# Questions tagged [entanglement]

For questions about the principle and application of quantum entanglement. It is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. (Wikipedia)

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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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### 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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### 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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### 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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### 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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Two of the most well known entangled states are the GHZ-state $|\psi\rangle = 1/\sqrt{2}\left( |0\rangle^{\otimes n} + |1\rangle^{\otimes n}\right)$ and the $W_n$-state, with $W_3 = 1/\sqrt{3}\left(|... • 1,517 15 votes 2 answers 2k views ### Is it true to say that one qubit in an entangled state can instantaneously affect all others? When a qubit is measured, there is a ‘collapse of the wave-function’ as a result is randomly chosen. If the qubit is entangled with others, this collapse will also effect them. And the way it affects ... • 11.3k 15 votes 2 answers 573 views ### Does higher channel fidelity imply higher entanglement fidelity? Consider two noisy quantum channels (CPTP maps),$\Phi_1^A$and$\Phi_2^A$, acting on a system$A$. Suppose that for any pure state$\left|\psi\right>\in \mathcal H_A$, $$F\big(\psi, \Phi_1^A(\psi)... • 151 14 votes 2 answers 2k views ### Why is an entangled qubit shown at the origin of a Bloch sphere? I'm unclear why the Bloch sphere representation of a maximally entangled qubit shows the state of the bit as being at the origin of the sphere. For example, this illustration shows the effect of ... • 241 14 votes 1 answer 3k views ### Why isn't there a contradiction between the existence of CNOT gate/entanglement and the no-cloning theorem? Of course I am not implying that I am right and the no cloning theorem is wrong, but I am trying to figure out what is wrong with my reasoning and yet I couldn't find the mistake. Based on Wikipedia ... • 243 14 votes 1 answer 5k views ### What does "bipartite" mean? This is a really easy question, but my mother language is not English and I get confused quite a lot reading Preskill notes. What does a bipartite system mean? Is this just that it "lives" in a ... • 535 14 votes 0 answers 581 views ### Relation between quantum entanglement and quantum state complexity Both quantum entanglement and quantum state complexity are important in quantum information processing. They are usually highly correlated, i.e., roughly a state with a higher entanglement corresponds ... • 333 13 votes 2 answers 2k views ### Does quantum computing already possess the level of abstraction to be explicable even without knowledge of physics? Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only ... 13 votes 1 answer 701 views ### What are min and max overlaps of a maximally entangled state with a separable state? Let A,B be Hilbert spaces of dimension d. Let \rho be some separable quantum state of the composite system AB. Given a maximally entangled state:$$\vert\phi\rangle = \frac{1}{\sqrt{d}}\sum_{i=... • 133 13 votes 2 answers 344 views ### 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 ... 13 votes 2 answers 613 views ### What are the possible non-entangling two-qubit gates? The non-entangling gates in$ SU_4 $contains the entire group of gates of the form $$SU_2 \otimes SU_2.$$ It also contains $$\zeta_8 SWAP= \zeta_8 \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 &... • 4,276 13 votes 3 answers 869 views ### What are the possible ways to visualise large, entangled states? What are the prominent visualizations used to depict large, entangled states and in what context are they most commonly applied? What are their advantages and disadvantages? • 1,646 12 votes 3 answers 2k views ### Why do we have to uncompute rather than simply set registers to zero? In implementing a quantum subroutine it is important to uncompute temporary registers after use, to ensure the output state of the subroutine is not entangled with them (which would affect its ... • 417 12 votes 3 answers 1k views ### 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 ... 12 votes 1 answer 748 views ### Where exactly does entanglement appear 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 ... • 263 11 votes 5 answers 918 views ### What is quantum entanglement, and what role does it play in 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 ... • 251 11 votes 2 answers 772 views ### What is the complexity of determining if a state is entangled? I have been looking around for an answer to this question but can't really come up with anything. Given some oracle, U, that maps | 0 \rangle to | \psi \rangle, is there some algorithm that ... • 423 11 votes 0 answers 203 views ### 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, ... 10 votes 2 answers 3k views ### 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 ... • 705 10 votes 3 answers 721 views ### Does the Quantum Fourier Transform (QFT) preserve entanglement? It is well known that entanglement in a quantum state is not affected when you perform a combination of 1-qubit unitary transformations. I have seen that the QFT can be decomposed into product of 1-... • 103 10 votes 2 answers 1k views ### How to show whether a bipartite high-dimensional 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, ... • 3,312 10 votes 1 answer 725 views ### 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 ... • 305 10 votes 2 answers 3k views ### 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 ... 10 votes 1 answer 649 views ### 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 ... • 488 10 votes 1 answer 278 views ### Understanding the M upper bound in the paper: "Multipartite entanglement and high-precision metrology" This paper is a paper in 2012 and cited by a lot of papers. And there does not exist comment in arxiv or error statement in PRA. But when I reading this paper, I think the right part of the eq(23) ... • 2,999 10 votes 1 answer 458 views ### 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 ... • 305 10 votes 0 answers 130 views ### Are there separable \rho that cannot be decomposed with less than \operatorname{rank}(\rho)^2 pure product states? In What separable \rho only admit separable pure decompositions with more than \mathrm{rank}(\rho) terms?, examples were given of separable states \rho with separable decompositions requiring ... • 25.5k 10 votes 0 answers 102 views ### Entanglement-assisted hashing bound for asymmetric depolarizing channels I reading the paper EXIT-Chart Aided Quantum Code Design Improves the Normalised Throughput of Realistic Quantum Devices, which proposes the use of QTCs in order to do quantum error correction for ... 10 votes 0 answers 213 views ### 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 ... • 3,827 9 votes 4 answers 1k views ### How can one imagine entanglement in a non-mathematical way? I understand the theoretical concept of an entanglement and what it means for our computation to have two entangled qubits, but what does it really mean when two qubits are entangled? How are they ... • 141 9 votes 2 answers 742 views ### 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 ... • 673 9 votes 2 answers 887 views ### What is the role of entanglement in quantum-computational speed-up? The way I see it, there are three main quantum properties utilized in quantum computing - superposition, quantum interference, and quantum entanglement. I'm looking to understand which one is ... 9 votes 1 answer 231 views ### 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 ... • 623 9 votes 1 answer 336 views ### 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 ... • 1,646 9 votes 1 answer 262 views ### 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 ... • 3,827 8 votes 3 answers 7k views ### What is a "maximally mixed state"? What is meant by maximally mixed states? Does this mean that there are partially mixed states? For example, consider \rho_{GHZ} = \left| {GHZ} \right\rangle \left\langle {GHZ} \right| and \rho_W =... • 285 8 votes 3 answers 830 views ### Unentangling a qubit from a system: can we convert \alpha|000\rangle+\beta|111\rangle into \alpha|00\rangle+\beta|11\rangle? Let's say I start with the following arbitrary qubits:$$ \color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\ \color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \... 8 votes 3 answers 1k views ### Is quantum computer without entanglement no better than anything classically achievable? Today I saw a tweet by Tom Wong which writes: "Did you know? Without quantum entanglement, quantum computers would be no better than traditional computers." But I remember I came up with ... • 377 8 votes 3 answers 2k views ### How to prepare mixed states on a quantum computer? I am a little bit confused by density matrix notation in quantum algorithms. While I am pretty confident with working with pure states, I never had the need to work with algorithm using density ... 8 votes 2 answers 924 views ### What is a separable decomposition for the Werner state? Consider the two-qubit Werner state, defined as $$\rho_z = z |\Psi_-\rangle\!\langle \Psi_-| + \frac{1-z}{4}I, \quad |\Psi_-\rangle\equiv\frac{1}{\sqrt2}(|00\rangle-|11\rangle),$$ for$z\ge0$. Using ... • 25.5k 8 votes 2 answers 921 views ### Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection$\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia: Quantum ... • 17.6k 8 votes 1 answer 729 views ### Parametrization of a two-qubit state A single-qubit state can be parametrized with real$\theta$and$\phi$as follows: $$|\psi(\theta, \phi)\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i \phi} \sin\frac{\theta}{2}|1\rangle.$$ I would ... • 2,684 8 votes 1 answer 156 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 ... • 173 8 votes 1 answer 574 views ### How does the conditional min-entropy$H_{\rm min}(A|B)_\rho$relate to the conditional entropy$H(X|Y)_\rho$? Suppose we have a classical quantum state$\sum_x |x\rangle \langle x|\otimes \rho_x$, one can define the smooth-min entropy$H_\min(A|B)_\rho$as the best probability of guessing outcome$x$given$\...
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 ...