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 ...
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181
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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, ...
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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 ...
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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 ...
8
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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 $V$. ...
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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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7
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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 ...
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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 ...
glS♦
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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 ...
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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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Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?
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♦
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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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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}
...
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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 ...
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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 ...
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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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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 ...
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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 ...
glS♦
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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♦
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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 ...
4
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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 ...
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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\...
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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.
...
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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 ...
4
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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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4
votes
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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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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( \...
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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 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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3
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answers
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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}{\...
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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 ...
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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 ...
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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\}\...
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3
votes
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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 ...
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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 ...
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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}}\...
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3
votes
1
answer
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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 ...
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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 ...
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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 ...
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How does Teleportation based Error Correction (TEC) detect and correct loss/erasure errors?
I'm looking at papers like Demonstration of teleportation-based error correction in the IBM quantum computer (page) 10 and Role of syndrome information on a one-way quantum repeater using ...
3
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0
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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} ...
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answers
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability
In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
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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 ...
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Please clarify the following orthogonal property (quantum anonymous voting)
I am a beginner at QC, currently going through a paper on Quantum Anonymous Voting. Please clarify the orthogonal property described in the following scenario.
Consider $n$ voters $V_{0}, V_{1}, V_{2}...
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79
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Understanding shared Bell states from quantum entanglement
I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3)
I have several things about this process that I don't understand, and I was hoping someone could ...
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3
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answers
63
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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 transposed $1$-...
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3
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answers
36
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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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68
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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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2
votes
1
answer
47
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Preparing a maximally entangled state among four qubits
I am trying to create the following states in Qiskit, but having trouble with the nested loops. Can someone help me create it?
$\left|\psi_o\right\rangle=\frac{1}{\sqrt{8}}\left(\sum_i \hat{\sigma}_{x,...
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2
votes
0
answers
70
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How to "separate" a separable density matrix?
If I have a bipartite system of two qubits $A$ and $B$, and the density matrix $\rho$ is separable, how do I decompose it into its separable parts?
That is, give $\rho$, expand it as follows:
$$\rho = ...
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