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)

Filter by
Sorted by
Tagged with
16 votes
1 answer
1k views

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?
DaftWullie's user avatar
51 votes
4 answers
33k views

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?
user avatar
15 votes
4 answers
5k views

General construction of $W_n$-state

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(|...
nippon's user avatar
  • 1,497
2 votes
2 answers
2k views

What is the result of measuring $\sigma_x$ on the state $|01\rangle+|10\rangle$?

I confused about how to calculate the probabilities and getting a certain result of measuring Bell's states with Pauli matrices as the operator. When you measure something, the state involved would be ...
Eara Shahirah's user avatar
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, ...
user820789's user avatar
  • 3,302
5 votes
1 answer
459 views

How do you build a circuit to make an equal superposition of $n$ outcomes?

Suppose we start with $|00...0\rangle$. We want to build an equal superposition over $|0\rangle + ... + |n-1\rangle$. When $n=2^m$ for some $m$, I know I can do this using $H^{\otimes m}$. What is the ...
George Li's user avatar
6 votes
2 answers
493 views

Is it true that for a quantum algorithm to be efficient it must feature a highly entangled state at some point?

I'm wrapping my head around how and why quantum computers can provide advantage over classical. A basic and naive argument is that the dimension of the Hilbert space of $n$ qubits grows as $2^n$. ...
Nikita Nemkov's user avatar
4 votes
1 answer
337 views

What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?

As shown e.g. in Watrous' book (Proposition 6.6, page 314), a separable state $\rho$ can always be written as a convex combination of at most $\mathrm{rank}(\rho)^2$ pure, separable states. More ...
glS's user avatar
  • 24.1k
-3 votes
1 answer
789 views

Quantum entanglement for faster-than-light (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 faster-than-light (FTL) ...
Christopher's user avatar
19 votes
3 answers
10k views

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 ...
Arshdeep Singh's user avatar
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 ...
orome's user avatar
  • 241
12 votes
3 answers
981 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 ...
user1271772's user avatar
  • 13.5k
8 votes
1 answer
556 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 $\...
john_smith's user avatar
7 votes
2 answers
607 views

How does quantum teleportation work with mixed shared states?

I am given the scenario that instead of the two parties (A & B) sharing the bell state $|\phi_+\rangle$ they share the mixture $\rho_\lambda = \lambda|\phi_+\rangle\langle\phi_+|+(1-\lambda)\frac{\...
Luca Ion's user avatar
7 votes
2 answers
812 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 ...
glS's user avatar
  • 24.1k
7 votes
1 answer
244 views

Can one quantify entanglement between different parts of a system?

Consider some state $|\psi\rangle$ of $n$ qubits. One can take any subsystem $A$ and compute its density matrix $\rho_A =Tr_{B} |\psi\rangle \langle\psi|$. The entanglement between subsystem $A$ and ...
Nikita Nemkov's user avatar
5 votes
1 answer
190 views

How to measure entanglement in an algorithm?

Entanglement in Algorithms Most algorithms in quantum computing find their strength in making use of entanglement. I am interested in evaluating the amount of entanglement generated within an ...
Jake Xuereb's user avatar
4 votes
2 answers
580 views

Is it possible to have entanglement between more than two qubits?

I am experimenting with concepts in Quantum Computing and I have landed on using entangled Qubits to perform certain actions. My question is this: is it possible to have (let's say) 3 entangled ...
Stephen Coady's user avatar
4 votes
2 answers
272 views

Entanglement distribution of W-State over different locations

I would like to create a quantum system with the gates for a W state where each qubit is at a different location. Entanglement distribution has been proven in several research articles. I'm new to ...
TimW's user avatar
  • 53
4 votes
0 answers
192 views

How to show that Werner states produce correlations explainable via local hidden variable models?

Werner states can be written as $$\rho_W= p\frac{\Pi_+}{\binom{n+1}{2}} +(1-p)\frac{\Pi_-}{\binom{n}{2}}, $$ with $\Pi_\pm\equiv\frac12(I\pm\mathrm{SWAP})$ projectors onto the $\pm1$ eigenspaces of ...
glS's user avatar
  • 24.1k
4 votes
1 answer
179 views

How to find a separable decomposition for $|\Psi^+\rangle\!\langle\Psi^+|+|\Phi^+\rangle\!\langle\Phi^+|$?

The state $$ \frac{1}{2}\left(| \phi^+ \rangle \langle \phi^+ | + | \psi^+ \rangle \langle \psi^+ | \right) $$ where $$ | \phi^+ \rangle = \frac{1}{\sqrt2} \left(|00 \rangle + | 11 \rangle \right) $...
Mahathi Vempati's user avatar
3 votes
2 answers
395 views

How to construct local unitary transformations mapping a pure state to another with the same entanglement?

$\newcommand{\Ket}[1]{\left|#1\right>}$In Nielsen's seminal paper on entanglement transformations (https://arxiv.org/abs/quant-ph/9811053), he gives a converse proof for the entanglement ...
Blitzkrieg555's user avatar
3 votes
1 answer
164 views

What does a quantum NOT operation do to an entangled set of qubits?

Quantum computing is not my field, so answers understandable to a layman will be most useful. Please forgive any incorrect terminology in my question! Assume that a set of the states of N qubits ...
S. McGrew's user avatar
  • 245
3 votes
1 answer
129 views

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 ...
user820789's user avatar
  • 3,302
3 votes
1 answer
1k views

Generalizing the circuit for quantum teleportation for $n$-qubit states?

So the usual quantum circuit I know for quantum teleportation allows for the teleportation of the state on a single qubit, in the following way: How easy is to generalize this algorithm to allow for ...
Mauricio's user avatar
  • 2,244
3 votes
1 answer
246 views

Can a single qutrit in superposition be considered entangled?

Often in quantum computing the idea of quantum superposition is introduced well before the concept of entanglement. I suspect this may be because our conception of (classical) computing privileges ...
Mark Spinelli's user avatar
3 votes
2 answers
2k views

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?
user820789's user avatar
  • 3,302
2 votes
2 answers
121 views

How do you transmit a single qubit of an entangled qubit over?

When we talk about superdense coding, we say that Alice and Bob share an entangled qubit and then after this, Alice transmits her qubit over to Bob after performing the necessary manipulation. What ...
snickers_stickers's user avatar
2 votes
2 answers
2k views

Qiskit CNOT-gate matrix mixup?

In the qiskit textbook chapter 1.3.1 "The CNOT-Gate" it says that the matrix representation on the right is the own corresponding to the circuit shown above, with q_0 being the control and ...
Alvo's user avatar
  • 23
1 vote
1 answer
139 views

Bit Flip, Separable state and Several Question about Cirq

1)I want to use noise model for my state and bit_flip is not defined on cirq. ...
quest's user avatar
  • 624
0 votes
2 answers
350 views

Trouble understanding the EPR Experiment

I fail to understand the EPR experiment. From Wikipedia: Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or −z. Suppose she gets +z. Informally speaking, ...
morpheus's user avatar
  • 359
24 votes
3 answers
2k views

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 $q_3$...
Peter's user avatar
  • 509
18 votes
2 answers
9k views

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 ...
JanVdA's user avatar
  • 1,148
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 ...
James Wootton's user avatar
14 votes
1 answer
4k 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 ...
CFRedDemon's user avatar
12 votes
2 answers
544 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 &...
Ian Gershon Teixeira's user avatar
11 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 ...
Sideshow Bob's user avatar
11 votes
0 answers
202 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, ...
Paul B. Slater's user avatar
10 votes
2 answers
745 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 ...
Loic Stoic's user avatar
10 votes
0 answers
211 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 ...
agaitaarino's user avatar
  • 3,807
10 votes
1 answer
445 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 ...
Midhun XDA's user avatar
9 votes
1 answer
257 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 ...
agaitaarino's user avatar
  • 3,807
9 votes
2 answers
684 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 ...
SalvaCardona's user avatar
8 votes
1 answer
628 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 ...
MonteNero's user avatar
  • 2,369
8 votes
2 answers
882 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 ...
Sanchayan Dutta's user avatar
8 votes
1 answer
421 views

Rotationally invariant maximally entangled states in higher dimensions

Is there a straightforward generalization of the $\mathbb{C}^2$ Bell basis to $N$ dimensions? Is there a rotational invariant Bell state in higher dimensions? If yes, then what is the form of that ...
Vijeth Aradhya's user avatar
7 votes
2 answers
8k views

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 ...
Archil Zhvania's user avatar
7 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 ...
user777's user avatar
  • 347
7 votes
0 answers
95 views

Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?

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 ...
glS's user avatar
  • 24.1k
7 votes
3 answers
283 views

Does entanglement allow enhanced communication efficiency?

From what I gather, communication is not possible with quantum mechanics. With the experiment on teleportation, entanglement is referred to as coordination and not communication. However, my belief is ...
Jose's user avatar
  • 99