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 to apply a Hadamard gate to the first qubit and then measure that first qubit in the computational basis
I am reading lecture notes from Ronald de Wolf on quantum computing and trying to solve exercise 7 from chapter 1. I am having a bit of trouble understanding exactly what I need to do and how to do it....
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Understanding a single qubit Pauli gadget in a quantum circuit
I'm trying to understand a Pauli gadget defined as $P = e^{-iαX} X^s$ in terms of ZX calculus since that is more intuitive to me.
My limited knowledge of quantum computing and the maths involved ...
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Is quantum computation effectiveness dependent on EPR non-locality?
Suppose 100 qubits are used to perform a quantum algorithm.
According to the EPR view, each of these 100 qubits already have pre-determined states before we start the computation, which are just ...
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How do I multiply a Bell state with a measurement operator?
A textbook that I am currently reading says the following: Alice and Bob share an entangled pair of qubits in the Bell state $(|00\rangle+|11\rangle)/\sqrt{2}$ . Alice performs a two outcome ...
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Is there a generalized quantum teleportation for n-qubit entangled states? [duplicate]
Quantum teleportation for single qubit is a fairly simple algorithm to follow. Even its extensions into the transportation of $n$ qubits is fairly simple: repeat the process $n$ times (or run $n$ ...
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Symmetries of maximally bi-partite pure entangled states
My question focuses on bi-partite pure systems, but I am also interested in answers focusing on 2-qubit systems (this is actually the case I'm mostly interested in).
While being written in a different ...
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Truncation techniques in the proof of Area Law
I am currently understanding on the proof of Area Law in paper "Rigorous RG algorithms and area laws for low energy eigenstates in 1D" (https://arxiv.org/abs/1602.08828). In terms of the ...
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When performing a projective measurement on a subsystem X entangled with another system Y, can the evolution of Y be unitary?
I am interested in the evolution of a subsystem Y entangled with another subsystem X.
X and Y are initially in a pure product state. They undergo some global joint evolution E (not necessarily unitary)...
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Is entanglement distillation possible between states of different fidelities?
I am looking for an algorithm that allows me to perform distillation from a pair of W-states of different fidelities. All the algorithms I found so far are focused on distilling identical states, ...
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What are hamiltonians in the context of quantum computing
Sorry if this question is a bit too generic or basic, but my background lies only in mathematics and computer science. I am currently writing my thesis on the topic of simulating quantum computing ...
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What is the Generalized Quantum Stein's Lemma and why is it important?
I'm sensing a lot of buzz about potential re-proofs of the Generalized Quantum Stein's Lemma - a generalization of the quantum counterpart to the classical Stein's Lemma, which is of some importance ...
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The rationale for the payoff function of the CHSH game
The payoff of the CHSH game is the characteristic function $\mathbf 1(x\cdot y=(a+b \mod 2))$. What is the rationale for picking this particular payoff function? Is it a consequence of the CHSH ...
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Transformation between the canonical basis and the degraded Bell basis
I would like to know if the following results of mine made are correct.
My goal is to express the canonical basis $ \{ |00\rangle , |01\rangle , |10\rangle , |11\rangle \} $ using a degraded Bell ...
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GHZ Definition - Does it all have to be $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\rangle$
Trying to dig a bit into GHZ States and the proper definition.
Trying to determine if GHZ state is strictly $|000\ldots\rangle$ or $|111\ldots\rangle$ or can it be $|010\ldots\rangle$ or $|101\ldots\...
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Comparative Analysis of Entanglement Measures: Von Neumann Entropy vs. Concurrence
I am seeking clarification on the comparative aspects of two prominent measures of entanglement: Von Neumann entropy and concurrence. My goal is to understand the key differences in how these measures ...
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How is $R_{ZZ}(\pi/2)$ gate maximally entangling?
IBM Qiskit website says $R_{ZZ}$ gate is maximally entangling at $\theta = \pi/2$.
But acting $R_{ZZ}$ on two qubits initialized as $ |00 \rangle $ still remains $ |00 \rangle $ so it is separable in ...
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DEJMPS and EXPEDIENT distillation protocols implementation in qiskit
I am new to Qiskit and distillation protocols. I am wondering if there is a tutorial or a link to the implementation of the DEJMPS and EXPEDIENT distillation protocols in Qiskit.
What I want to ...
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For a Nqbit, prove that $\langle|\alpha_i|^2\rangle=1/2^N$ and that $\langle|\alpha_i \alpha_j|^2\rangle= 2^{\delta_{ij}-N}/(1+2^N) $
In the following article it is written that:
This is done by using spherical coordinates in a $2^N$ -dimensional real space,where $N$ is the number of qubits to be teleported. We thus find that $\...
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How can I move a C.NOT over a circuit
I am doing some Quantum Computing Exercises and I am curious on how you go from left to right in this picture...
I see not only how the c-not moves but also a new bond between X gates in second and ...
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Super-dense coding by adding quantum correlations between classical bits
Consider the following non-local game between Alice, Bob (who are spatially separated but share a maximally entangled state) and a referee:
Referee samples two question bits "$x,y$" and ...
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Why do Bell states have all real coefficients?
Canonically, the four Bell or EPR states for 2-qubit systems are given by:
$|\Phi^{\pm}\rangle = \frac{1}{\sqrt{2}} \left( |00\rangle \pm |11\rangle\right)$
$|\psi^{\pm}\rangle = \frac{1}{\sqrt{2}} \...
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How to calculate guessing probability for quantum key distribution?
There are 3 Projections $P_1$, $P_2$, and $P_3$ corresponding to 3 inputs $x = 1, 2, 3$ for Alice. Similarly, the same projections are used by Bob for $y = 1, 2, 3$. Each input has 2 outcomes, $a = 1, ...
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Is the real span of symmetric product states equal to the set of Hermitians with image in the symmetric space?
It is easy to see that the real span of the set of product states is equal to the set of Hermitian operators (see e.g Can every bipartite state be written as $\rho_{AB} = \sum_{ij} c_{ij}\sigma_A^i\...
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Relative entropy of entanglement
In the formula for the relative entropy of entanglement, one has:
\begin{eqnarray}
E_R(\rho)=\text{min}_{\sigma\in S}\text{Tr}\left(\rho\log\rho - \rho\log \sigma\right)
\end{eqnarray}
where $\rho$ is ...
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Use of maps in quantum coding schemes
Suppose we construct a quantum coding scheme in which Alice and Bob agree on a number of things in advance, including, say, a bijection $\gamma$ between two sets of vectors (which live in different ...
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What is the minimum number of separable states (not necessarily pure) needed to decompose arbitrary separable states?
For a bipartite separable quantum state $\rho$ acting on Hilbert space $H\otimes H'$ with $\dim H=D$ and $\dim
H'=D'$, what is the minimum number of separable state needed for a decomposition? That ...
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CHSH game sharing a general state
For the CHSH game if the players share a general two-qubit state $\rho = \frac{1}{4} \sum_{i,j = 0}^{3} M_{ij} (\sigma_i \otimes \sigma_j)$, then the maximal violation is $2 \sqrt{\lambda_1^2 + \...
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Are transversal entangling gates possible for stabilizer codes other than CSS?
It is well known that CSS codes can have lots of transversal entangling gates. For example, $ CNOT $ is exactly transversal on 2 blocks of any $ [[n,1,d]] $ CSS code. And https://arxiv.org/abs/1304....
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Stabilizers of higher dimensional maximally entangled state of non-$2^k$ dimension
Excluding normalization, the Bell state $\vert 00\rangle + \vert 11\rangle$ has stabilizers $XX$ and $ZZ$. I am interested in the stabilizers of the maximally entangled state on $d$-dimensions i.e.
$$\...
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Sampling a Haar Random State Conditioned on Having Low Entanglement Entropy
After applying exponentially, or even polynomially many random local gates to a fixed input state, the resulting distribution of the output state $\lvert\psi_{out}\rangle$ will (be very close) to Haar ...
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Nontrivial channel that is identity only on separable states?
Is there a channel that acts like the identity channel on any separable state but acts non-trivially on at least one entangled state? If not, is there a proof that such a channel cannot exist?
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Why a basis in super dense quantum coding?
In the classical super dense quantum coding scheme of Bennet and Wiesner (1992), the authors start from an element in the Bell base (which consists of $4 = 2^2 = 2 \times 2$ states, in dimension $4$), ...
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Tests of entanglement between one and many qubits
I have a 5-qubit state $|\psi \rangle$, which has a physical interpretation that the middle qubit is the "impurity" with spin $s_{imp} = 1/2$. The rest 4 qubits highlight the presence of ...
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CHSH game sharing more general states
In the CHSH game, when the players share EPR states they can achieve best the winning rate of approximately 85% which can be proved through the Tsirelson's bound. I wonder what the best winning rate ...
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Is purity convex in time?
Is the purity $\mathrm{Tr}[\rho(t)^2]$ of a quantum state $\rho(t)$ that evolves according to a time-independent Lindbladian $\partial_t \rho = \mathcal{L}[\rho]$ convex in time $t$?
I suspect the the ...
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What is the stabilizer rank of the W state?
The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state
The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal
$r$ such that \begin{equation} |{\psi}\rangle = \...
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Why do we need to put the control qubit in superposition in Bell State?
I'm new to quantum computing, so I hope you don't find this question tedious. However, after watching many hours of lectures and reading online, I still don't 100% understand why we need to initialize ...
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Do we consider the entangled-based protocol E91 to be a device-independent protocol?
Since both rely on Bell inequalities to maintain security, does the Ekert protocol rely on trustworthiness of the devices?
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How to calculate the number of m-partitions of an N-partite quantum state?
I am reading the structure of multipartite entanglement from section 3.3.
It is stated there that the number of possible partitions of $N$ parties into $m$ parts is given by $\frac{m^N}{m!}$.
I could ...
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How do two-way protocols allow to extract entanglement from states like Werner's?
As discussed in [Lo and Popescu 1999], it is always possible to distill entanglement from pure bipartite states using a one-way protocol. The gist of the idea, as I understand it, is Proposition 1 in ...
glS♦
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Can Bell states be reexpressed with respect to arbitrary local bases?
Suppose I take the Bell state $\Phi^+ = \vert 00\rangle + \vert 11\rangle$.
Is it true that I can choose any basis with basis vectors $\vert b_0\rangle$ and $\vert b_1\rangle$ and reexpress the same ...
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How to mathematically describe the action of CNOT on the control qubit alone?
Basically the title. From what I know, starting from the $|{+0}\rangle$ state where the reduced density matrix of the first qubit $|+\rangle$ is $\frac{1}{2}\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{...
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doesn't a reset on an entangled qubit collapse a superposition?
When I reset an entangled qubit then measure it looks a superposition isn't collapsed to a certain states.
In my experiment, the state just before applying a reset is:
$$\frac{1}{2}(|000⟩+|011⟩+|101⟩+|...
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Prove that convex combinations of product states admit a hidden variable model
Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
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Uniqueness, absolutely maximally entangled states, and the 3 qutrit code
There is a well known $ [[3,1,2]]_3 $ qutrit stabilizer code with stabilizer generators $ XXX $ and $ ZZZ $. This code is related to a $ [[4,0,3]]_3 $ qutrit stabilizer state with stabilizer ...
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In e91 protocol, if one of the bases combination was not chosen, what should be done to avoid division by zero?
In e91 protocol, if one of the bases combination was not chosen, what should be done in this case to avoid division by zero?
One solution that comes to mind is setting the whole value to zero, but is ...
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What is the F12 rule for the Game of Life
This is more of a help call to find a specific rule set for the game of life. I'm currently reading the "Entanglement in the Quantum Game of Life", however they refere to the classical F12 ...
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In quantum teleportation, why does measuring entanglement not destroy the whole state?
In quantum teleportation, we have three qubits. Sender, receiver and ancillary. First, we entangle the ancillary and target qubit. Next, we entangle ancillary and sender qubits. Now, the whole system ...
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E91-Protocole the type of Bell state use in this protocol
my question is, what is the type of the Bell state used in Ekert-91
link for Bell states in question
correlated or anti-correlated.
And if they can use both of them , how do Alice & Bob know ...
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Benefits of using quantum encrypted keys
Considering, in a perfect world everyone has the capability to create a quantum key. What would the benefits of using quantum encrypted keys instead of using classically encrypted keys? Besides the ...
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