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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60 views

Pauli Matrix tolerant and encoding

I'm stumped by these questions in Chuang's book. If I have a state $|ψ\rangle=1/2\sqrt2(1+M_0)(1+M_1)(1+M_2)|0\rangle_7$, where $$M_0=X_0X_4X_5X_6; M_1=X_1X_3X_5X_6; M_2=X_2X_3X_4X_6$$ I rewrite its ...
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Two qubit state + Depolarizing channel = Bell diagonal state?

In multiple sources, e.g. RGK, KGR, it is stated (without proof) that if you take any two qubit state and send it through a depolarizing channel, the resulting state would be a Bell-diagonal state. ...
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What is the meaning of measuring a Bell state with Pauli operators?

There will be a certain value of getting the probability when measuring any Bell's state with Pauli operators such as observable X, Y, or Z. What is the meaning behind all this measurement? the result ...
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How to relate the result of measuring Pauli operators on Bell states with the quantum entanglement? [closed]

how to relate the result of measuring Pauli operators such as observable X and observable Y on the Bell's state with the quantum entanglement? In which way to say that there are correlated to each ...
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What are the possible results of measuring $X$ and $Z$ on the state $|01\rangle+|10\rangle$?

When calculating the probability of getting +1 on X-basis on the first qubit of Bell's state $|01\rangle+|10\rangle$, the result is 1/2 with the state after measurement |++⟩ while the probability of ...
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43 views

Can the following Bell states have probability amplitudes other than 1/2 and still be entangled?

From my understanding, a qubit is entangled when the state of one qubit depends on the other, and vice versa. Can the following bell states have probability amplitudes other than 1/2 and still be ...
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Is there a way to entangle to a dirty qubit?

Let's say I do something to a qubit, and I want to entangle it to a 2nd one, like this: ...
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1answer
36 views

Positive conditional quantum entropy for entangled state

The quantum conditional entropy $S(A|B)\equiv S(AB)-S(A)$, where $S(AB)=S(\rho_{\rm AB})$ and $S(B)=S(\rho_{\rm B})$ is known to be non-negative for separable states. For entangled states, it is known ...
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Probabilities of entangled state. Quantum measurement [duplicate]

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 ...
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2answers
158 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 ...
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2answers
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Transforming $|100\rangle$ state into $|000\rangle + |111\rangle$ state using only Hadamard and CNOT gates

Hi, How to convert $|100\rangle$ 3-qubit quantum state into $\frac{1}{\sqrt{2}}(|000\rangle + |111\rangle)$ state using only Hadamard and CNOT gates? Also, is output state an entangled one?
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Is the set of two-qubit absolutely separable states convex?

Companion question on MathOverflow Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as \begin{equation} 1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0. ...
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1answer
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Is Grover's algorithm only applicable to a pure state?

I've been trying to perform Grover's algorithm on entangled states, e.g. $|00\rangle + |11\rangle$. However, the algorithm apparently doesn't seem to amplify the amplitude of the state $|11\rangle$ ...
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Difference between Bell's inequality and CHSH

In this section of the Scholarpedia article on Bell's theorem, the first paragraph comments that Bell's original inequality is not ideal for experimental verification because it requires perfect anti-...
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What is k-state and how to go about creating a circuit?

The k-state is given by: $$ |𝐾⟩ = \dfrac{\sqrt{3}|100⟩ βˆ’ 𝑒^{𝑖π/4}|010⟩ + \sqrt{2}|001⟩}{ \sqrt{6}}$$ I am fairly new to quantum computing and do not have much background in the field. I understand ...
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70 views

Cirq-Measuring a State with Rotation Matrix

I have this state: $$p |\text{GHZ}\rangle \langle \text{GHZ}| + (1-p)\rho$$ And after creating this state I have this code lines: ...
3
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1answer
115 views

How to sample from the uniform distribution over the tensor product of two Bloch spheres?

For some context, I am trying to assess the capacity that certain two qubit gates have to create entanglement. To do this I am using the idea of "entangling power", where one takes their ...
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1answer
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Is there a clear boundary between quantum coupling and quantum entanglement?

I have a few questions in understanding the difference between coupling and entanglement in quantum systems: Is there a clear boundary between quantum coupling and quantum entanglement? If two quantum ...
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Bit Flip, Seperable state and Several Question about Cirq

1)I want to use noise model for my state and bit_flip is not defined on cirq. ...
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1answer
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Multiple Bipartite Entangled State in Cirq

I am trying to create this state: rho = = q . rho_{1,2} + r . rho_{2,3} + s . rho{1,3} + (1-q-r-s) . rho_separable And I wrote this code: ...
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How does a $d\times\ell$ matrix of rank $\ell$ and with singular values all equal to 1 imply it is maximally entangled

From this question, gls states that given $\Pi\equiv\sum_i |\eta_i\rangle\!\langle i|$ and $\Psi\equiv\sum_i|\psi_i\rangle\!\langle i|$, if $\Pi^\dagger\Psi=I_{d\times\ell}$, then $\Psi$ is "...
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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 ...
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0answers
34 views

How is the Ebit measurement (or Bell state measurement), if Charlie has an entangled state?

Assume Charlie has an entangled state like $\psi_{00}|00\rangle+\psi_{11}|11\rangle,$, and he wants to send one of the share qubits to Alice and then Alice does a Bell state measurement and then tells ...
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Can $|\Psi\rangle\simeq\sum_k |u_k\rangle|v_k\rangle$ be maximally entangled even if $\{|u_k\rangle\}_k,\{|v_k\rangle\}_k$ are not orthonormal?

Let $\newcommand{\ket}[1]{\lvert#1\rangle}\{\ket{u_k}\}_k,\{\ket{v_k}\}_k\subset\mathcal H$ be orthonormal bases in an $N$-dimensional space. It then follows that the state $$\ket\Psi = C\sum_{k=1}^N \...
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1answer
49 views

Is there any difference between a quantum- and classically-controlled gate if I know my basis?

Consider an unrealistic 2-qubit plus 1 ancilla bit-flip error correction code (images generated by quirk), where I know by some means or other that an error may have happen on qubit0 (represented by ...
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1answer
50 views

What linear map is needed for acting on a maximally entangled state?

I was reading a textbook and I encountered this question. I was wondering why we don't consider $M^\dagger$ instead of $M^{T}$, so I didn't show this relation, could you please help me to show below ...
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1answer
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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 ...
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How are Franson Interferometers used to prove security in Photonic QKD Experiments?

I am currently reading this paper about Quantum Key Distribution Protocols which use Franson Interferometers to secure against eavesdroppers. I am having trouble understanding how the interferometers ...
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Can local projections increase entanglement?

Consider a generic bipartite pure state $\newcommand{\ket}[1]{\lvert #1\rangle}\ket\Psi\equiv \sum_k \sqrt{p_k}\ket{u_k}\otimes\ket{v_k}\in\mathcal X\otimes\mathcal Y$, where $p_k\ge0$ are the Schmidt ...
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Keeping data around in an entangled state: use cases

I'm following the IBM Quantum roadmap and really excited to see what the next 3 years bring. As part of the unveiling, they mentioned that the 1000 Qubit machine goal will really stabilize things with ...
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Is there a measurable of entanglement for a many-body system?

After having a discussion with a quantum computing colleague, a question came up: is there any meaningful way to measure entanglement (or something related to it) in a solid-state many body system ...
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1answer
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Give an explicit derivation of the exact formula for the two-qubit absolute separability Hilbert-Schmidt probability $\approx 0.00365826$

The two-qubit eigenvalue ($\lambda_i$ >= 0, $i=1,\ldots,4$, $\lambda_4=1-\lambda_1-\lambda_2-\lambda_3$) condition of Verstraete, Audenaert, de Bie and de Moor AbsoluteSeparability (p. 6) for ...
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1answer
65 views

What would be measured if you measure two entangled qubits at exactly the same time?

What would be measured if you measure two entangled qubits at exactly the same time?
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Can Alice and Bob distinguish entangled state coefficients?

Suppose Alice and Bob share the quantum state $\frac{1}{\sqrt 2}(|x\rangle + (-1)^b |y\rangle)$ for some $x\neq y \in \{0,1\}^2$ and $b \in \{0,1\}$. They both do not know $x,y$, and use some ...
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1answer
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Is entanglement nonincreasing on average by local operations for all possible ensemble decompositions?

We know for a pure state conversion $|\psi \rangle \rightarrow_\textrm{LOCC} |\phi \rangle$ via local operation and classical communication (LOCC), an entanglement monotone should not increase, that ...
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1answer
83 views

Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings. Say you ...
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Is the square root of SWAP gate “maximally entangling”?

I'm not sure if this is a good question for the site, but here goes. On the "Quantum logic gate" Wikipedia page, it is said that: The $\sqrt{\mathrm{SWAP}}$ gate is not, however maximally ...
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1answer
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Is this a Bell test?

Inspired by this article which uses a $|+\rangle$ state as a control for a $CSWAP$, I realised you can conditionally measure a qubit by (maybe) swapping it with an empty ancilla, measuring it and (...
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2answers
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Example of a two-qudit state whose measurement outcomes are independent in one basis but dependent in another

If you have a pure composite system whose two subsystems are in a product state, then the outcomes of measuring the subsystems (in any basis) are statistically independent. If the subsystems are ...
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1answer
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Prove entanglement in the final state of the Deutsch-Jozsa circuit

I am asked to prove the following: Consider the Deutsch-Jozsa circuit. The output of the circuit is of the form $|\psi\rangle \otimes \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)$. Prove that the state$|\...
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1answer
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Defining dimension of an operator in qutip

My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip ? context: If I have my density operator ...
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1answer
64 views

Is there a name for $Z_{1}(|\mathrm{GHZ}\rangle)$?

The GHZ state is defined as $|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}$. Is there a name for the phase flipped GHZ state, i.e. $Z_1(|\mathrm{GHZ}\rangle)=\frac{|000\rangle - |...
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Reduced Density Matrix Equation of Motion to describe an Ellipse

Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
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Are all pure entangled states `robust'?

Let $\mathcal{H}_A \otimes \mathcal{H}_B$ be the tensor product of two finite dimensional Hilbert spaces, let $d = \operatorname{dim}(\mathcal{H}_A \otimes \mathcal{H}_B)$ and let $| \psi \rangle \in \...
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3answers
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In the three-qubit bit flip code, why can the first bit flip without impacting the entanglement with the other qubits?

The principle of the three-qubit Bit Flip Code is straight forward at first sight. Using CNOT you basically encode $$a|0\rangle + b|1\rangle $$ to $$ a|000\rangle + b|111\rangle$$ using ...
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1answer
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How to get the state of an individual qubit in a composite system?

Given a composite system with $N$ qubits represented by some $2^N$-dimensional vector, how would I get the quantum state of an individual qubit? Note that I understand some states are not separable ...
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54 views

Generalized construction of W basis

Although this question deals with the construction of a W-state, I was looking for a general way to find all the orthogonal W-states, given a number of qubits. For example, for three qubits, the first ...
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1answer
82 views

Quantum circuit not giving right results

I am trying to write a quantum circuit that implements swapping. The initial state is $$\phi^+_{12}\phi^+_{34},$$ where particles $(1,4)$ belong to $A$ and $(2,3)$, belong to $B$. After A's ...
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27 views

Could entangled particles be used for communication? [duplicate]

As you probably know, when 2 particles are entangled, they share some properties, even when separated long distances. If 2 devices each had entangled particles, would it be possible to communicate ...
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1answer
100 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 ...

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