# Questions tagged [locc-operation]

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

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### Can a SLOCC protocol work only in one direction?

Two states $|\psi\rangle$ and $|\phi\rangle$ are equivalent under SLOCC protocol if $|\psi\rangle$ can be converted to $|\phi\rangle$ and vice versa via LOCC with a finite probability of success. Thus ...
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### Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
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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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### 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 ...
1 vote
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### Can you project on an orthogonal basis for a multipartite system using only local measurements and classical communication?

Say Alice possesses one qubit, and Bob two, and that the joint state is $|\psi_{A, B_1, B_2}\rangle = \alpha|n_1\rangle + \beta |n_2\rangle$, where $|n_1\rangle$ and $|n_2\rangle$ are orthonormal ...
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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 ...
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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-...
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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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### 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 ...
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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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