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# Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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### Does anyone has some code for Mathematica or Python to convert a diagonal matrix into Dirac (bra-ket) notation?

I have the following matrix which I have to translate into Dirac's notations. \begin{array}{cccccccc} \frac{1}{2} \left(q_0+q_3\right){}^2 & 0 & 0 & 0 & 0 & 0 & 0 & \frac{...
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### Nielsen & Chuang Excercise Question on CSS code

I was reading the CSS ( Steane Code) from the Nielsen & Chuang book. It asked in Ex. 10.27 to prove that $$|x+C_2\rangle\equiv \dfrac{1}{\sqrt{|C_2|}}\sum_{y\in C_2}(-1)^{u.y}|x+y+v\rangle$$ and ...
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### Secret sharing though quantum operations

I have a secret say $s$. I have a dealer $D$ and three participants $A, B, C$. I want to share this secret $s$ in such a way that the participation of all $3$ is essential to reconstruct the secret. ...
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### The Elevator Problem [closed]

Today I(z) walked into an elevator and did not press the key to the floor to which I wanted to go. As there were 2 other people x and y who had pressed the keys 2 and 3 respectively. I wanted to go ...
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### How to generate quantum circuit for the following transformation? [on hold]

$$|j\rangle|k\rangle\mapsto|j\rangle|(j+k+1\,)\text{ mod }m\rangle.$$ How to extend the basic qubit quantum gates to get the above transformation?
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### Help in understanding an exercise on observable / measurement

I'm working through Quantum Computing for Computer Scientists (Yanofsky & Mannucci, 2008), and am getting a little confused about Observables. From what I understand an observable is a question ...
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### Are all operations simply matrix multiplication?

In the most simple example I can think of, we have: a linear operator $A$, which is also a 2 x 2 matrix. a vector $|v_i⟩$, which can be considered a 2 x 1 matrix. If we see an example of an ...
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### Is $\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}e^{2\pi ixj \left/\phantom\vert\!{N} \right.}|j\rangle |j\rangle$ a valid entangled quantum state?

$$\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}e^{2\pi i x j \left/ {\phantom\vert\!\!} N \right.}\,\left|j\right\rangle_h\left|j\right\rangle_t$$ For a valid state we should have sum of probabilities = 1. ...
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### Find the reduced density matrix for a four-qubit system

I have the state vector $|p\rangle$ made up of 4 qubits. Say system A is made up of the first and second qubits while system B is made up of qubits 3 and 4. I want to find the reduced density matrix ...
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### (Quantum Computing/Machine Learning) Estimate of the absolute value of the probability amplitude of |0⟩ in the superposition?

You are given a source of an unknown qubit state. You make measurements in the computational basis, that is, your measurement is $\{|0\rangle \langle0|,|1\rangle \langle 1|\}$. You observe that you ...
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### Find the local unitary that takes the bell state to a state phi that has an extractable bell state

I have a state $|p\rangle$ that has an extractable Bell state and I want to write it as a Bell state, $|b\rangle$, with a local unitary acting on one side. Basically I am trying to find a local ...
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### Is there any meaning for a density operator if we omit the j-th row and column in quantum mechanics?

Assume we have a density operator (Hermitian, PSD, with trace 1, where PSD means positive semi-definite) called A for a particle. $v_i$ shows the i-th eigenvector of A and $\lambda_i$ shows the i-th ...
Consider the density matrix $\rho=|\psi\rangle\!\langle\psi|$ of a random pure state in an $N$-dimensional space (in other words, an $N$-dimensional qudit, $|\psi\rangle\in\mathbb C^N$), $\rho_{ij}=... 1answer 52 views ### Bloch Sphere - Rotation Matrix A qubit is given in the following form:$\left|\psi\right\rangle = \cos\left(\dfrac{\theta}{2}\right)\left|0\right\rangle + e^{i\phi}\sin\left(\dfrac{\theta}{2}\right)\left|1\right\rangle$. Let's ... 1answer 34 views ### Non maximally entangled states for QKD Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones? 2answers 26 views ### The correct set of measurement operators on a mutiple qubit system I was wondering if the complete set of measurement operators for a state :$|\phi \rangle=c_{00}|00\rangle+c_{01}|01\rangle+c_{10}|10\rangle+c_{11}|11\rangle$Would be given by :$P_0\otimes I=|00\...
For example, the ibmqx2 computer has the most recent readout error of $4.40 \cdot 10^{-2}$. Does this mean per 1000 measurements, 44 faulty results exist?