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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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 \...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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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 \...
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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 ...
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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 ...
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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 ...
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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 $|S\rangle$, ...
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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
$$\mathcal A\...
glS♦
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What are examples of weakly optimal witnesses?
While discussing witnesses, in https://arxiv.org/abs/0811.2803 the authors mention (page 16 of the arxiv version, below Eq. (32)) that a necessary condition for a witness $W$ to be optimal is that it ...
glS♦
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Entanglement generation for commuting Hamiltonian
Consider an $n$ qubit Hamiltonian $H$ given by
\begin{equation}
H = \sum_{i=1}^{m} H_i,
\end{equation}
where each $H_i$ is a $k$-local term and it holds that
\begin{equation}
e^{H} = e^{H_m} \cdot e^{...
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A separable pure bipartite quantum state must be a product state
I'm looking for the simple argument to prove that a separable pure bipartite quantum state is in fact a product state. This question comes from a statement in Wikipedia on separable states: In the ...
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Prove that an entanglement witness is optimal iff it's zero on a spanning set of product states
I am reading about entanglement witnesses from here.
In section 2.5.2, it is written that
Furthermore, a witness $\mathcal{W}$ is called optimal, if there is no other witness, which is finer than $\...
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How is the expression $\frac{\|\rho^{T_B}\|-1}{2}$ obtained from the definition of negativity?
In quantum information theory, negativity is defined as summation of the absolute values of negative eigenvalues of the partial transposed density matrix. The expression of negativity is given as
$$
\...
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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 ...
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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? ...
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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^...
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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?...
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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
$$|\Psi\rangle = \sum_{i=1}^n \sqrt{\alpha_i}|i,i\rangle,
\qquad |\Phi\rangle = \sum_{i=1}^n \sqrt{\beta_i}|i,i\...
glS♦
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cirq entanglement qubits
The following code originates from a third-party, although, I have added the commented line containing "UNCOMMENT THE START OF THIS LINE".
...
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Is it possible to derive a Schmidt decomposition for a mixed state?
It is relatively simple to derive the Schmidt decomposition of a pure state $|{\psi}\rangle \in H_A \otimes H_B$ with the SVD decomposition theorem. There are plenty of examples (lecture notes, books, ...
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How can a third party learn the coefficient of a shared $2n$-qubits state using a classical message from each one?
Suppose Alice and Bob share the $2n$-qubits state $$|\phi _{x,y,b} \rangle = \frac{1}{2}(|x\rangle + (-1)^b |y\rangle)$$
where $x,y$ are $2n$-length strings of $0$ and $1$, $b$ is a bit, and $x \ne y$....
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Pseudo telepathy with 3 people that share the state $\frac{1}{2}(|000\rangle -|011\rangle-|101\rangle-|110\rangle)$
The problem is similar to the pseudo-telepathy where Alice, Bob and Charlie are given bits $a,b,c \in \{0,1\}$ such that $a \oplus b \oplus c=0$, and their goal is to output the bits $A,B,C$ without ...
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Two-photon N00N state through Mach-Zehnder interferometer
I am interested in modelling a two-photon N00N state sent through a Mach-Zehnder interferometer, which consists of a beam-splitter (50:50), a phase shift operator on the first mode, a phase shift ...
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Can Alice and Bob convince the cops that they don't share any entanglement?
Suppose Alice and Bob are arrested for killing Eve, and are taken to two different interrogation rooms. The police quiz Alice and separately Bob, asking them a bunch of different questions along the ...
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What operations are allowed in LOCC?
I have a question regarding a wording from an exercise book:
“Two states psi and phi of a composite system are said to be 'LOCC equivalent' if each can be converted to the other using only local ...
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Truthfulness of Entanglement Fidelity
In [1] Schumacher introduced Entanglement Fidelity
$$F_e(\rho^Q, \mathcal{E}^Q) = \sum_\mu (\text{Tr}(\rho^Q A^Q_\mu))(\text{Tr}(\rho^Q {A^Q_\mu}^\dagger)). \tag{1}$$
which is conjectured to quantify ...
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What happens to $|y\rangle \sum_{x}|x\rangle|f(x) + g(y)\rangle$ when we throw away the first register?
Let's suppose, that applying $\mathbf{H}$ (Hadamard operator) to the first register of the state $c \cdot \sum_{x}|x\rangle|f(x)\rangle$ ($f$ is a permutation, $c$ is a normalization factor), and ...
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Is there a measure for entanglement of $n$-qubit system?
I am working on a topic related to an $n$-qubit system. I should obtain the entanglement.
As I searched, I could not find any measure to obtain the entanglement of a mixed $n$-qubit system.
Is there ...
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Does the entanglement entropy work for mixed states?
I know for a pure state $\rho$, if its subsystems are mixed then $\rho$ is entangled.
Is the result true if $\rho$ is mixed state?
Is the above law generalized for a $n$-qubit state?
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quantum teleportation with shared state and teleported state in bloch representation
Suppose that two parties (Alice and Bob) share an entangled state
$$ \rho_F = F \lvert \phi^+ \rangle \langle \phi^+ \rvert + \frac{1-F}{3} \left( I \otimes I - \lvert \phi^+ \rangle \langle \phi^+ \...
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Why divide $\theta$ by 2 when doing the Bell's Inequality Experiment?
I understood the CHSH game correlations by watching Prof. Vazirani's video. I also understood that the correlation between two measures taken from different basis are related by the cosine of the ...
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Optimal pure state decomposition of bipartite mixed states
Suppose I have a 2-qubit mixed state given by $\rho$ whose concurrence is $C$. I am interested in finding the optimal pure state decomposition of $\rho=\sum_{i=1}^4 p_i|ψ_i⟩⟨ψ_i|$ such that $C(\psi_i)=...
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Qnode model gradient of inputs (not parameters!) question
I am trying to use qml to do physics informed quantum machine learning within Tensorflow. I know with TF, to get derivatives of the network's inputs (df/dx, for example), you can use with tf....
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Entangled qubit systems always maximally entangled?
For a bibpartite system $A,B$ with $A\in\mathcal{H}_A$ and $B\in\mathcal{H}_B$, the Schmidt decomposition of its state $| \psi \rangle_{AB}$ is :
\begin{equation}
| \psi \rangle_{AB}= \sum_{i=0}^{\min ...
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Why can't you efficiently simulate quantum computers on classical computers
I have just started learning about quantum computers, and my understanding of quantum mechanics is very limited. However, I can not find an answer to my question. So my question can be divided into ...
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How to compute the state resulting from measuring a single photon in a cluster state?
I was reading the book ''Introduction to Optical Quantum Information Processing" by Pieter Kok and Brendon Lovett and on page 199 they talk about cluster states and the circuit model of Quantum ...
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Disentanglement of qubits from output of CNOT gate
Suppose we have a control qubit with initial state $\binom{a}{b}$ and a target qubit with initial state $\binom{c}{d}$.What a CNOT does is transform the state of the target qubit into:
$\begin{pmatrix}...
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State of qubit after gate and measurement
Suppose we have a gate with 1 control qubit and 1 target qubit:
Lets say the state of the control qubit initially was $\begin{pmatrix}
a\\
b
\end{pmatrix}$ and the state of the target qubit was ...
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Prove that an entanglement witness satisfies $\operatorname{tr}(W)>0$ and $\operatorname{tr}(W)^2\ge \operatorname{tr}(W^2)$
If $W$ is an entanglement witness ($W \neq 0$), prove that
(a) $ tr(W) >0$
(b) $ tr(W)^2 > tr(W^2)$
For (a), by definition, since $ |ab\rangle$ is separable, thus $tr(\rho W)=\langle ab | W| ab \...
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Equivalence of two unitary transformation with respect to local operations
Suppose that $U_1$ and $U_2$ are two (entangling) operators that act on a quantum system consisting of several subsystems. Is there any criterion to tell if these two are equivalent up to applying ...
2
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0
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52
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Measuring an entangled quantum state
I have this exercise to solve, but I can't figure out how to proceed.
First, I don't think the state proposed is valid (the probabilities don't sum up to 1).
'Secondly, given that it should be an ...
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A measure of entanglement created by a unitary operation
Let $U$ be a unitary matrix acting on a 3-qubit system. If there is no correlation among any pairs of the three qubits, the unitary operation can be represented as $U = U_1 \otimes U_2 \otimes U_3$, ...
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1
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Why can't we do pure state tomography using interference with a known reference state?
I am new to quantum tomography, and right now I am trying to understand tomography with pure states. It's my understanding if we have the amplitude magnitudes as well as relative phases, we can ...
2
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0
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Mutual information of shared state is larger than expectation values
Im trying to prove the following identity for a special case:
Alice and Bob share the Bell state
\begin{align*}
|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle).
\end{align*}
Consider the ...
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