# Tag Info

### How do I show that a two-qubit state is an entangled state?

A two qudit pure state is separable if and only if it can be written in the form $$|\Psi\rangle=|\psi\rangle|\phi\rangle$$ for arbitrary single qudit states $|\psi\rangle$ and $|\phi\rangle$. ...
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### What does it mean for two qubits to be entangled?

For a simple example suppose you have two qubits in definite states $|0\rangle$ and $|0\rangle$. The combined state of the system is $|0\rangle\otimes |0\rangle$ or $|00\rangle$ in shorthand. Then if ...
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### What is a "maximally mixed state"?

The maximally mixed state is a quantum state whose density matrix is proportional to the identity matrix. Physically, it may be interpreted as a uniform mixture of states in an orthonormal basis. The ...
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### What are min and max overlaps of a maximally entangled state with a separable state?

The minimum overlap is zero and the maximum overlap is $\frac{1}{d}$. The overlap is a linear function of $\rho$ and the set $S$ of separable states is convex, so the overlap is both minimized and ...
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### Is entanglement transitive?

TL;DR: It depends on how you choose to measure entanglement on a pair of qubits. If you trace out the extra qubits, then "No". If you measure the qubits (with the freedom to choose the optimal ...
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### Is entanglement necessary for quantum computation?

Short answer: yes One has to be a little bit more careful setting up the question. Thinking about a circuit as being composed of state preparation, unitaries, and measurements, it is always in ...
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### General construction of $W_n$-state

Yes, there are several implementations of this algorithm in the Superposition quantum kata (tasks 14 and 15): For $n = 2^k$, you can use a recursive algorithm: create a W state on the first $2^{k-1}$ ...
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### Does entanglement allow enhanced communication efficiency?

First, about teleportation, you say that you think quantum communication takes place in the protocol, but it doesn't. They only share an EPR pair they created together, hence the coordination and ...
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### Qiskit CNOT-gate matrix mixup?

Qiskit uses "little endian" bit ordering. That means, if A and B are $2 \times 2$ unitary matrices then $B \otimes A$ (note the order) is equivalent to applying $A$ to first qubit and $B$ to ...
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### Why is an entangled qubit shown at the origin of a Bloch sphere?

Let $(x,y,z)$ be a point in the unit ball with $x^2+y^2+z^2 \leq 1$. The state associated with this point is \begin{eqnarray*} \rho &=& \frac{1}{2} (I_2 + x \sigma_x + y \sigma_y + z \sigma_z)\...
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### Does Controlled-U gate entangle qubits?

For any controlled-$U$, if the input state is $|+\rangle|\phi\rangle$ where $|\phi\rangle$ is not an eigenstate of $U$, then the output state is entangled. This immediately deals with trivial cases ...
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### What are the possible non-entangling two-qubit gates?

There are no other non-entangling gates in $SU(d^2)$ in any dimension $d=2,3,\dots$. Note that the global phase is irrelevant to the problem, so we lose no generality by considering non-entangling ...
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### Is it true to say that one qubit in an entangled state can instantaneously affect all others?

If Alice and Bob have an entangled pair of qubits and Alice locally measures her qubit, it does not affect local state of the Bob's qubit in any way. Mathematically, if Alice measures but does not ...
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### When was the first use of the word Entanglement?

I managed to get access to the paper mentioned in the question. Schrödinger in 1935 (the same year the original EPR paper was published) wrote in English: "By the interaction the two representatives (...

### Is entanglement transitive?

This isn't an answer, but instead just some background facts that are important to know about in order to avoid "not even wrong" territory on these types of questions. "Entanglement" is not all-or-...
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### How to show whether a bipartite high-dimensional system is entangled?

Determining whether a given state is entangled or not is NP hard. So if you include all possible types on entanglement, including mixed states and multipartite entanglement, there is never going to be ...
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### Maximally mixed states for more than 1 qubit

For two probability distributions, there is a clear notion how to say which one is more mixed: $\vec p$ is more mixed than $\vec q$ if it can be obtained from $\vec p$ by a mixing process, this is, a ...
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### Why is an entangled qubit shown at the origin of a Bloch sphere?

The Bloch sphere only represents the state of a single qubit. What you’re talking about is taking a multi-qubit state, and representing the state of just one of those qubits on the Bloch sphere. If ...
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