Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [locc-operation]

For questions related to quantum operation obtainable via local operations and classical communication.

39 questions
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What is the Generalized Quantum Stein's Lemma and why is it important?

I'm sensing a lot of buzz about potential re-proofs of the Generalized Quantum Stein's Lemma - a generalization of the quantum counterpart to the classical Stein's Lemma, which is of some importance in statistical inference and hypothesis…
Mark Spinelli
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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 other by means of LOCC if and only if they are…
Steve J.
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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 communication can be written as $$\sum_k…
glS
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What is an example of a separable measurement that is not LOCC?

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 $\lbrace N_i \rbrace$ where the effects $N_i$…
MrRobot
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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 operators $M$ be given by $$ M = \sum_x |x\rangle\langle…
user114158
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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 the maximum probability of transforming the state…
Aleph
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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?
User101
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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}\rangle = \frac{1}{\sqrt{2}}(|01\rangle +…
user16106
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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 $\mathbb{C}^2 \otimes \mathbb{C}^n$ as stated?
John Doe
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How to convert a partially entangled state into maximally entangled using SLOCC

Let's say I have a generic partially entangled two-qubit state with Schmidt decomposition $$|\psi\rangle_{AB} = \sqrt{\alpha} |00\rangle_{AB} + \sqrt{\beta}|11\rangle_{AB}.$$ I know from Lo and Popescu (1999) and Vidal (1999) that the optimal…
Alessandro Romancino
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Performing Binary Operations on Classical Bits

I am trying to prepare the n-qubits GHZ state using LOCC on Qiskit. The implementation uses the result of some mid-circuit measurements for later operations. I am now using something like with circ.if_test((cr[0],1)): with…
Sami Farrag
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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. In particular, I'm interested in protocols that deal…
Bentanglement
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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. We are allowed to use additional qubits to get…
FreeAssange
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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 let $\ket\psi,\ket\phi$ be two bipartite states…
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 LOCC? My approach so far har been to write out $$…
user114158
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