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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 ...
Anindita Sarkar's user avatar
2 votes
1 answer
55 views

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 $|\psi_i\rangle$ ...
Pratapaditya Bej's user avatar
2 votes
1 answer
152 views

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 ...
Alex1111's user avatar
4 votes
2 answers
394 views

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 ...
Alessandro Romancino's user avatar
1 vote
0 answers
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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 ...
Abelaer's user avatar
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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 ...
Sami Farrag's user avatar
3 votes
2 answers
160 views

What's the best entangling circuit to measure the Peres-Wootters double-trine state?

The early-90's, pre-teleportation work of Peres and Wootters studied the now-called double-trine or Mercedes-Benz states of two qubits in one of three product states: $$|A\rangle\otimes|B\rangle=|s_i\...
Mark Spinelli's user avatar
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0 answers
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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
0 votes
1 answer
119 views

perform a SWAP measurement using local operations and classical feedback

I am interested in performing a SWAP measurement, namely, measure 2 qubits and project their state onto either the triplet state manifold $\{|00\rangle, |11\rangle, |01\rangle + |10\rangle\}$ or the ...
Lior's user avatar
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How does trace norm of a state change after measurement? Why is the 1-LOCC norm less?

I recently asked this question about the meaning of a quantum classical channel in a paper I read. The answer I accepted provided an explanation for the 1-LOCC norm (which I asked about) which is ...
Loic Stoic's user avatar
1 vote
1 answer
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An intuitive definition of "One-way LOCC distance"

I am reading up on this paper which covers many aspects about fidelity, separability, and came across the "One way LOCC-distance" in section 2.4. Below is an excerpt: I am having trouble ...
Loic Stoic's user avatar
1 vote
1 answer
198 views

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\...
Steve J.'s user avatar
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2 votes
1 answer
155 views

Prove that there are infinitely many two-qubit 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. ...
Steve J.'s user avatar
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8 votes
1 answer
165 views

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 ...
Steve J.'s user avatar
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4 votes
1 answer
87 views

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. ...
FreeAssange's user avatar
3 votes
2 answers
524 views

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&...
Joseph Briones's user avatar
2 votes
1 answer
61 views

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 \...
SVMteamsTool's user avatar
0 votes
1 answer
26 views

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{\...
Pratapaditya Bej's user avatar
2 votes
2 answers
193 views

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. ...
Visipi's user avatar
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1 answer
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How to prove that there are only two entanglement classes of $3$-qubit states?

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}} \...
Steve J.'s user avatar
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2 votes
1 answer
98 views

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 ...
BlackHat18's user avatar
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4 votes
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237 views

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's user avatar
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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}\...
user16106's user avatar
  • 123
3 votes
0 answers
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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's user avatar
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6 votes
1 answer
227 views

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 ...
user114158's user avatar
4 votes
1 answer
256 views

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's user avatar
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4 votes
2 answers
338 views

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 ...
user114158's user avatar
4 votes
2 answers
288 views

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^...
user114158's user avatar
5 votes
1 answer
244 views

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's user avatar
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5 votes
1 answer
628 views

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 ...
MrRobot's user avatar
  • 253
5 votes
1 answer
571 views

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 ...
Aleph's user avatar
  • 551
5 votes
1 answer
528 views

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 \...
John Doe's user avatar
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