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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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Why a basis in super dense quantum coding?

In the classical super dense quantum coding scheme of Bennet and Wiesner (1992), the authors start from an element in the Bell base (which consists of $4 = 2^2 = 2 \times 2$ states, in dimension $4$), ...
Melville's user avatar
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Tests of entanglement between one and many qubits

I have a 5-qubit state $|\psi \rangle$, which has a physical interpretation that the middle qubit is the "impurity" with spin $s_{imp} = 1/2$. The rest 4 qubits highlight the presence of ...
Soumyadeep sarma's user avatar
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1 answer
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CHSH game sharing more general states

In the CHSH game, when the players share EPR states they can achieve best the winning rate of approximately 85% which can be proved through the Tsirelson's bound. I wonder what the best winning rate ...
qmww987's user avatar
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Is purity convex in time?

Is the purity $\mathrm{Tr}[\rho(t)^2]$ of a quantum state $\rho(t)$ that evolves according to a time-independent Lindbladian $\partial_t \rho = \mathcal{L}[\rho]$ convex in time $t$? I suspect the the ...
nlupugla's user avatar
7 votes
1 answer
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What is the stabilizer rank of the W state?

The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal $r$ such that \begin{equation} |{\psi}\rangle = \...
Ian Gershon Teixeira's user avatar
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2 answers
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Why do we need to put the control qubit in superposition in Bell State?

I'm new to quantum computing, so I hope you don't find this question tedious. However, after watching many hours of lectures and reading online, I still don't 100% understand why we need to initialize ...
M.C's user avatar
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2 votes
2 answers
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Do we consider the entangled-based protocol E91 to be a device-independent protocol?

Since both rely on Bell inequalities to maintain security, does the Ekert protocol rely on trustworthiness of the devices?
ibtissam's user avatar
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How to calculate the number of m-partitions of an N-partite quantum state?

I am reading the structure of multipartite entanglement from section 3.3. It is stated there that the number of possible partitions of $N$ parties into $m$ parts is given by $\frac{m^N}{m!}$. I could ...
Anindita Sarkar's user avatar
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How do two-way protocols allow to extract entanglement from states like Werner's?

As discussed in [Lo and Popescu 1999], it is always possible to distill entanglement from pure bipartite states using a one-way protocol. The gist of the idea, as I understand it, is Proposition 1 in ...
glS's user avatar
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Can Bell states be reexpressed with respect to arbitrary local bases?

Suppose I take the Bell state $\Phi^+ = \vert 00\rangle + \vert 11\rangle$. Is it true that I can choose any basis with basis vectors $\vert b_0\rangle$ and $\vert b_1\rangle$ and reexpress the same ...
Joey's user avatar
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How to mathematically describe the action of CNOT on the control qubit alone?

Basically the title. From what I know, starting from the $|{+0}\rangle$ state where the reduced density matrix of the first qubit $|+\rangle$ is $\frac{1}{2}\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{...
Jack Nathan's user avatar
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doesn't a reset on an entangled qubit collapse a superposition?

When I reset an entangled qubit then measure it looks a superposition isn't collapsed to a certain states. In my experiment, the state just before applying a reset is: $$\frac{1}{2}(|000⟩+|011⟩+|101⟩+|...
taketoshi kinoshita's user avatar
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Prove that convex combinations of product states admit a hidden variable model

Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
truebaran's user avatar
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Uniqueness, absolutely maximally entangled states, and the 3 qutrit code

There is a well known $ [[3,1,2]]_3 $ qutrit stabilizer code with stabilizer generators $ XXX $ and $ ZZZ $. This code is related to a $ [[4,0,3]]_3 $ qutrit stabilizer state with stabilizer ...
Ian Gershon Teixeira's user avatar
1 vote
1 answer
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In e91 protocol, if one of the bases combination was not chosen, what should be done to avoid division by zero?

In e91 protocol, if one of the bases combination was not chosen, what should be done in this case to avoid division by zero? One solution that comes to mind is setting the whole value to zero, but is ...
Mohamed Elsheikh's user avatar
2 votes
1 answer
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What is the F12 rule for the Game of Life

This is more of a help call to find a specific rule set for the game of life. I'm currently reading the "Entanglement in the Quantum Game of Life", however they refere to the classical F12 ...
Qubii's user avatar
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In quantum teleportation, why does measuring entanglement not destroy the whole state?

In quantum teleportation, we have three qubits. Sender, receiver and ancillary. First, we entangle the ancillary and target qubit. Next, we entangle ancillary and sender qubits. Now, the whole system ...
Mayukh Mukherjee's user avatar
1 vote
1 answer
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E91-Protocole the type of Bell state use in this protocol

my question is, what is the type of the Bell state used in Ekert-91 link for Bell states in question correlated or anti-correlated. And if they can use both of them , how do Alice & Bob know ...
Badr Eddin's user avatar
3 votes
1 answer
54 views

Benefits of using quantum encrypted keys

Considering, in a perfect world everyone has the capability to create a quantum key. What would the benefits of using quantum encrypted keys instead of using classically encrypted keys? Besides the ...
Snarz's user avatar
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1 answer
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How to analyse a quantum circuit with an uncertain gate F?

The following quantum circuit consists of two CNOT gates in the middle of the circuit. The two-qubit input quantum register $|x\rangle$ is an arbitrary quantum state and can be set by the user. The ...
Xiling's user avatar
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1 answer
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Entanglement-based attack on E91 protocol

My first question is if the bell pair that Alice and Bob share for the E91 protocol matters since I've seen different resources use different pairs for the explanation. My second question is say they ...
Omeglac's user avatar
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How to understand the idea of maximal entanglement intuitively?

I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
Omeglac's user avatar
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Can we perform teleported-error-correction with noisy Bell pairs?

It is well-known that in https://arxiv.org/abs/quant-ph/0312190 that error correction can be performed by teleportation on the logical level, so prepare one logical Bell pair and (logical?) Bell ...
AndyLiuin's user avatar
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Efficient Clifford simulation and entropy of reduced density matrices

Suppose I have a Clifford circuit $C$ and I want to estimate the entanglement entropy of a subset of two qubits, say, $\{q_0, q_1\}$, i.e. the quantity $$S(\rho_{q_0 q_1}) = - \text{Tr}[\rho_{q_0 q_1} ...
jth's user avatar
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What is the general form for GHZ and W class states?

I am reading the following paper on mixed three-qubit states. It states that any three–qubit pure state can be written as (equation 1 of the paper) $|\psi_{GHZ}\rangle=\lambda_0 |000\rangle+\lambda_1 ...
Anindita Sarkar's user avatar
4 votes
2 answers
230 views

Can a non-local unitary operator preserve separability

Consider a $2$-qubit system with Hilbert space $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$. A pure separable state in $\mathcal{H}$ is of the form $\lvert \psi_1 \rangle \otimes \lvert \...
Silly Goose's user avatar
3 votes
1 answer
113 views

How does quantum teleportation not lose information?

This may be a bit of an elementary question, but I think understanding it will help me understand fundamentally what makes quantum algorithms a bit magical. Alice starts with a message she wants to ...
Y. S.'s user avatar
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Maximum entanglement entropy of a random circuit

Consider the random quantum circuit below where the gates are randomly taken from SU(4) accordingly with the Haar measure. I am looking to determine an upper bound on the entanglement entropy between ...
Emilio Pezaroglo's user avatar
1 vote
1 answer
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Does measurement in different bases allow for FTL communication?

Imagine for a moment that we could distinguish between arbitrary quantum states. We’ll show that this implies the ability to communicate faster than light, using entan- glement. Suppose Alice and Bob ...
Nir Sharma's user avatar
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Is entanglement trainable?

There exists a famous result from Google that the gradients of the parameters of quantum neural networks (QNN) vanish exponentially with the number of qubits in the quantum circuit. Their result ...
jsbaker's user avatar
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Is a state in the GHZ entanglement class iff it's true 3-partite entangled and at least one of its reduced states is mixed?

Consider 3-qubit state. In W. Dür et al. (2000), it is stated that a 3-qubit state can be 3-partite entangled in 2 different ways. We call it entanglement classes. GHZ state is a representative of one ...
Piotr Masajada's user avatar
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1 answer
54 views

Special entangled tripartite state

Suppose three particles a, b and c a is entangled with b, a is entangled with c, b and c are separatable Is it possible?
reza's user avatar
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1 answer
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Why does Lidar define a decoherence-free subspace as "a subspace that undergoes purely unitary evolution"

In this paper from 2014, Lidar defines: "an open system which undergoes purely unitary evolution (possibly only in a subspace of its Hilbert space) is said to be decoherence-free." Why is ...
Silly Goose's user avatar
2 votes
1 answer
114 views

Minimizing $1 - \text{Tr}(\Phi(\rho,U)^2)$

I am looking for a computationally efficient way to minimize the following function. Let $$\Phi(\rho, U) = \text{Tr}_2(U\rho U^\dagger)$$ be a reduced density matrix where $\rho = \overline{\rho}_1 \...
Silly Goose's user avatar
0 votes
1 answer
36 views

Synthesizing quantum circuits from unitary matrices vs quantum state vectors, and determining qubit entanglement

I'm studying how to build quantum circuits and understand qubit entanglement. The following are my two confusing questions. I would greatly appreciate any assistance or insights regarding these ...
Jayce's user avatar
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1 vote
1 answer
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Does entanglement vanishes when an electron runs from the s orbital?

In the s orbital of a helium atom there are two entangled electrons. They are entangled because they have different spins. Suppose we give energy to one electron and let it runs from the atom. Does ...
reza's user avatar
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1 vote
1 answer
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On difference in the number of two-qubit stabilizer states that are separable (36) vs those that are maximally entangled (24) and partial entanglement

We have a set of two-qubit stabilizer states. There are 60 of them: 36 separable and 24 maximally entangled (MES). I was wondering whether we can somehow compare the size of the set of partially ...
Sutasu's user avatar
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1 vote
1 answer
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Is there a proof that any pure two-qubit Partially entangled state lies somewhere in between a separable and maximally entangled state?

Intuitively this seems true, but is there a proof of the following: We have two-qubit pure state. Given a Partially entangled state (PES) $|P\rangle$ we can always find a separable state $|S\rangle$, ...
Sutasu's user avatar
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1 answer
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Are there unextendable product sets in $\mathbb{C}^2\otimes\mathbb{C}^2$?

Following the notation in Watrous' book, page 353, an unextendable product set in a bipartite space $\mathcal X\otimes \mathcal Y$ is a set of orthonormal product vectors of the form $$\mathcal A\...
glS's user avatar
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2 votes
2 answers
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What are examples of weakly optimal witnesses?

While discussing witnesses, in https://arxiv.org/abs/0811.2803 the authors mention (page 16 of the arxiv version, below Eq. (32)) that a necessary condition for a witness $W$ to be optimal is that it ...
glS's user avatar
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Entanglement generation for commuting Hamiltonian

Consider an $n$ qubit Hamiltonian $H$ given by \begin{equation} H = \sum_{i=1}^{m} H_i, \end{equation} where each $H_i$ is a $k$-local term and it holds that \begin{equation} e^{H} = e^{H_m} \cdot e^{...
BlackHat18's user avatar
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3 votes
1 answer
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A separable pure bipartite quantum state must be a product state

I'm looking for the simple argument to prove that a separable pure bipartite quantum state is in fact a product state. This question comes from a statement in Wikipedia on separable states: In the ...
JMark's user avatar
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1 answer
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Prove that an entanglement witness is optimal iff it's zero on a spanning set of product states

I am reading about entanglement witnesses from here. In section 2.5.2, it is written that Furthermore, a witness $\mathcal{W}$ is called optimal, if there is no other witness, which is finer than $\...
Anindita Sarkar's user avatar
2 votes
1 answer
40 views

How is the expression $\frac{\|\rho^{T_B}\|-1}{2}$ obtained from the definition of negativity?

In quantum information theory, negativity is defined as summation of the absolute values of negative eigenvalues of the partial transposed density matrix. The expression of negativity is given as $$ \...
Anindita Sarkar's user avatar
2 votes
2 answers
232 views

What is the relation between the purity of a bipartite state and its subsystems?

I know for a separable state $\rho_{AB}$ we have $$P_{AB}= P_{A}=P_{B}=1$$ Where P is purity. What if the relation between the purities when the bipartite state is entangled? Is there any inequality ...
reza's user avatar
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What does one-tangle says in an n-qubit system?

One-tangle is negativity with respect to qubit x. I know in a 3 qubit system if one-tangle with respect to qubit x is 0, then qubit x is separatable. Is this statement generalized for n-qubit systems? ...
reza's user avatar
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1 vote
1 answer
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If $\rho_{AB}$ is a separable then the partial transpose w.r.t to A is PSD

Def: The partial transpose of a linear operator $\rho_{AB}$ over a Hilbert space $H_A \otimes H_B$ w.r.t A is defined for a linear operator $\rho_{AB}=\rho_A \otimes\rho_B$ as $\rho^{T_A}_{AB}=\rho_A^...
some_math_guy's user avatar
3 votes
1 answer
56 views

Is a multipartite state entangled if and only its reduced states are mixed?

In general, a bipartite pure state $ρ$ is entangled if and only if its reduced states are mixed rather than pure. Is this statement generalized to multipartite states? Is there any resource about that?...
reza's user avatar
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2 votes
1 answer
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What are toy examples of single-copy entanglement conversion?

In (Vidal 1999) they prove that, given any pair of pure bipartite states written as $$|\Psi\rangle = \sum_{i=1}^n \sqrt{\alpha_i}|i,i\rangle, \qquad |\Phi\rangle = \sum_{i=1}^n \sqrt{\beta_i}|i,i\...
glS's user avatar
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1 vote
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cirq entanglement qubits

The following code originates from a third-party, although, I have added the commented line containing "UNCOMMENT THE START OF THIS LINE". ...
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