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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How to decode 2-bit message from 2 entangled qubits

I'm trying to do exercise 3 of this quantum course Alice and Bob prepare an EPR pair in the Bell + state. They each take one qubit home. Suddenly, Alice decides she wishes to convey one of 4 ...
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Why does entanglement not increase the classical capacity of a channel?

In a recent paper, the authors quote an older work of Bennett, Shor and others and make the following statement While entanglement assistance can increase achievable rates for classical point-to-...
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Are inseparable states with positive partial transposition nonlocal?

In Horodecki, Horodecki and Horodecki (1998), Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?, the authors remark in the conclusions (beginning of pag. 4, ...
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Resultant state after teleportation?

Consider that Alice has an entangled state $$\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}e^{2\pi i\frac{x_1}{N}j}\left|j\right>_h\left|j\right>_t\left|j\right>_k$$ Now, Alice transfers/teleports $|j\...
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What is the resultant composite quantum state after the transfer?

Suppose Alice has the following state $|\Psi\rangle = \frac{1}{\sqrt2} (|10\rangle + |11\rangle)$ If Alice transfers 1st qubit to Bob then is this the resultant composite system state after transfer? ...
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What is the state after entangled qubit transfer?

Suppose Alice has 2 qubit entangled state and wants to send 1st qubit to Bob. q1) Now what is left with Alice? Both 1st and 2nd qubits or only 2nd qubit? q2) Does the overall composite quantum ...
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In the CHSH inequality, how can I know which term is supposed to have the minus sign?

I try to follow the calculation from IBMQ experience regrading of Entanglement and Bell test which they derive the value of question as \begin{equation} C=\langle A B\rangle-\left\langle A B^{\prime}\...
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Measuring a single qubit in 2 bit entangled state

consider a 2 qubit entangled state ($\sqrt 3/2)\left|00\right> + (1/2)\left|11\right>$ Q1) Is the above entangled state a valid one? q2) If valid then What is the probability of measuring the ...
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What is the probability of measuring $|j\rangle$ with $j\in\{0, 1, 2, … N-1\}$?

Consider the state $$\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}e^{2\pi i\frac{x_1}{N}j}\left|j\right>_h\left|j\right>_t.$$ In the above entangled state, what is the probability of getting $|j\rangle_t$ ...
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Is it possible to have entanglement with different sized parties or with more than 2 parties?

All the entanglement I've see is between 2 parties that have the same number of qubits. Is it possible to have entanglement where each party has a different number of qubits? Is it possible to have ...
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Quantum Teleportation expression in bell basis

Suppose i want to transmit a qubit $\alpha|0\rangle_A+\beta|1\rangle_A$, I send this with the Bell state $s(|0\rangle_B|0\rangle_C +|1\rangle_B|1\rangle_C)$, where particle $C$ is for the first ...
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Unitary operator confusion

Given a unitary operator $u_3=|1\rangle\langle 0|+|0\rangle\langle 1|$, which i know is the $X$ operator or flip gate, so that $X|0\rangle=1$, $X|1\rangle=0$. Now given a bell state $|\Psi^-\rangle_{...
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Determining the quantum secret

I earlier posted I question Representing a Bell measurement on non adjacent qubits for which I got an excellent answer. Now I want to build upon that and do further analysis which is where I am stuck. ...
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Non maximally entangled states for QKD

Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
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If Alice and Bob share a Bell state, can Alice send her individual qubit to a third party?

Suppose Alice wants to send Bob information. Each of them has been sent each of the qubits of the Bell state in advance. Suppose Alice has the first qubit and Bob has the second. $|\Phi^+\rangle = \...
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In what ways can qubits be used for applications that do not require entanglement?

Many good questions on this site have explored how entanglement lies at the boundary between the quantum world and the classical. For example in computational speedups, or teleportation or superdense ...
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Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem?

Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake. Based on Wikipedia ...
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Change entangled far Qbit state without mesaure it

Hello I entangled with Qsharp a far QBit (Bob)to a 3 Qbit register that is also entangled to another marked qbit for a Grover search. When I look for the value 4 with Grover search the Bob qbit is ...
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What implementation changes should be done in maxcut code using VQE?

In the paper, "Quantum algorithm implementations for beginners" in the section XVII. QUANTUM SIMULATION OF THE TRANSVERSE ISING MODEL (page 54-58), the authors have plotted energy $E$ vs magnetic ...
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Entangling marked qubit with part of the register in Grover's search

Can the marked qubit be associated only with half of the register? I mean if I can ask the oracle if the $2$ low qubits from a $4$ qubit register have a certain value. I ask this to know if I can ...
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How can a CNOT gate change the control qbit (e.g. in the Deutsch Oracle problem)?

It is very confusing how the CNOT gate can change the properties of the controlled qubit (possibly because I am still stuck in the classical programming mindset): Many books have explained the ...
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What is the difference between entangled and separable states or electron spin-singlets?

What is the difference between entangled states and separable states or electron spin-singlets?
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Does entanglement allow communication of user specified information or not?

At first when I heard about entanglement, I thought "Neat, so we can make a manipulation on our quantum computer here in such a way that can be interpreted as a binary output somewhere else, and have ...
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What are the two qubits in the state $a\lvert 00\rangle+b\lvert11\rangle$?

What are the $2$ qubits of the state $a\lvert 00\rangle+b\lvert11\rangle$? Are they $a'\vert0\rangle+b'\vert1\rangle$ and $c'\vert0\rangle+d'\vert1\rangle$? How are they measured, and what would be ...
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Geometric interpretation of 1-distillability

This is a sequel to Motivation for the definition of k-distillability Geometrical interpretation from the definition of 1-distillability The eigenstate $|\psi\rangle$ of the partially ...
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Motivation for the definition of k-distillability

Definition of k-distillability For a bipartite state $\rho$, $H=H_A\otimes H_B$ and for an integer $k\geq 1$, $\rho$ is $k$-distillable if there exists a (non-normalized) state $|\psi\rangle\in ...
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Understanding the classification of quantum states based on partial transposition: representations of the bipartite density matrix

I'm going through some slides on the PPT/NPT criteria along with Horodecki's paper, and I'm kind of stuck. Let's take this slide: Firstly, why can we write a bipartite density matrix as $\sum_{...
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How to prove the following bosonic entanglement expression?

Based on the article given by J. L. Ball, I. Fuentes-Schuller, and F. P. Schuller, Phys. Lett. A 359, 550 (2006) had used the following expression of von-Neumann entropy \begin{equation} S = - \...
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GHZ - measuring particles

I'm referring to an earlier question. It involves secret sharing based on the different measurement directions 3 people i.e Alice Bob and Charlie do. Now there is a block in the referred paper which ...
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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}...