# 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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### Mutual information of shared state is larger than expectation values

Im trying to prove the following identity for a special case: Alice and Bob share the Bell state \begin{align*} |\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle). \end{align*} Consider the ...
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### Are there quantum algorithms to estimate the partial transpose?

The entanglement negativity and the positive partial-transpose criteria play important roles in quantifying the amount of entanglement for mixed states. Yet, because these measures generally involve ...
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### Can you apply a CNOT gate on qubits in MBQC that aren´t next to each other?

Is it possible to apply a CNOT gate in MBQC to qubits that aren´t next to each other?
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### How to show that the GHZ state is absolutely maximally entangled?

A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
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### How to convert a partially entangled state into maximally entangled using SLOCC

Let's say I have a generic partially entangled two-qubit state with Schmidt decomposition $$|\psi\rangle_{AB} = \sqrt{\alpha} |00\rangle_{AB} + \sqrt{\beta}|11\rangle_{AB}.$$ I know from Lo and ...
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### Adding measurement circuits to the singlet state circuit and want to create single circuit

I am trying to add the measurement of Alice and bob's circuit to the singlet circuit. Actually, I am trying to build the e91 protocol. But it is giving me an error like this. ...
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### Is possible to write a separable state as a finite or countable infinite sum of product states?

Let us consider the tensor product of two finite Hilbert spaces $\mathcal{H}_1\otimes \mathcal{H}_1$. According to Watrous book, the set of separable states is the convex hull of the set of product ...
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### Recent references establishing connections between stabilizer error correction and entanglement distillation procedures

I know some concrete entanglement distillation protocols (from this review). I also know there are connections between error-correction codes and entanglement distillation (again this review but also ...
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### What is the difference between quantum teleportation and quantum entanglement with dense coding?

What is the actual difference between quantum teleportation and quantum entanglement with dense coding. Wikipedia says: Quantum teleportation is a technique for transferring quantum information from ...
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### Creating entangled states via Rydberg blockade

I was watching a talk by Prof. Mikhail Lukin and I have a silly question. In the talk, he discussed that a typical procedure for generating a Bell pair consists of using the Rydberg blockade on two ...
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### Can qubits be entangled without being classically corelated?

I have read before that classical correlations between qubits does not guarantee entanglement, but is the opposite also true? Consider a 3 qubit system, prepared as follows: $1-$ A Hadamard gate is ...
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### Can we use entanglement for cascaded measurements

My question is as follows: Suppose we have two entangled states, for example, a GHZ state where $|000\rangle$ and $|111\rangle$ are entangled Now, suppose the $|111\rangle$ state is entangled with ...
1 vote
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### Is it possible to produce an entangled state by measuring an unentangled state?

Wondering if it's possible to produce an entangled state by measuring an unentangled state. I tried a few examples, but it seems it's not possible.
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### Using bell state shared between two nodes to perform a CNOT gate between different qubits across the nodes

Consider a distributed quantum computer, where two qubit gates can be performed between qubits in the same individual quantum information processor (QIP), but not in separate ones. Suppose each QIP ...
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### Use of maximally entangled states in dense coding and quantum teleportation

In studying about the procedures of superdense coding and quantum teleportation, I have seen that maximally entangled states are used in both cases to show that how entanglement can be used as ...
1 vote
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### Why can't we use a two-qubit entangled state to send information faster than light? [duplicate]

I think this question is more suitable for physics, but I am using a quantum computing example to understand why this should not work. Note that I am not a physicist and I know only the basics of ...
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### Superluminal communication via entanglement transceivers

I know that this has been disregarded but I could not follow up since I'm new and it's an old post anyway. I understand the reason that superluminal communication via entanglement won't work. Is that ...
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### Upper bound on entanglement entropy of a Product State for any possible partition of the Joint System

Let $|\psi\rangle$ be an $n$ qubit quantum state on a line with Von Neumann entanglement entropy at most $r$ with respect to any bipartition of the qubits (does not have to be a contiguous bipartition)...
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### Conditions for entangling $A$ with $C$ via an interaction on $AB$

I have three qubits in subsystems $A$, $B$, $C$. System $A$ initially contains some state $\rho_A$, and $BC$ contains a bipartite pure state $|\psi\rangle_{BC}$. I apply a unitary operation $U$ acting ...
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### What is a general entangled bipartite system?

Is there a general pure entangled bipartite system that all other entangled bipartite systems are a special case of it?
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### CNOT and quantum entanglement

I have the following problem: "Consider two parties: Alice in possession of the one-qubit state |ψ⟩ = α|0⟩ + β|1⟩, and Bob who starts with a qubit in the state |0⟩ Show that Alice can teleport ...
1 vote
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### Is quantum mutual information an entanglement measure?

For a bipartite system, the quantum mutual information is defined via the Von Neumann entropy as follows: $$I(A:B)=S(A)+S(B)-S(AB).$$ It's always positive. Is it an entanglement measurement? Also how ...
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### Quantum Computer Basics [closed]

I am a newbie to Quantum Computing world. My collage professor asked me to do presentation on quantum computing. I have read many articles online but still I think I am not satisfied with what I found....
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### Are there non trivial two-party stabilizers in bipartite entanglement for product states?

In this recent paper where the authors discuss finite classification of entanglement types, on pg. 29 in appendix A, it is claimed that in bipartite entanglement for product state $|00\rangle$ there ...
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### Understanding entanglement distillation via stabilizer codes?

I am having some trouble understanding the distillation of EPR pairs using a stabilizer code. This idea goes back to the paper by Bennet, DiVincenzo, Smolin, and Wooters. The idea (I think) is that $k$...
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### Why are all Rényi entropies equal for Clifford dynamics?

In this paper, by Adam Nahum et al., the authors trivially states that "For Clifford dynamics all Rényi entropies are equal ... " which is not trivial to me. Is there a paper or lecture ...
1 vote
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### How to compute a partial trace of the form ${\rm Tr}_S [s^\dagger b- s b^\dagger, \vert \psi \rangle \langle \psi \vert \otimes \rho_B]$?

Let us consider a entangled state for the signal-idler system in its Schmidt decomposition form \begin{align} \vert \psi \rangle_{SI} = \sum_{\alpha} \sqrt{p_{\alpha}} \vert w_{\alpha} \rangle_S \vert ...
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### How to get the counts of measurement in QSIM simualtor

I had generate Bell State, $\frac{1}{\sqrt{2}}(|01\rangle - |10\rangle)$ now when I measured that in $Z$ basis how can I get the state of individual qubit separately and not the probability of the ...
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### Understanding quantum computing power of entanglement

I read here that the power of quantum computing lies in the fact that the Hilbert space size of a $n$ qubits register grows exponentially with $n$, but only when entangled. I would like to understand ...
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### Distributing entanglement using entanglement swapping

I've read papers that consider the problem of sharing entanglement between A and C with an intermediate B. A and B share an entangled state and so do B and C. Then, entanglement swapping is used to ...
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### Entanglement entropy of a projector

In this paper the author goes from the equation (13): $\rho_A = \frac{|G_A|}{2^{N_A}}\mathcal{P}^{(\overrightarrow k_A)}$, where $\mathcal{P}^{(\overrightarrow k_A)}$ is a projector acting on a ...
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### DumpRegister sometimes blank?

I'm just getting into the baffling world of Quantum Computing so forgive me if this is straightforward... I'm using Microsoft's Q# simulator so I know I'm allowed to peek into the internals of a Qubit ...
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### Any evidence it won't be exponentially harder to add more qubits?

I appreciate quantum circuits can solve certain problems exponentially faster than classical circuits. Q. Are there reasons to believe it won't be double as hard to build a quantum computer with i+1 ...
### General structure of the state with $I(A:B|C)_{\rho}{=}2 \log_2 \{\min (d_A, d_B)\}$
The conditional quantum mutual information (CQMI) of a state $\rho^{ABC}$ respects the dimension bound $I(A:B|C)_{\rho}{\leq}2 \log_2 \{\min (d_A, d_B)\}$ (Mark Wilde's book, exercise 11.7.9). One ...