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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If one not within the academic field had a verifiable solution to P versus NP problem, how, and why, would one go about submitting it?

Asking for a friend. The exclusivity/elitism of the field (and the dominance-human hierarchy), as well as the outcomes of "exploitation of "discoveries" throughout history have friend leaning away ...
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Entanglement to the nth butterfly degree?

Two days ago, I asked if entanglement was natural and nearly unavoidable if two quantum particles touched or flimsy and fragile in this thread: Entanglement - Natural and Unavoidable or Difficult to ...
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More than one Schmidt coefficient implies entanglement?

I'm studying Quantum Information Theory by Mark M. Wilde, and I got stuck in solving the exercise 3.8.2 in page 100. The exercise is to show that a pure bipartite state is entangled if and only if it ...
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Entanglement - Natural and Unavoidable or Difficult to Do and Flimsy?

I’m hoping the quantum community here might weigh in with some thoughts on something that is bothering me regarding quantum entanglement…something that seems as big a disagreement in the quantum world ...
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24 views

Uniform superposition of states with one qubit set to $|1\rangle$ and others to $|0\rangle$

I am wondering what a circuit should look like if I want to prepare the state of the following form: $$ |0\rangle^{\otimes n} \mapsto \dfrac{ |1000\ldots0\rangle + |0100\ldots0\rangle + |0010\ldots0\...
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139 views

Simple algebraic explanation for normalizing states

I'm wondering how a set of three 0-state qubits, each prepared identically, like so: When considered together, may produce the fraction: along with their combined states. This is the entire circuit....
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What is a local operator?

I have a sort of basic question. I think an operator that acts on $n$-partite states is defined (up to permutation of parties) to be local if it can be written as $$A = A_1 \otimes_{i=2}^n \mathbb{I}...
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Bell states from EPR pair of two-level atoms [closed]

Considering a case in which we prepare an entangled EPR pair from two two-level atoms interacting with a cavity, one prepared in ground state and the other in excited state but moving in at a later ...
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How does Quantum Teleportation works? [duplicate]

I've started learning Quantum Computing from the Qiskit Textbook and was able to easily understand or work out everything until it came to the working of Quantum Teleportation I can understand the ...
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1answer
75 views

Is Quantum Entanglement the one-dimensional spatial relationship between two particles as described by mathematics?

Is Quantum Entanglement the one-dimensional spatial relationship between two particles as described by mathematics? By one dimensional I mean, when they travel at opposite directions their spin is ...
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Computation of a reduced density matrix

On wikipedia, the article on quantum entanglement gives an example of the computation of a reduced density matrix. I would like to understand precisely what's going on with the computation. First the ...
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Given partial states, can one construct the best estimate of the full state?

Given some partial states $\rho_{AB}$ and $\sigma_{AC}$, is there a general procedure to construct a state $\delta_{ABC}$ such that the following sum of trace distances $$||\text{Tr}_C(\delta_{ABC}) -...
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What is the implementation of the state in superdense coding?

What is the implementation of quantum superdense coding protocol if the sender and receiver share the entangled state $ \frac{1}{\sqrt{2}} (\left| 01 \right> - \left| 10\right>) $?
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Generalising the standard quantum teleportation protocol: what are the possible unitaries?

Consider the standard quantum teleportation scheme. Let the first register hold the state $\newcommand{\ket}[1]{|#1\rangle}\ket\psi$ to be teleported, and the second register be the one shared between ...
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Do Bell state measurements satisfy the completeness condition from the no-signalling theorem?

Do Bell state measurements satisfy the completeness condition from the no-signalling theorem? In a quantum experiment involving unitary evolution and projective measurements,  do Bell state ...
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1answer
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computing a quantum circuit by hand (CNOT on non-computational basis states)

I'm trying to compute the state of a particular circuit using Dirac notation but I get stuck after a while .. you can find the circuit there. The numerical coefficients do not matter and I want to ...
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Does the Quantum Fourier Transform (QFT) preserve entanglement?

It is well known that entanglement in a quantum state is not affected when you perform a combination of 1-qubit unitary transformations. I have seen that the QFT can be decomposed into product of 1-...
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128 views

Is back in time (classical) information transfer possible (based on delayed choice entanglement swapping)?

Delayed choice entanglement swapping. Two pairs of entangled photons are produced, and one photon from each pair is sent to a party called Victor. Of the two remaining photons, one photon is sent to ...
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What are the different ways of representing unitary gates in terms of the matrix?

What are the different ways of representing unitary gates in terms of the matrix? In other words what would be the two different matrices which on multiplication give you unitary gate matrix?
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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? [duplicate]

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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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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54 views

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 already possess the level of abstraction 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
57 views

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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46 views

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
90 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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112 views

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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135 views

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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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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53 views

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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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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60 views

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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50 views

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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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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