# 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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### 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 ...
33 views

### 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. ...
47 views

### 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 ...
34 views

### 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 ...
69 views

### 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 ...
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 ...
43 views

### 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: ...
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 ...
39 views

### 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 ...
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 ...
64 views

### 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?
88 views

### 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. ...
53 views

### 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 $|11\rangle$ ...
51 views

### 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-...
46 views

### What is k-state and how to go about creating a circuit?

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

### 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 ...
33 views

### 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. ...
21 views

### 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 "...
70 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 ...
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 ...
175 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 ...