Questions tagged [locc-operation]
For questions related to quantum operation obtainable via local operations and classical communication.
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Proof that Bell state can be transformed into any 2-qubit state $\vert\psi\rangle$ under LU
In the Dür, 2000 paper, he gave a statement that
(...) Any state $\vert\psi\rangle$ can be obtained from Bell State with certainty
From his paper too, it's known that we can transform $\vert\psi\...
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Prove that there are infinitely many entanglement classes under LU
Dur, 2000 states that
(...)But even in the simplest systems, $|\psi\rangle$ and $|\phi\rangle$ are typically not related by LU, and continuous parameters are needed to label all equivalence classes.
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Is LOCC equivalence the same as LU equivalence?
I'm currently learning on LOCC transformations. In the Dur, 2000 paper, there is a statement that
(...) two pure states $|\psi\rangle$ and $|\phi\rangle$ can be obtained with certainty from each ...
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How Quickly Can We Entangle a Pair of Unentangled Qubits Without Using Pre-existing Entanglement?
The Set-Up
Let's say we want to entangle two qubits $\phi_a,\phi_b$ (at locations $a$ and $b$ respectively) that are spatially separated by distance $d$ (in natural units) at a given instance of time.
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Can EPR pairs be established with only classical communication?
EPR pairs are used in superdense coding and quantum teleportation, but these protocols assume that Alice & Bob "share" half of an entangled quantum state.
How does this "sharing&...
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Show that any two product states of the same dimension are LU-equivalent
States $|Ψ \rangle$, $|Φ\rangle$ on $C_d⊗C_{d′}$ are said to be equivalent up to Local Unitarities (LU-equivalent) if there exist unitaries $U : C_d → C_d$ and $V : C_{d′} → C_{d′}$
such that:
$|Ψ \...
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Filtering operation is trace decreasing?
Let $\rho$ is a bipartite state.
W is a local filtering operation that acts on a subsystem of the state $\rho$.
After the local filtering operation $\rho$ emerges into a $\tilde{\rho}$ i.e
$\tilde{\...
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Is there a non-deterministic protocol for entanglement generation between distant parties?
I'm aware that one can imperfectly clone entanglement that's shared between two parties (i.e. Bell pairs) using deterministic quantum cloning machines to produce two, lower fidelity entangled states.
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How to prove that there are only 2 classes in 3 qubits entangled state?
Given 2 non-biseparable classes of 3 qubits (more generally tripartite) entangled states :
$|GHZ\rangle = \frac{1}{\sqrt{2}} \left(|000\rangle + |111\rangle\right) $
$|W\rangle = \frac{1}{\sqrt{3}} \...
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Universal resource for measurement based quantum computation
Consider universal resources for measurement based quantum computation, as defined here:
We are now ready to formulate the following definition. A family $\Psi$
is called a universal resource for MQC ...
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Can LOCC operations take product states to non-product states?
Given a product state $\rho^{(1)} \otimes \rho^{(2)}$, can this state become non-product state under LOCC? Can LOCC create correlations between two systems?
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Are mixtures of pairs of Bell states perfectly distinguishable by local operations?
Consider the four Bell states
$$ |\psi^{00}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle), \hspace{2mm}
|\psi^{01}\rangle = \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle),\hspace{2mm}
|\psi^{10}\...
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What are examples of "LOCC linked" quantum instruments?
Define a quantum instrument $\mathfrak J$ as a collection of completely positive (CP) maps $(\mathcal E_j:j\in\Theta)\subset\mathrm{CP}(\mathcal H)$, such that $\sum_j \mathcal E_j$ is also trace-...
glS♦
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Are perfectly LOCC-indistinguishable states necessarily identical?
Let $\rho,\sigma\in\text{L}(\mathcal{H}_{XAB})$ be given by
$$ \rho = \sum_x |x\rangle\langle x|\otimes p_x\rho_x, \quad \sigma = \sum_x |x\rangle\langle x|\otimes q_x\sigma_x, $$
and consider ...
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CHSH test using unbounded operators
I want to perform a CHSH inequalities test using operators $A \, \& B$ and their combinations each possessed by Alice and Bob, which obey the following commutator relation.
$$[A, B] = 2C$$
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Prove that $A\preceq B$ implies $A=\Psi(B)$ for some channel $\Psi$
Define $\newcommand{\PP}{\mathbb{P}}\newcommand{\ket}[1]{\lvert #1\rangle}\newcommand{\tr}{\operatorname{tr}}\newcommand{\ketbra}[1]{\lvert #1\rangle\!\langle #1\rvert}\PP_\psi\equiv\ketbra\psi$, and ...
glS♦
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Are separable, orthogonal states LOCC distinguishable?
Consider two states $\sigma_0,\sigma_1\in\text{L}(\mathcal{H}_{AB})$, and suppose $\sigma_0,\sigma_1$ are separable and orthogonal. Is it possible to distinguish between $\sigma_0,\sigma_1$ through ...
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Are Bell states distinguishable through LOCC?
Define $|\psi^{00}\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ and $|\psi^{01}\rangle = \frac{1}{\sqrt2}(|00\rangle - |11\rangle)$, and consider the state
$$ |0\rangle\langle 0|^C\otimes |\psi^...
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Why can any LOCC operation be written as $\sum_k (A_k\otimes B_k)\rho(A_k^\dagger\otimes B_k^\dagger)$?
This statement can be found in Vedral et al. 1997, eq. (1).
More precisely, given a bipartite state $\rho_{AB}$, they claim that any operation on $\rho_{AB}$ involving local operations plus classical ...
glS♦
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What is an example of a measurement that is LOCC but not separable?
Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)?
Given an ensable of states $\rho^{N}$, a separable measurement on it is a POVM ...
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How to transfer non maximally entangled state to maximally entangled?
Let a three-qubit state shared between Alice, Bob and Charlie stationed at distant laboratories be
$$\psi_{ABC}=\frac{\sqrt{2}}{\sqrt{3}}|000\rangle+\frac{1}{\sqrt{3}}|111\rangle.$$
How to evaluate ...
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How is the measurement described in the LOCC wikipedia a measurement on the product state $\mathbb C^2\otimes\mathbb C^n$?
I'm currently busy learning about the basics of quantum information theory. Does anyone know how the measurement described in the wiki link LOCC is a measurement on the product space $\mathbb{C}^2 \...
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