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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Using Grover on entangled states

I am trying to implement Grover's algorithm on an entangled state. The idea is that I will have a state $\sum_x\alpha_x|f(x),x\rangle$ and I want to measure the $x$, for which $f(x)=0$. Note that $f$ ...
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A notational confusion in a Bell like inequality

In the tripartite Bell type inequality know as Svetlichny inequality, given in this (freely available) article. The quantity $M_{ijk} = Tr [\rho(\sigma_i \otimes \sigma_j \otimes \sigma_k)]$, $i,j,k\...
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For bipartite mixed state, if one part is pure, then the global mixed state is a product state?

In Nielsen and Chuang, the chapter about Schmidt decomposition, there is an interesting result states that for a bipartite pure state $|\psi\rangle_{AB}$, if part A is a pure state, then $|\psi\...
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Density matrix after measuring Bell state in CHSH game

In these notes, the author says the following about the CHSH game Does Alice and Bob’s ability to succeed more than 75% of the time mean that they are communicating? Well, we know it’s not possible ...
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In the E91 protocol, how can Alice and Bob detect Eve if she waits to measure until A&B publish their bases?

I'm studying the E91 protocol. Suppose Eve has a qubit entangled with Alice's and Bob's qubits. I understand how Alice and Bob can detect Eve if Eve measures before A&B by testing Bell's ...
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Show by example that a linear combination of entangled states is not necessarily entangled

$\newcommand{\bra}[1]{\langle#1\rvert} % Bra \newcommand{\ket}[1]{\lvert#1\rangle} % Ket \newcommand{\qprod}[2]{ \langle #1 | #2 \rangle} %Inner Product \newcommand{\braopket}[3]{\langle #1 | #2 | #3\...
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Separable decomposition of states near the maximally mixed state

This question concerns the neighborhood of separable states around the maximally mixed state in a bipartite system; I will restate the theorem as it appears in Watrous' The Theory of Quantum ...
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Entanglement entropy and depth

I wanted to verify two intuitions about the entanglement entropy of quantum states. Consider an $n$ qubit quantum state, prepared by a depth $d$ circuit acting on $|0\rangle^{\otimes n}$ and a ...
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Where does Deutsch's algorithm use entanglement?

I have read that to be useful, all quantum algorithms must use entanglement somewhere. However, reading several tutorials describing Deutsch's algorithm, I haven't seen any mention of how entanglement ...
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Can we somehow measure the strength of an entanglement? [duplicate]

If I have a list of qubits, is there any formula how to calculate the strength of their entanglement? Something like a correlation coefficient.
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Why is entanglement so important if it introduces dependent information?

I still don't understand, why is entanglement such a crucial property of a quantum algorithm. If I understand it, it means that the information between different qubits is somehow correlated, which ...
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What is a simple example of "weak entanglement" in a two-qubit system?

Bell states produce maximal entanglement between two qubits. On the other hand, two unentangled qubits provide no (i.e. minimal) entanglement at all. However, I haven't seen any example of a weak ...
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Prove that $|(\langle \psi|_{A} \otimes \langle \phi|_{B})|\theta\rangle_{AB}|^{2}<1$ for entangled $|\theta\rangle_{AB}$

I am trying to show that $|\langle \psi|_{A} \otimes \langle \phi|_{B}|\theta\rangle_{AB}|^{2}<1$ given $|\theta\rangle$ is an entangled state, and as such has schmidt rank >1. Decomposing it, ...
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Volume law spread after Hamiltonian evolution

Start with an $n \times n$ lattice, with each qubit initialized to the state $|0\rangle$. Then, apply the Hadamard gate on each qubit. Then, evolve the system under the Hamiltonian \begin{equation} ...
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How to measure a correlated operator $Z_1Z_2$?

I was reading this articl and I am stuck trying to understand equation $(60)$, which reads $$\langle\psi|\Lambda_{1,2}(X)Z_1\Lambda_{1,2}(X)|\psi\rangle=\langle\psi|Z_1Z_2|\psi\rangle$$ where $\Lambda(...
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Does QFT exploit entanglement?

I was studying the quantum circuit for the Quantum Fourier Transform (QFT) on the Mike & Ike, and they write the result of the transformation as a product state. More precisely they wrote the ...
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How is the creation of entangled two-photon states such as $|00\rangle\pm|11\rangle$ compatible with the conservation of angular momentum?

Quoting, "Spin is the simplest example — two photons would either be (+1 and -1) or (-1 and +1), two electrons would either be (+½ and -½) or (-½ and +½) — and you don’t know which is which until ...
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Are measurement probabilities on the two qubits of a maximally entangled state equal? [closed]

Suppose we get the Bell state $$ |\Phi ^{+}\rangle ={\frac {1}{{\sqrt {2}}}}(|0\rangle _{A}\otimes |0\rangle _{B}+|1\rangle _{A}\otimes |1\rangle _{B}). $$ If we now apply a unitary operator $U$ ...
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Can you detect if the collapse of an entangled pair using a Hadamard gate?

I'm trying to understand how the Hadamard gate works with entangled pairs. If I have two particles A and B which are entangled and have gone through a Hadamard gate to become super-positioned Qubits, ...
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Does entanglement entropy follow a volume or an area law for 2D cluster states?

Consider a 2D cluster state defined on a rectangular lattice, which is universal for one way quantum computers. For a description of the state, see for example question 2 in this problem set. Now, ...
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Can the spin-1/2 720° rotation trick apply to qubits?

The idea of a 4π rotation to return an electron to its original state instead of just a single 2π rotation exists - but can this idea apply to qubits or entangled qubits? Are there any use cases for ...
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Are $(|00\rangle-|11\rangle)/\sqrt2$ and $(|11\rangle-|00\rangle)/\sqrt2$ the same quantum state?

The state $(|00\rangle-|11\rangle)/\sqrt2$ is an entangled state. If we think about the state $(|11\rangle-|00\rangle)/\sqrt2$, is this also entangled, but with maybe a phase change? The above two can ...
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Why doesn't this simpler teleportation idea work?

This circuit: The first (upper) qubit is the one we want to teleport, so could start it any state, call $\alpha|0\rangle+\beta|1\rangle$. Our goal is to teleport it to the third (bottom) bit. After ...
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What is the difference between the two entanglement circuits?

For a three qubits system to be in an entanglement(GHZ) state, the circuit can be built as per Qiskit, Here, the control bit of the second X gate is on q0. what if the control bit is shifted to q1. ...
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What are the typical gate times for single-qubit and 2-qubit gates for ion trap, superconducting, neutral atom, photonic, spin QC?

What are the typical gate times for single-qubit and 2-qubit gates for -- ion trap, -- superconducting, -- neutral atom, -- photonic, -- spin quantum computers based on today's technologies?
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How many physical qubits are needed to encode a logical qubit on ion trap, superconducting, neutral atom, photonic QC?

How many physical qubits are needed to encode a logical qubit on an -- ion trap, -- superconducting, -- neutral atom, -- photonic, -- spin quantum computer based on today's technologies?
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Are the first and second qubits of the state $| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle$ entangled with each another?

State of qubits: $\frac{1}{2} (| 111 \rangle + | 010 \rangle + | 101 \rangle + | 000 \rangle)$ Are the first and second qubits of this register entangled with each another?
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What does it mean to be in a superposition of eigenstates in a LC oscillator?

In superconducting qubits, we use a circuit with a specific type of inductor and quantize the Hamiltonian. Because it's an anharmonic oscillator, we say that it has states -- $|0\rangle$ and $|1\...
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Can entangled photons create entanglement in material particles?

Is it possible that two entangled photons when absorbed by two material particles, say two atoms, lead to the entanglement of these atoms? Is there any published research on this topic?
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Can LOCC operations take product states to non-product states?

Given a product state $\rho^{(1)} \otimes \rho^{(2)}$, can this state become non-product state under LOCC? Can LOCC create correlations between two systems?
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What is the Schmidt number of generalized GHZ and W states?

Consider generalizations of the GHZ state and the W state to $n$ qubits. What is the Schmidt number of these two states for any bipartition $ c n $ and $(1 - c) ~n $, for $c < 1$? Does it depend on ...
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Finding Wigner function of four maximal entangled Bell state

How can we find a Wigner function for the four maximally entangled Bell states $(|00\rangle \pm |11\rangle)/\sqrt{2}$, $(|01\rangle \pm |10\rangle)/\sqrt{2}$? I have used the basis where labels for ...
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What does the partial trace of $|W\rangle$ states represent physically?

Given the W-state $|W\rangle = |001\rangle + |010\rangle + |100\rangle$, where $|ijk \rangle $implies $|i\rangle_A \otimes |j\rangle_B \otimes |k \rangle_C$, the partial trace over first qubit turns ...
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What is meant by "double speed" in dense coding protocol?

As mentioned in this article, "This (densecoding) lets you transmit at double speed until the pre-delivered qubits run out." What is meant by double speed here?
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Does the controlled Pauli Z gate cause entanglement?

I'm trying to understand the relationship between the factorability of a 2 qubit gate and that gate's ability to cause entanglement. I've begun by considering the controlled Pauli Z gate. After ...
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What conditions on the coefficients of a bipartite pure state imply it being entangled?

With $\{ |e\rangle_j \}_{j=1}^{dim. \mathcal{H}_A}$ for $\mathcal{H}_A$ and $\{|f\rangle_j \}_{j=1}^{dim. \mathcal{H}_B}$ for $\mathcal{H}_B$, the product state reads \begin{equation} |u\rangle \...
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What are examples of "LOCC linked" quantum instruments?

Define a quantum instrument $\mathfrak J$ as a collection of completely positive (CP) maps $(\mathcal E_j:j\in\Theta)\subset\mathrm{CP}(\mathcal H)$, such that $\sum_j \mathcal E_j$ is also trace-...
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Generalizing the circuit for quantum teleportation for $n$-qubit states? [duplicate]

So the usual quantum circuit I know for quantum teleportation allows for the teleportation of the state on a single qubit, in the following way: How easy is to generalize this algorithm to allow for ...
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Is it possible to collapse a superposition into a preset state such that all entangled qubits collapse to the same state?

Ideally, I'd be able to apply an operation to qubit 0 that would collapse the superposition to a set state (say 1) on qubit 0 & 1. The operation applied to qubit 0 would be a one qubit operation (...
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How to show that Werner states produce correlations explainable via local hidden variable models?

Werner states can be written as $$\rho_W= p\frac{\Pi_+}{\binom{n+1}{2}} +(1-p)\frac{\Pi_-}{\binom{n}{2}}, $$ with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...
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Can changing reference frames generate entanglement in identical particles?

Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...
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Is there any simple mathematical proof that measurement destroys entanglement?

Is there a simple mathematical way to prove that measurement destroys entanglement? I can see that this is indeed true if I just take a specific measurement on an entangled state. What I am looking ...
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Why can no pair of single qubits look like $\frac{1}{\sqrt2}(|00\rangle+|11\rangle$)?

I've just started to learn Quantum Computing and, to do it, I'm reading the course "Introduction from Quantum Computing" by IBM. Now, I'm reading the chapter "Entangled states", ...
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How to implement a quantum array

I'm trying to implement a quantum array. That is one that stores qubits and can be indexed via qubits. I can create one that handles setting values fairly easy. Have two registers, one for the ...
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Do entangled measurements across multiple copies help in state distinguishability?

Consider two density matrices $\rho$ and $\sigma$. The task is to distinguish between these two states, given one of them --- you do not know beforehand which one. There is an optimal measurement to ...
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How to analyze the following quantum circuit?

I'm trying to analyze the following quantum circuit The goal here is to analyze the final outputs at q3 & q4. For inputs, at q0 & q1, one of the Bell state $$|\psi\rangle = \frac{|01\rangle + ...
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Is the CNOT in the standard three-qubit circuit for the GHZ state necessary?

This is a very basic question about the GHZ state. I know the standard construction: A Hadamard on one qubit, and then CNOT gates with targets on all the other ones. However, why can't I just have $n$...
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How much information is stored in entangled states (IBM report Quantum Decade)?

In its report Quantum Decade, IBM claims that we need 512 classical bits to represent two-qubits entangled state (see graphic on pg. 2 in the report). This seems a little bit odd to me. Lets have a ...
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What is a maximal entangled multipartite state?

We know the four Bell states are the maximal entangled states for two-qubit states, and we know if a state cannot be written as the tensor product by its subsets, then it is a entangled state, so is ...
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What is the difference between having a single-qubit state and knowing a result of a measurement you want to perform on it?

In the quantum teleportation protocol Alice can send Bob an unknown quantum state $|\psi\rangle$. If the only thing Bob does with $|\psi\rangle$ is to measure it in some basis, I guess it would be ...

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