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 ...
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1answer
152 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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2answers
231 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, ...
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92 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 ...
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1answer
85 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 \...
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137 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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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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240 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
140 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 ...
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1answer
108 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
86 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
69 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 ...
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1answer
76 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
132 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 ...
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2answers
260 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 ...
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2answers
96 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
82 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: ...
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1answer
134 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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1answer
85 views

Probabilities of entangled state. Quantum measurement [duplicate]

I confused about how to calculate the PROBABILITIES and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
2
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2answers
407 views

What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?

I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
3
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2answers
137 views

Transforming $|100\rangle$ state into $|000\rangle + |111\rangle$ state using only Hadamard and CNOT gates

Hi, How to convert $|100\rangle$ 3-qubit quantum state into $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$ state using only Hadamard and CNOT gates? Also, is output state an entangled one?
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111 views

Is the set of two-qubit absolutely separable states convex?

Companion question on MathOverflow Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as \begin{equation} 1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0. ...
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1answer
94 views

Is Grover's algorithm only applicable to a pure state?

I've been trying to perform Grover's algorithm on entangled states, e.g. $|00\rangle + |11\rangle$. However, the algorithm apparently doesn't seem to amplify the amplitude of the state $|11\rangle$ ...
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1answer
154 views

Difference between Bell's inequality and CHSH

In this section of the Scholarpedia article on Bell's theorem, the first paragraph comments that Bell's original inequality is not ideal for experimental verification because it requires perfect anti-...
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1answer
55 views

What is k-state and how to go about creating a circuit?

The k-state is given by: $$ |𝐾⟩ = \dfrac{\sqrt{3}|100⟩ − 𝑒^{𝑖π/4}|010⟩ + \sqrt{2}|001⟩}{ \sqrt{6}}$$ I am fairly new to quantum computing and do not have much background in the field. I understand ...
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1answer
146 views

Cirq-Measuring a State with Rotation Matrix

I have this state: $$p |\text{GHZ}\rangle \langle \text{GHZ}| + (1-p)\rho$$ And after creating this state I have this code lines: ...
4
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1answer
233 views

How to sample from the uniform distribution over the tensor product of two Bloch spheres?

For some context, I am trying to assess the capacity that certain two qubit gates have to create entanglement. To do this I am using the idea of "entangling power", where one takes their ...
3
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1answer
137 views

Is there a clear boundary between quantum coupling and quantum entanglement?

I have a few questions in understanding the difference between coupling and entanglement in quantum systems: Is there a clear boundary between quantum coupling and quantum entanglement? If two quantum ...
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1answer
65 views

Bit Flip, Seperable state and Several Question about Cirq

1)I want to use noise model for my state and bit_flip is not defined on cirq. ...
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1answer
33 views

Multiple Bipartite Entangled State in Cirq

I am trying to create this state: rho = = q . rho_{1,2} + r . rho_{2,3} + s . rho{1,3} + (1-q-r-s) . rho_separable And I wrote this code: ...

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