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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Further entangling two ebits to obtain $|0000\rangle + |1111\rangle$ state

I have two ebits $e1$ and $e2$ and my 4-qubit system is in the state: $$(|00\rangle + |11\rangle) (|00\rangle + |11\rangle)$$ Ignoring the normalizing constants for now. As mentioned, I need to ...
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How to decompose arbitrary gates in Qiskit?

I have been exploring quantum computing, I have no idea of decomposing arbitrary gates in Qiskit. Can someone help me with an example?
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1answer
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What is “quantum internet” and what is its relation with quantum entanglement?

In a recent news "Scientists Make Major Breakthrough In ‘quantum Entanglement’ That Could Change How The Internet Works" Scientists have managed to entangle two "quantum memories" at a distant ...
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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 ...
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Can I generate 4 entangled states (each 5 qubits) on a 5 qubit quantum computer?

Suppose that I have a 5 qubit quantum computer and want to generate 4 entangled states (each of 5 qubits) Single 6 qubit entangled state. Are these 2 cases possible? I am a beginner please help!
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Applying density matrix based criterion to verify separability

In order to figure out if a given pure 2-qubit state is entangled or separable, I am trying to compute: the density matrix, then the reduced density matrix by tracing out with respect to one of the ...
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Vetting the Circuit Gate for a 3 Qubit Entanglement [duplicate]

While I've seen plenty of examples on how to entangle two qubits, I've (unfortunately) not seen any on the generalized version of entangling multiple qubits, nor how you know your circuit is correct. ...
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Does quantum computing possess the level of abstraction already 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 ...
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The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?

I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
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1answer
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Controlled NOT gate using multiple control qubits in Q#

I am trying to implement the Grover's search algorithm using Q# and I am not able to implement the oracle (black box) part for the search of state $|1010\rangle$. How to implement the controlled NOT ...
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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 \...
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Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
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How to know if any two arbitrary qubits are entangled? [duplicate]

Suppose there are two quits called q1 and q2. They are in two different superposition states. If we represent their states on ...
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1answer
84 views

How many $n$-qubit states are entangled?

My question is a bit broad, but my concern is mainly on understand the ratio between the number of possible linear combinations that can be decomposed in a direct product of states and the number of ...
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2answers
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What is the property of any entangled pair of qubits?

We know that any of the Bell states has the special property that the second qubit will be found in a state which is predictable based on measuring one of the qubits. But assuming any other pair of ...
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Problem involving entanglement swapping

I'm trying to solve a problem. I have my own approach to it, as the one in the textbook seems overly complicated. I tried using my own approach, but I'm not sure if what I found was a coincidence or ...
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2answers
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How to identify entanglement in a given pure state?

If I have either of the following states: $$\left|\psi_0\right\rangle = \frac{1}{2}\left|0000\right\rangle + \frac{1}{2}\left|0011\right\rangle + \frac{1}{2}\left|1100\right\rangle + \frac{1}{2}\left|...
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Why do purifications only differ by a local unitary?

Let's consider $\rho_A$ a density matrix. I introduce a space $B$ and an entangled state $|\Psi\rangle$ (the purification) so that: $$\newcommand{\tr}{\operatorname{Tr}}\rho_A = \tr_B(|\Psi\rangle \...
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DIQKD protocol a few questions

I'm refering to this paper here and unfortunately I have a few questions which I don't understand. 1) Page 3: by round, what do the authors actually mean? Is it right to say it's basically how many ...
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1answer
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Repetition code encoder circuit

The repetition code encodes $\vert \psi \rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle \rightarrow \vert \psi \rangle = \alpha \vert 000 \rangle + \beta \vert 111 \rangle$ using the ...
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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)...
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What is the difference between “intraphoton” and “interphoton” entanglement?

I am trying to better understand the following: What is the difference between Intraphoton Entanglement and Interphoton Entanglement? I am new in this field and i want to proceed some work on ...
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
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Maximally entangled state definition, and orthonormal basis of maximally entangled state

My questions are probably more about details but the answer will help me to precisely understand the mathematical structure. My questions are related to page 14 of this pdf. Mathematical context: ...
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1answer
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SWAP gate on 2 qbits in 3 entangled qbit system

Suppose I had 3 entangled qbits and I wanted to apply a SWAP gate on the first and third qbit. Because it's entangled I can't decompose it into individual states, and because the qbits are not ...
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1answer
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What is the diference between classic probabilities and quantum probabilities? [closed]

So, I'm really trying my best to understand how quantum computers work. This is how I think they work: There is a set of qubits; Then an algorithm is put in action by the use of quantum gates that ...
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5answers
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Can quantum chips be spied on?

Not sure if this is a stupid question, but can quantum chips be spied on? I heard that quantum particles(?) can be "entangled". So is it possible that a chip manufacturer (who wishes to spy) can ...
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1answer
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Entanglement entropy's role in quantum information

I am just new to the concepts of entanglement entropy and how it is used to measure the entanglement in systems. I want to know the role of entanglement entropy in quantum information, in general.
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Proof that quantum entanglement does not increase the asymptotic capacity of classical channel

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the ...
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354 views

Why does measuring one qubit after the other in this entangled system alter the result?

Suppose I have the following circuit where q0 and q1 are measured one after the other. The simulation results state that the state 00 occurs 75% of the time, and the state 11 occurs 25% of the time. ...
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3answers
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Non-entangled two qubit system get information about the individual particle states after CNOT

I'm trying to make a quantum computing mod for a game, (apologies if the notation is wrong I'm new to QM). Let's say I have 2 qubits that are both $\frac{1}{\sqrt{2}}(|0⟩ + |1⟩)$ and I put them ...
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1answer
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Can quantum entanglement be expressed in terms of knot theory?

While writing this answer I was wondering whether the analogy of the nature of entanglement in the GHZ state with Borromean rings is more than a mere analogy (cf. Aaronson's lecture). The question ...
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Understanding the monogamy of entanglement with respect to GHZ States

Given the GHZ state wrt n = 3: $\frac{|000⟩ + |111⟩}{\sqrt{2}}$, I'm trying to understand how the principle of monogamy of entanglement manifests here. I came across this explanation. Let’s say ...
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Please clarify the following orthogonal property (quantum anonymous voting)

I am a beginner at QC, currently going through a paper on Quantum Anonymous Voting. Please clarify the orthogonal property described in the following scenario. Consider $n$ voters $V_{0}, V_{1}, V_{2}...
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1answer
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How to measure one of the qubits in a two-qubit register?

How do I measure the first qubit of an entangled vector, say \begin{pmatrix} 1 \\ -1 \\ 0 \\ 0 \\ \end{pmatrix} is what I get on the end of Deutsch's algorithm. If I get it right, I should now ...
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Is quantum superposition state a truth or an assumption?

Please, be patient with my question I already read that there is a heuristic that makes superposition a fact of reality. In addition, this superposition, when observed, it has a state of 0 or 1. ...
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Does this setup violate relativity?

Suppose Alice needs to transmit a bit of information about something which happened just before $t = 0$ to Bob who is light years away from Alice. Entangled pairs of qubits, $\left|00\right> + \...
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336 views

Explanation of output produced by the following quantum circuit

I've recently started reading about quantum computing and I apologize in advance if this is (and I think it probably is) a very simple question. I've created the following circuit. I believe I ...
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2answers
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Give an explicit example of a $d = 4$ SIC-POVM

For $q=e^{2 \pi i/3}$, the set of $d^2$ vectors ($d=3$) \begin{equation} \left( \begin{array}{ccc} 0 & 1 & -1 \\ 0 & 1 & -q \\ 0 & 1 & -q^2 \\ -1 & 0 & 1 \\ -q &...
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Entanglement and teleportation in quantum annealing and parallel computation

In classical optimization problems, some objective function's surface serves as a landscape for finding its minimum through minimization algorithms. Instead of your typical U-shaped objective ...
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1answer
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Expectation Value of Stabilizer

Given that operator $S_M$, which consists entirely of $Y$ and $Z$ Pauli operators, is a stabilizer of some graph state $G$ i.e. the eigenvalue equation is given as $S_MG = G$. In the paper 'Graph ...
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1answer
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Is it possible to have entanglement between more than two qubits?

I am experimenting with concepts in Quantum Computing and I have landed on using entangled Qubits to perform certain actions. My question is this: is it possible to have (let's say) 3 entangled ...
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Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices for a graph $G = (V,E)$ and $B = V\setminus A$ the corresponding complement ...
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1answer
81 views

Secret sharing though quantum operations

I have a secret say $s$. I have a dealer $D$ and three participants $A, B, C$. I want to share this secret $s$ in such a way that the participation of all $3$ is essential to reconstruct the secret. ...
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How does a single-qubit gate affect other qubits?

An instructional quantum computing article I'm reading (How the quantum search algorithm works) states that the following circuit takes $\vert x\rangle\vert 0\rangle$ to $−\vert x\rangle\vert 0\rangle$...
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Entanglement and distributed consensus

Are there any distributed consensus protocols which make use of quantum phenomena for improved performance? For example, symmetry breaking with a shared quantum state.
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Faster than light data transmission using entanglement [duplicate]

I am not a scientist, so that's why I've come here...to hopefully find out if this would be possible. Ok, so I started learning about quantum entanglement and I stumbled upon an idea for instant data ...
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199 views

Query on paper on entanglement in graph states

Quick question on the paper Entanglement in Graph States. On page 14. a definition of a graph state: Given $|+\rangle=\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$. Let $G=(V,E)$ be a graph. The ...
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1answer
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Why is $\rho$ NPT if and only if $\rho^{\otimes N}$ is NPT?

In Horodecki et al. (1998), to prove that distillability implies having a negative partial transpose (being NPT). The authors use the fact that "a state $\rho$ is NPT if and only if $\rho^{\otimes N}$ ...
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How to measure entanglement in an algorithm?

Entanglement in Algorithms Most algorithms in quantum computing find their strength in making use of entanglement. I am interested in evaluating the amount of entanglement generated within an ...

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