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Questions tagged [quantum-entanglement]

For questions about the principle and application of quantum entanglement, the phenomenon that the states of two qubits can only be described as the state of one system, to quantum computers.

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How to calculate the number of ebits in a graph state?

Given an arbitrary graph state $|G\rangle$ represented by the graph $G$, can one use the graphical structure to calculate the number of ebits (entanglement bits) present in the state? If so, how?
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Is there a relation between the factorisation of the joint conditional probability distribution and Bell inequality?

[I'm sorry, I've already posted the same question in the physics community, but I haven't received an answer yet.] I'm approaching the study of Bell's inequalities and I understood the reasoning ...
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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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Can two states with the same entanglement be transformed into each other using local unitaries?

Take two pure bi-partite states $\psi$ and $\phi$ that have the same amount of entanglement in them as quantified by concurrence (does the measure make a difference?). Can any such states be ...
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Is entanglement an operation or a stored state for qubits?

I am going through this video of Quantum Computing for Computer Scientists. I am not able to understand the entanglement state of qubits. Is entanglement just an operation, or is it a state which ...
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CNOT Gate on Entangled Qubits

I was trying to generate Greenberger-Horne-Zeilinger (GHZ) state for $N$ states using quantum computing, starting with $|000...000\rangle$ (N times) The proposed solution is to first apply Hadamard ...
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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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Compact encoding of Boolean formula as oracle

As in the title, I have a doubt regarding the implementation of a boolean formula used as an oracle for a quantum algorithm. The problem is that so far I could reproduce the formula as a quantum ...
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Is entanglement necessary for quantum computation?

Entanglement is often discussed as being one of the essential components that makes quantum different from classical. But is entanglement really necessary to achieve a speed-up in quantum computation?
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When you act on a multi-qubit system with a 2-qubit gate, what happens to the third qubit?

I am learning to manipulate Qbits and recently I saw the teleportation algorithm. I read about it in two places: Wikipedia and Lecture Notes from Ronald de Wolf (Page 7, 1.5 Example: Quantum ...
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How is entanglement achieved between two particles in quantum computing?

Many texts (especially meant for public consumption) discussing quantum mechanics tend to skim over exactly how entanglement is achieved. Even the Wikipedia article on quantum entanglement describes ...
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What are the possible ways to visualise large, entangled states?

What are the prominent visualisations used to depict large, entangled states and in what context are they most commonly applied? What are their advantages and disadvantages?
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Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in ...
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How to represent a qubyte?

I was not able to locate any visuals online. The visual I have in my head is a cube w/ bloch spheres as the eight vertices. I am also curious about a matrix representation, although I am not sure ...
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Realization of Quantum Shadowgraphy

I recently found out about shadowgraphy and was wondering if a technique like this could be used to: Visually show entanglement Suffice as a measure (e.g. continous partial trace) Most useful ...
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Are Absolutely Maximally Entangled states maximally entangled under all entanglement monotones?

In Ref. [1] absolutely maximally entangled (AME) states are defined as: An $\textrm{AME}(n,d)$ state (absolutely maximally entangled state) of $n$ qudits of dimension $d$, $|\psi\rangle \in \mathbb{...
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Difference between 3 qubits, 2 qutrits & 1 six level qunit

What is the difference between 3 qubits, 2 qutrits and a 6th level qunit? Are they equivalent? Why / why not? Can 6 classical bits be super-densely coded into each?
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How to show that an n-level system is entangled?

"How do I show that a two-qubit state is an entangled state?" includes an answer which references the Peres–Horodecki criterion. This works for $2\times 2$ and $2\times3$ dimensional cases; however, ...
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Generalization of n-th level entangled system

I have seen qubits, qutrits & entangled bits (e-bits) a decent amount. I have also seen qunits/qudits for n-th level qubits. What I am trying to wrap my head around is the differences between n-th ...
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What is the applicability of quantum network coding?

As the title suggests, I want to know what the applicability of quantum network coding is, besides the EPR pair construction between distant pairs of 'Users-Targets'. Can quantum network coding be ...
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How to check if 2 qubits are entangled? [duplicate]

I know that 2 qubits are entangled if it is impossible to represent their joint state as a tensor product. But when we are given a joint state, how can we tell if it is possible to represent it as a ...
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How do I show that a two-qubit state is an entangled state?

The Bell state $|\Phi^{+}\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle )$ is an entangled state. But why is that the case? How do I mathematically prove that?
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How to implement the 4 Bell states on the IBM Q (composer)?

I would like to simulate the 4 "Bell States" on the IBM composer? How can I best implement those 4 Bell states using the existing set of gates ? Here below you see the definition of the 4 Bell ...
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Bell Inequality violations at large distances

Could anyone point to some references examining Bell inequality violations at large distances please? I see many times, in pop science articles and research literature alike, that the quantum ...
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Is entanglement transitive?

Is entanglement transitive, in a mathematical sense? More concretely, my question is this: Consider 3 qubits $q_1, q_2$ and $q_3$. Assume that $q_1$ and $q_2$ are entangled, and that $q_2$ and $q_3$...
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Entanglement in Shor's algorithm

One deals with the notion of superposition when studying Shor's algorithm, but how about entanglement? Where exactly does it appear in this particular circuit? I assume it is not yet present in the ...
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When was the first use of the word Entanglement?

Schrödinger wrote a letter to Einstein after the 1935 EPR paper, and in that letter Schrödinger used the German word "Verschränkung" which translates into "entanglement", but when was the word first ...
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Are there connections between long-range entanglement and topological quantum computation?

Long-range entanglement is characterized by topological order (some kinds of global entanglement properties), and the "modern" definition of topological order is the ground state of the system cannot ...
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Entanglement distillation by local operations and post-selection using one entanglement pair

Consider the state $|X\rangle = \sqrt{0.9} |00\rangle + \sqrt{0.1} |11\rangle$, shared between Alice and Bob, who are located far apart. Alice brings in an ancilla qubit at her location (left-most ...
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Is it true to say that one qubit in an entangled state can instantaneously affect all others?

When a qubit is measured, there is a ‘collapse of the wave-function’ as a result is randomly chosen. If the qubit is entangled with others, this collapse will also effect them. And the way it affects ...
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Using a fractional number of classical bits within quantum teleportation

Recently, I heard that there can be transfer of rational classical bits (for example 1.5 cbits) from one party to another via quantum teleportation. In the Standard Teleportation Protocol, 2 classical ...
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How to keep track of entanglements when emulating quantum computation?

I am trying to build a quantum computation library as my university project. I am still learning all the aspects of the Quantum Computing field. I know there are efficient libraries already for ...
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Density operators and separable states

I know that a density operator is separable if it can be written in the form: $$ \rho =\sum_k a_k \rho^A_k \otimes \rho^B_k\tag{1}$$ where $$a_k \ge 0,\quad \sum_k a_k=1\tag{2}$$ My question is ...
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Markov Chain expressed in Density Matrix formalism

Suppose we have two states of a system where I tell you that there is a probability $p_1$ of being in state $1$, and probability $p_2$ of being in state $2$. The total state can be written as a vector ...
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Upper Bounds for QMA Quantum Merlin Arthur, and QMA(k)

QMA(Quantum Merlin Arthur), is the quantum analog of NP, and QMA(k) is the class with $k$ verifiers. These are important classes when studying Quantum Complexity theory. QMA(k) is QMA with $k$ ...
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What happens if two separately entangled qubits are passed through a C-NOT gate?

Suppose I transform a state as follows: I start with the state $\lvert 0\rangle \otimes \lvert0\rangle \otimes \lvert0\rangle \otimes \lvert 0 \rangle$. I entangle the 1st and 2nd qubits (with an H ...
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What is the maximum separation between two entangled qubits that has been achieved experimentally?

Considering two entangled flying qubits, as far as I know, there is no physical limit for separating them without losing quantum information. See: Is there any theoretical limit to the distance at ...
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Local operations and classical communication (LOCC) on quantum system

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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What are the current solutions to generate entangled qubits in the solid state?

Pairs of entangled qubits (or Bell pairs, or EPR pairs) are a fundamental resource for quantum computing, in the sense that any computational platform that cannot generate entanglement will also be ...
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Decoherence of spin-entangled triplet-pair states in the solid state: local vs delocalized vibrations

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 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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How are EPR Pairs used in quantum computing?

Context Lately, I have been reading a scholarly paper entitled An Introduction to Quantum Computing for Non-Physicists which discusses the EPR Paradox. The paper states that: Einstein, Podolsky ...
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What does it mean for two qubits to be entangled?

I have done some sort of online research on qubits and the factors making them infamous i.e allowing qubits to hold 1 and 0 at the same time and another is that qubits can be entangled somehow so that ...
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Is there any classical analogy for quantum entanglement? [closed]

I want to know if there is any classical analogy for understanding quantum entanglement.
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Quantum entanglement and quantum error correction

I want to understand what quantum entanglement is and what role does it play in quantum error correction. NOTE: As per the suggestions of @JamesWootton and @NielDeBeaudrap, I have asked a separate ...
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What are some popular myths or common misconceptions about quantum computing? [closed]

The most down-voted question at the moment is about using entanglement for faster-than-light communication. Much like how the word “laser” replaced “magic” in the vernacular not too long ago, what ...
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How does evolving a two-qubit state through a CNOT gate entangle them?

Reading into CNOT gate I understand that, mathematically, such a gate entangles the control qubit and the target. (the resulting state is $\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$) However, looking ...
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Quantum entanglement for FTL network communication?

Quantum entanglement is 2 atoms that are paired together and when you stop one from spinning the other also stops with the same spin. Can you use these pairs to have FTL communication between 2 ...