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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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Partial Transpose and Positive Operators

Question: For 2x2 and 2x3 systems, is the partial transpose the only positive but not completely positive operation that is possible? Why this came up: The criteria for detecting if a state $\rho$ is ...
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Concurrence for a two qubit state

The concurrence for a state $\rho$ as defined here is \begin{equation} C(\rho) = {\rm max}\{0, \lambda_1-\lambda_2-\lambda_3-\lambda_4\}. \end{equation} Where $\lambda_i$ are the eigenvalues of matrix ...
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Construction of optimal ensemble to show quantum steerability

In Wiseman et al. (2007), in the process of deriving necessary and sufficient conditions for the steerability of some classes of states, the authors show (lemma 1, page 3) how to construct an optimal ...
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Better Way Of Separating Two CQ-States

I have this cq-state: $$\frac{1}{2} \times (|0\rangle \langle0|_A \otimes \rho^0_E + |1\rangle \langle1|_A \otimes \rho^1_E)$$ Where Alice (A) is classical and an adversary Eve (E) has some ...
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Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?

Context: Three coins on the table. Each is either heads or tails. You can uncover any one of the three coins, revealing whether it is heads or tails but then you choose two the other two coins ...
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Can “experimental data from a quantum computer” be used to test separability probability conjectures?

An article entitled "Experimental data from a quantum computer verifies the generalize Pauli exclusion principle" by Scott E. Smart, David I. Schuster, and David A. Mazziotti has just appeared In the ...
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Transmission of information over long distances

I am reading that entangled particles can share information across long distances and the speed is usually faster than the speed of light...so am I right in assuming that future communications in the ...
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Why do we have to uncompute rather than simply set registers to zero?

In implementing a quantum subroutine it is important to uncompute temporary registers after use, to ensure the output state of the subroutine is not entangled with them (which would affect its ...
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Defining entanglement for systems with more than two qbits

Introductory textbooks I've read define entanglement as when your product state cannot be factored into the tensor product of individual quantum states. But consider a three-qbit system: $C_{2,0}H_2|...
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Why is an entangled qubit shown at the origin of a Bloch sphere?

I'm unclear why the Bloch sphere representation of a maximally entangled qubit shows the state of the bit as being at the origin of the sphere. For example, this illustration shows the effect of ...
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Grover's algorithm with W-state

In the general form of Grover's algorithm, we start with the uniform superposition of n qubits. Now, suppose instead that we start with a generic state, for example ...
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A quantum circuit with entanglement with Eve

I'm trying to work through a self-made exercise, which may be ill formed as a question. Any general advice in dealing with these types of problems is also much appreciated! I'm looking at a quantum ...
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Shared entanglement to copy orthogonal states

Assume that Alice and Bob are allowed to share entanglement and are spatially separated. Alice is given an unknown state and asked to measure this in the computational basis to obtain $\vert 0\rangle$ ...
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Notation for two entangled registers

Suppose I have two registers x and y, of length m and n bits respectively. I want to initialize my system to contain an equal superposition of all $2^{n+m}$ states, then apply an oracle function (in ...
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Graph state and maximally entangled state

How can I show that a multi-qudit graph state $|G\rangle$ is the maximally entangled state? What kind of measure of entanglement can be used to quantify the amount of entanglement in a given graph ...
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How to analyze highly entangled quantum circuits?

I came across a quantum circuit very similar to the phase estimation circuit, which is shown below: In the ...
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How to transfer non maximally entangled state to maximally entangled?

Let a three-qubit state shared between Alice, Bob and Charlie stationed at distant laboratories be $$\psi_{ABC}=\frac{\sqrt{2}}{\sqrt{3}}|000\rangle+\frac{1}{\sqrt{3}}|111\rangle.$$ How to evaluate ...
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Controlling high-dimensional Hilbert spaces with a single qubit

In superdense coding, you can use one qubit to control the Hilbert space of two qubits and steer it into 4 mutually orthogonal states, so that measurement of both qubits together will not have a ...
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Are there any test examples of Octave and Quantum Entanglement?

I read this research paper. I have octave and the package running. This is an example of what I did so far - octave:3> s1 = state(normalize(ket([1,0])+ket([0,1]))) s1 = 0.00000 0.00000 0....
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Maximally mixed states for more than 1 qubit

For 1 qubit, the maximally mixed state is $\frac{\mathrm{I}}{2}$. So, for two qubits, I assume the maximally mixed state is the maximally mixed state is $\frac{\mathrm{I}}{4}$? Which is: $\frac{1}{...
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BB84 attack with entangled qubits example

BB84 attack with entangled qubits example Hi, I'am interested in an attack for BB84 protocol with entangled quibits. Lets say Alice sends a qubit $x$ in state $\left|1\right>_x$ to Bob and Eve ...
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How can blackholes be fast information scramblers?

I noticed that there was already a post discussing the fast scrambling property of black holes. But it seems no satisfactory answer was given. As mentioned by L. Susskind et. al, the fast scrambling ...
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Relation between quantum entanglement and quantum state complexity

Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ...
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The classical simulation of 2D graph state and the measurement based quantum computation

In my former post on Physics SE I deduced a contradiction in the classical simulation of 2D graph state and the classical simulation of general measurement-based quantum computation. In Norbert's ...
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How to simulate quantum entanglement variation in different quantum gates?

I'm trying to study quantum entanglement variation during quantum computation with 4 qubit systems comprising a variety of quantum gates. How can I simulate this variation on MATLAB? Is there any ...
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Does entanglement correlate qubits a $100\%$ of the time?

$\newcommand{\qr}[1]{|#1\rangle}$Say I begin with $4$ qubits $\qr{+}\qr{+}\qr{+}\qr{+}$ forming a register $B$. Name these qubits as $b_3, b_2, b_1, b_0$. Also, let $C$ be another register $\qr0\qr0\...
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Quantum teleportation: second classical bit for removing entanglement?

I have read about how Alice can send Bob a qubit $\alpha |0\rangle + \beta|1\rangle$ if they share an EPR pair. This gives an initial state: $(\alpha |0\rangle + \beta|1\rangle) \otimes (\frac{1}{\...
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Many-Worlds Interpretation and GHZ States

I'm working through a problem set, and I've come across the following problem: In this problem, you'll explore something that we said in class about the Many-Worlds Interpretation of quantum ...
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Suggest, partly based upon limited numerical results, possible “elegant” exact formulas for Bures two-qubit separability probability

Lovas and Andai (https://arxiv.org/abs/1610.01410) have recently established that the separability probability (ratio of separable volume to total volume) for the nine-dimensional convex set of two-...
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Relating min-entropy with conditional entropy

Suppose we have a classical quantum state $\sum_x |x\rangle \langle x|\otimes \rho_x$, one can define the smooth-min entropy $H_\min(A|B)_\rho$ as the best probability of guessing outcome $x$ given $\...
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General construction of $W_n$-state

Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|...
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Rotationally invariant maximally entangled states in higher dimensions

Is there a straightforward generalization of the $\mathbb{C}^2$ Bell basis to $N$ dimensions? Is there a rotational invariant Bell state in higher dimensions? If yes, then what is the form of that ...
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Applying CNOT with local operations and two EPR pairs

Suppose Alice and Bob hold one qubit each of an arbitrary two-qubit state $|\psi \rangle$ that is possibly entangled. They can apply local operations and are allowed classical communication. Their ...
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Protocol for entaglement swapping

Suppose there are 3 parties, of which 2 pairs share an EPR pair and can communicate classically. What is a protocol that results in the third pair sharing an EPR pair? That is the problem I'm given, ...
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Entanglement state preparation by using amplitude values

I have an algorithm that uses QRAM, after accessing the given QRAM that store M d-dimensional classical vectors, the state of the index register and the data register become entangled. But for now I ...
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How to calculate the number of ebits in a graph state?

Given an arbitrary graph state $|G\rangle$ represented by the graph $G$, can one use the graphical structure to calculate the number of ebits (entanglement bits) present in the state? If so, how?
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Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

[I'm sorry, I've already posted the same question in the physics community, but I haven't received an answer yet.] I'm approaching the study of Bell's inequalities and I understood the reasoning ...
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Photon Entanglement using SPDC

Are there any good references where from I can learn about photon entanglement using spontaneous parametric down-conversion (SPDC)?
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Can two states with the same entanglement be transformed into each other using local unitaries?

Take two pure bi-partite states $\psi$ and $\phi$ that have the same amount of entanglement in them as quantified by concurrence (does the measure make a difference?). Can any such states be ...
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Is entanglement an operation or a stored state for qubits?

I am going through this video of Quantum Computing for Computer Scientists. I am not able to understand the entanglement state of qubits. Is entanglement just an operation, or is it a state which ...
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CNOT Gate on Entangled Qubits

I was trying to generate Greenberger-Horne-Zeilinger (GHZ) state for $N$ states using quantum computing, starting with $|000...000\rangle$ (N times) The proposed solution is to first apply Hadamard ...
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Estimate/determine Bures separability probabilities making use of corresponding Hilbert-Schmidt probabilities

For two-qubit states, represented by a $4\times 4$ density matrix, the generic state is described by 15 real parameters. For ease of calculation, it can help to consider restricted families of states, ...
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Compact encoding of Boolean formula as oracle

As in the title, I have a doubt regarding the implementation of a boolean formula used as an oracle for a quantum algorithm. The problem is that so far I could reproduce the formula as a quantum ...
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Is entanglement necessary for quantum computation?

Entanglement is often discussed as being one of the essential components that makes quantum different from classical. But is entanglement really necessary to achieve a speed-up in quantum computation?
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When you act on a multi-qubit system with a 2-qubit gate, what happens to the third qubit?

I am learning to manipulate Qbits and recently I saw the teleportation algorithm. I read about it in two places: Wikipedia and Lecture Notes from Ronald de Wolf (Page 7, 1.5 Example: Quantum ...
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How is entanglement achieved between two particles in quantum computing?

Many texts (especially meant for public consumption) discussing quantum mechanics tend to skim over exactly how entanglement is achieved. Even the Wikipedia article on quantum entanglement describes ...
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What are the possible ways to visualise large, entangled states?

What are the prominent visualisations used to depict large, entangled states and in what context are they most commonly applied? What are their advantages and disadvantages?
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Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in ...
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How to represent a qubyte?

I was not able to locate any visuals online. The visual I have in my head is a cube w/ bloch spheres as the eight vertices. I am also curious about a matrix representation, although I am not sure ...
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Realization of Quantum Shadowgraphy

I recently found out about shadowgraphy and was wondering if a technique like this could be used to: Visually show entanglement Suffice as a measure (e.g. continous partial trace) Most useful ...