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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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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 ...
XXDD's user avatar
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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, ...
Paul B. Slater's user avatar
10 votes
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Are there separable $\rho$ that cannot be decomposed with less than $\operatorname{rank}(\rho)^2$ pure product states?

In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
glS's user avatar
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10 votes
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Entanglement-assisted hashing bound for asymmetric depolarizing channels

I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ...
Josu Etxezarreta Martinez's user avatar
10 votes
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Entanglement transfer of spin-entangled triplet-pair states between flying qubits and stationary qubits

The context: We are in the solid state. After a photon absortion by a system with a singlet ground state, the system undergoes the spin-conserving fission of one spin singlet exciton into two spin ...
agaitaarino's user avatar
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8 votes
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Query on Reduced Graph States

Reduced graph states are characterized as follows (from page 46 of this paper): Let $A \subseteq V$ be a subset of vertices of a graph $G = (V,E)$ and $B = V\setminus A$ the complement of $A$ in $V$. ...
John Doe's user avatar
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7 votes
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Five qubits can be entangled in how many ways?

It is well-known that there are two ways to entangle three qubits (https://arxiv.org/abs/quant-ph/0005115) and nine ways to entangle four qubits (https://arxiv.org/abs/quant-ph/0109033). I found in a ...
R.G.J's user avatar
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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 ...
Sanchayan Dutta's user avatar
7 votes
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62 views

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 ...
glS's user avatar
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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 ...
XXDD's user avatar
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Verification of local unitary equivalence between two pure states

This might be a non-trivial and hard problem. I've been thinking about this for days but couldn't find a good answer, so I hope any of you could give me a good answer/intuition for me to move forward. ...
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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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Explanation of the generalized SWAP test: the permutation test?

I am reading this paper on the state separability problem, and came across the term “Permutation Test.” This is on page 7 section 2.3. Apparently, the more famous SWAP test is a special case of ...
TwentyCents's user avatar
5 votes
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How to get to the formula for the entanglement of formation of two-qubit states?

An explicit formula for the entanglement of formation $E(\rho)$ for an arbitrary two-qubit state $\rho$ was given by Wooters in Entanglement of Formation of an Arbitrary State of Two Qubits. The ...
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What is the difference between "entanglement distillation" and "entanglement purification"?

To my understanding, entanglement distillations is transformation of several copies of weakly entangled states into fewer copies of more strongly entangled states using local operations and classical ...
metkuma12's user avatar
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Finding a class $C$ of bipartite PPT states such that entanglement of $\rho \in C$ implies entanglement of $\rho + \rho^{\Gamma}$

Consider an entangled bipartite quantum state $\rho \in \mathcal{M}_d(\mathbb{C}) \otimes \mathcal{M}_{d'}(\mathbb{C})$ which is positive under partial transposition, i.e., $\rho^\Gamma \geq 0$. As ...
mathwizard's user avatar
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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-...
Paul B. Slater's user avatar
5 votes
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72 views

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 ...
Paul B. Slater's user avatar
4 votes
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177 views

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 ...
Mark Spinelli's user avatar
4 votes
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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 $U = U_1 \otimes U_2 \otimes U_3$, ...
user185671631's user avatar
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What are good pedagogical introductions to entanglement distillation?

I have a basic understanding of what entanglement distillation entails, up to the typical subspace projection protocol described in Nielsen & Chuang, and I would like to read more on the subject. ...
Bentanglement's user avatar
4 votes
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86 views

Quantum entanglement as topological entanglement

According with Aravind: the Hopf link, L2a1, corresponds to the Bell state $\frac{1}{\sqrt 2}\big (|00\rangle+|11\rangle\big )$, the Borromean link (L6a4) can be considered as GHZ state $\frac{1}{\...
Juan Ospina's user avatar
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Is it ever beneficial to communicate qubits that aren't EPR pairs?

When Alice wants to send a qubit $q$ to Bob, she doesn't have to send $q$ itself. She can instead generate an EPR pair $(a, b)$, send $b$ to Bob, and teleport $q$ to Bob by consuming $(a,b)$ and ...
Craig Gidney's user avatar
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Must two separable states that are $\epsilon$-close in trace distance admit close separable decompositions?

$\newcommand{\complex}{\mathbb{C}}$ Let $n$ and $m$ be positive integers. Does there exist a continuous function $f: [0,1] \rightarrow [0,1]$ such that $f(0)=0$, and whenever two separable density ...
Ben's user avatar
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Relation between geometric and discrete circuit complexity

Geometric complexity of a unitary, as introduced for example here https://arxiv.org/abs/quant-ph/0502070, measures the length of a geodesic connecting the identity matrix and a given unitary in the ...
Nikita Nemkov's user avatar
4 votes
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125 views

Volume law spread after Hamiltonian evolution

Start with an $n \times n$ lattice, with each qubit initialized to the state $|0\rangle$. Then, apply the Hadamard gate on each qubit. Then, evolve the system under the Hamiltonian \begin{equation} ...
Tom Clancy's user avatar
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218 views

How to show that Werner states produce correlations explainable via local hidden variable models?

Werner states can be written as $$\rho_W= p\frac{\Pi_+}{\binom{n+1}{2}} +(1-p)\frac{\Pi_-}{\binom{n}{2}}, $$ with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...
glS's user avatar
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4 votes
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Can changing reference frames generate entanglement in identical particles?

Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...
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How much information is stored in entangled states (IBM report Quantum Decade)?

In its report Quantum Decade, IBM claims that we need 512 classical bits to represent two-qubits entangled state (see graphic on pg. 2 in the report). This seems a little bit odd to me. Lets have a ...
Martin Vesely's user avatar
4 votes
0 answers
187 views

How to efficiently construct quantum circuits of oracles in multi-target quantum search?

In standard Grover's quantum search with only one target or its extension of multi-target quantum search, one of the two key parts is to quantize the boolean function $$f(x):\{0,1,\cdots,N-1\}\...
Chao-Hua Yu's user avatar
4 votes
0 answers
124 views

Why does the entanglement entropy give the number of singlets required to create a given state?

I've read that, given a bipartite pure state $|\Phi\rangle$, its entanglement (equivalently here, von Neumann) entropy $E(\Phi)$ gives the asymptotic number of singlets required to create $n$ copies ...
user15342's user avatar
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4 votes
0 answers
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What is the relationship between entanglement and quantum correlation?

What is the relationship between entanglement and quantum correlation? Are they synonym? Sometimes, these two words look like synonym; people use one word to explain another, These states are not a ...
da_miao_zi's user avatar
4 votes
0 answers
62 views

Modeling building blocks for quantum computation

If I would design library for quantum computation I would naively consider a sequences of entangled qudits with unit length as a building blocks. I.e., unit length elements from $$\mathbb{C}^{d_{1}}\...
Fallen Apart's user avatar
4 votes
0 answers
79 views

A question in classical and quantum information

Let $\rho, \sigma \in \mathfrak{D}(A)$ with $\operatorname{supp}(\rho) \subseteq \operatorname{supp}(\sigma),$ and spectral decomposition $$ \rho=\sum_{x} p_{x}\left|\psi_{x}\right\rangle\left\langle\...
299792458's user avatar
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0 answers
160 views

Is the set of two-qubit absolutely separable states convex?

Companion question on MathOverflow Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as \begin{equation} 1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0. ...
Paul B. Slater's user avatar
4 votes
0 answers
106 views

Is there a measurable of entanglement for a many-body system?

After having a discussion with a quantum computing colleague, a question came up: is there any meaningful way to measure entanglement (or something related to it) in a solid-state many body system ...
Dr. T. Q. Bit's user avatar
4 votes
0 answers
79 views

Reduced Density Matrix Equation of Motion to describe an Ellipse

Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
draks ...'s user avatar
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Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
Paul B. Slater's user avatar
4 votes
0 answers
90 views

Proof that quantum entanglement does not increase the asymptotic capacity of classical channel

Consider a classical channel $N_{X\rightarrow Y}$ which takes every input alphabet $x\in X$ to output alphabet $y\in Y$ with probability $P(y|x)_{Y|X}$. It is stated in many papers that even if the ...
user1936752's user avatar
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4 votes
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161 views

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 ...
Nakul Aggarwal's user avatar
4 votes
0 answers
58 views

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 ...
Stephen Diadamo's user avatar
4 votes
0 answers
47 views

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 ...
Sanchayan Dutta's user avatar
4 votes
0 answers
88 views

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( \...
Paul B. Slater's user avatar
4 votes
0 answers
65 views

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 ...
Paul B. Slater's user avatar
3 votes
0 answers
37 views

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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3 votes
0 answers
24 views

Are there non trivial two-party stabilizers in bipartite entanglement for product states?

In this recent paper where the authors discuss finite classification of entanglement types, on pg. 29 in appendix A, it is claimed that in bipartite entanglement for product state $|00\rangle$ there ...
Sanjana's user avatar
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3 votes
0 answers
334 views

Entangling attack on BB84 protocol

I am trying to solve the exercise 5.3 from the book "A Gentle Introduction to Quantum Computing". The exercise reads as follows: Suppose Eve attacks the BB84 quantum key distribution of ...
Jorge Vázquez Pérez's user avatar
3 votes
0 answers
70 views

Why does $\sigma_y$ seem to have a special role in the two-qubit concurrence?

The concurrence of a two-qubit state $\rho$ can be written as $$\mathcal C(\rho) = \max(0, \lambda_1-\lambda_2-\lambda_3-\lambda_4),$$ where $\lambda_i$ are the eigenvalues of $|\sqrt\rho\sqrt{\tilde\...
glS's user avatar
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3 votes
0 answers
77 views

What are examples of "LOCC linked" quantum instruments?

Define a quantum instrument $\mathfrak J$ as a collection of completely positive (CP) maps $(\mathcal E_j:j\in\Theta)\subset\mathrm{CP}(\mathcal H)$, such that $\sum_j \mathcal E_j$ is also trace-...
glS's user avatar
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3 votes
1 answer
214 views

What are the possible gates that I can use to vary input states before CNOT?

We know that the noise of the $\text{CNOT}$ gate varies depending on the input state before it. What are the gates that I can put in the place of the 4 identity gates above to change the input state ...
Gem's user avatar
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