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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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GHZ - measuring particles

As referred to an earlier question Quantum secret Sharing using GHZ state paper It involves secret sharing based on the different measurement directions $3$ people i.e Alice Bob and Charlie do. Now ...
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Equivalent determinant condition for Peres-Horodecki criteria

The Peres-Horodecki criteria for a 2*2 state states that if the smallest eigenvalue of the partial transpose of the state is negative, it is entangled, else it is separable. According to this paper (...
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What is the motivation for Weyl matrices in quantum information theory?

Quantum Entanglement and Geometry — Andreas Gabriel (2010) — Sec: 2.3.4 ~p. 11 Another basis for $d\times d$-dimensional matrices that has proven to be quite useful in quantum information theory is ...
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Quantum secret Sharing using GHZ state paper

I am reading a paper on Quantum Secret Sharing Quantum Secret Sharing using GHZ states I have doubts regarding the initial phase of the paper, which are: Let me state what things I read and ...
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What is the definition of Bell state on a n-qubit system?

Question 1: The bell state for a 2-qubit system has been defined in Neilsen and Chuang's book as the set of maximally entangled states spanned by $\{|00\rangle + |11\rangle, |00\rangle - |11\rangle, |...
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Can entangled qubits be disentangled without using code or software?

Is there a way to revert two entangled qubits to a separate state without using code...like restarting a quantum computer? Note: By "restarting a quantum computer", I do not mean restarting a virtual ...
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What are nontrivial examples of $n$-sharable bipartite states?

A bipartite state $\newcommand{\ket}[1]{\lvert #1\rangle}\rho_{AB}$ is said to be $n$-sharable when it is possible to find an extended state $\rho_{AB_1\cdots B_n}$ such that partial tracing over any ...
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Observing that some action has happened in an entanglement scenario

Hobbyist quantum programmer here and just getting back into the swing of things by speccing out some fun apps in my head and trying to build them to learn more about the whole ecosystem which is ...
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Simultaneous eigenstate of commuting observables and their tensor product

So this is about something from Preskill's notes on Quantum Computation and Information, Chapter 4, page 3. Imagine we have a maximally entangled state (Bell state). We can identify the Bell state by ...
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What happens when an operator is applied only to some bits of a mixed state?

What happens when an operator is applied only to some bits of a mixed state? For instance, assume $\vert x\rangle\vert f(x)\rangle$ is entangled. Then what is the result of $\vert Ux\rangle\vert f(x)\...
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Why do we use complex-conjugate instead of complex-conjugate-transpose when calculating the concurrence?

When we use the formula to calculate two-qubit entanglement, like these: $$ C(\rho)=\max \left\{\sqrt{e_{1}}-\sqrt{e_{2}}-\sqrt{e_{3}}-\sqrt{e_{4}}, 0\right\}\tag{18} $$ with the quantities $...
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Structural Physical Approximation of Partial Transpose

To make the partial transpose a complete positive and therefore physical map, one has to mix it with enough of the maximally mixed state to offset the negative eigenvalues. The most negative ...
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How are witness operators physically implemented?

Let's take an example of an entanglement witness of the form $W = | \phi \rangle \langle \phi | ^{T_2}$ where $ | \phi \rangle $ is some pure entangled state. If I wanted to test some state $\rho$, I ...
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Explicit 16⨯16 matrix representations of two-qudit entanglement witnesses

I have a set of $16 \times 16$ two-qudit density matrices. I would like to study the bound-entanglement for this set, making use of entanglement witnesses for which explicit matrix representations are ...
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Are entanglement witnesses of this form optimal?

One can make an entanglement witness by taking the partial transpose of any pure entangled state. Consider $|\phi \rangle $ as any pure entangled state. Then $W = | \phi \rangle \langle \phi |^{T_2} ...
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Does a 5-partite state with these entanglement properties exist?

Is there a 5-partite state such that if two parties each hold 2 shares of the state, without knowing what shares the other party holds, they can create a Bell pair between them and know which qubit in ...
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Proof of joint entropy theorem

From section 11.3.2 of Nielsen & Chuang: (4) let $\lambda_i^j$ and $\left|e_i^j\right>$ be the eigenvalues and corresponding eigenvectors of $\rho_i$. Observe that $p_i\lambda_i^j$ and $\...
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Is generating usable entanglement difficult?

I'm a theorist and I assume that I can use entanglement resources for practical use freely, but is this really the case? Is generating entanglement and storing it for long enough periods of time such ...
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Superoperator cannot increase relative entropy

Note: Cross-posted on Physics SE. So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy: $$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || ...
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Complexity analysis of separability in the multipartite case

It's well known that determining whether a bipartite mixed state is separable or entangled is a $\mathsf{NP}$-hard problem under some accuracy estimates (cf. this TCS SE discussion). Now I'm curious ...
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What does “bipartite” mean?

This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ...
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Is there a two-qudit Choi entanglement witness $W^{(+)}$?

Example 2 in arXiv:1811.09896 states that the "Choi EW (entanglement witness) $W^{(+)}$ obtained from the Choi map in $d=3$ $\ldots$ is given by \begin{equation} W^{(+)} = \frac{1}{6} \left( \sum_{i=0}...
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Is $ |x,y,z\oplus f(x,y)\rangle$ entangled?

Let $f(x,y)$ be a random 2n- to 1-bit function. Consider the quantum circuit $|x,y,z\rangle \to |x,y,z\oplus f(x,y)\rangle$. Is the new state entangled in general? Is it entangled if $x,y$ are $...
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Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao

Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
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What are the ranges of the four $q$ parameters in the magic simplex of Bell states formula?

Equation (7) in the 2012 paper, "Complementarity Reveals Bound Entanglement of Two Twisted Photons" of B. C. Hiesmayr and W. Löffler for a state $\rho_d$ in the "magic simplex" of Bell states \begin{...
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How does the probability of measurement turn out to be negative?

c) Compute $$\text{Prob}(\uparrow_\hat{n}\uparrow_\hat{m}) \equiv \text{tr}(\pmb{E}_A(\hat{n})\pmb{E}_B(\hat{n})\pmb{p}(\lambda)), \tag{4.164}$$ where $\pmb{E}_A(\hat{n})$ is the projection of ...
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Quantum teleportation with “noisy” entangled state

This is actually an exercise from Preskill (chapter 4, new version 4.4). So they are asking about the fidelity of teleporting a random pure quantum state from Bob to Alice, who both have one qubit of ...
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What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?

For two particular (twelve-and thirteen-dimensional) sets of two-retrit states (corresponding to 9 x 9 density matrices with real off-diagonal entries), I have been able to calculate the Hilbert-...
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Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?

On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
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How is the expression for the optimal entanglement witness derived?

In the Bertlmann 2009 paper in the Annals of Physics (here), an optimal witness operator for an entangled state $\rho$, given that the closest separable state to it is $\rho_0$ is given by: $$A_{\...
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What does it mean that copying a state is impossible but creating a copy of by entangling is possible?

Why is it that copying an unknown qubit is impossible but creating a copy of the standard computational basis is possible by entangling it to existing qubits? And why one is possible and the other isn'...
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EPR states with permuted qubits

Suppose I prepare following state consisting of (for example) three EPR pairs: $$\lvert\Psi\rangle = \frac{\lvert00\rangle+\lvert11\rangle}{\sqrt{2}}\otimes\frac{\lvert00\rangle+\lvert11\rangle}{\...
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What do entanglement cost and distillable entanglement have to do with measuring entanglement?

So far what I have learned is that von-Neumann entropy is a tool to measure or quantify information and therefore entanglement for a given pure state system. However, similar concepts emerge from the ...
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Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere

The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection $\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia: Quantum ...
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How to prove teleportation does not violate no-cloning theorem?

For a given teleportation process as depicted in the figure, how one can say that teleporting the qubit state $|q\rangle$ has not cloned at the end of Bob's measurement?
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What is the general variety corresponding to the Segre embedding for $n$-qubit systems?

It is well known that entanglement is precisely the difference between the Cartesian product and the tensor product. The space where every point corresponds to a state is the projective Hilbert space, ...
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How we can describe entanglement from measurement and resource perspectives?

When we read books on quantum computing and information theory, specifically in entanglement we find some distinguishability between those who focus on entanglement as a resource or use it as an ...
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Convex Combination of Separable States

The state $$ \frac{1}{2}\left(| \phi^+ \rangle \langle \phi^+ | + | \psi^+ \rangle \langle \psi^+ | \right) $$ where $$ | \phi^+ \rangle = \frac{1}{\sqrt2} \left(|00 \rangle + | 11 \rangle \right) $...
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The relationship between entanglement of vector states to matrix operations

I don't understand something which is I believe pretty fundamental. It's said that an operation represented by a matrix A is an entanglement if A can't be written as a tensor product of other matrices....
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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 ...