Questions tagged [bloch-sphere]

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Three dimensional visualization of a qutrit

My question is in reference to the paper "Three dimensional visualization of a qutrit"(https://arxiv.org/abs/1601.07361). The author's start with a symmetric two qubit density matrix written in the ...
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Bloch sphere hyperspatial multiqubit superpostion

What potentials can extend for a hyper-spatial diagram from a Bloch Sphere in terms of delineating multi-qubit superpositions extending from a quasi-periodic phase index upon reduction of the wave ...
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Maximum number of “almost orthogonal” vectors one can embed in Hilbert space [closed]

In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared ...
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How to compute the axis of a rotation expressed as a combination of Pauli matrices? [closed]

An exercise asked to compute the axis and the angle of the rotation $THTH$. $(S.1)$ is easy to understand by using the identity $exp(i\theta A) = \cos(\theta) \mathbb1 + i \sin(\theta) A$ for $A$ s.t....
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Constraints on higher-dimensional Bloch vectors

I'm interested in the constraints on the $(4^n-1)$-dimensional generalized Bloch vector (the Bloch vector for $n$ qubits). To the best of my knowledge, these are not analytically characterized for ...
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How to transform coordinates of two-level system's eigenstates from spherical to momentum space?

In almost all references for some two-level quantum system (for example, this Wikipedia article), arbitrary eigenstates are defined in spherical coordinates, and can be written separately as follows (...
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Can all expectation values be constructed using only tensor products of local Pauli operators?

I understand that the Pauli operators and the identity matrix span the space of complex 2x2 matrices. Let's say you have two qubits and you can perform projective meausurements. So you can measure ...
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Alternatives to Bloch Sphere? [closed]

The Bloch Sphere is a geometrical representation of the state space of a qubit system. I'm wondering if there are other natural geometrical representations one could use as alternatives to the Bloch ...
136 views

Why are the bloch vector elements u and v also the inphase and quadrature components of the transition dipole moment?

The bloch vectors are given by $$u=\frac{1}{2}(\rho_{ge}+\rho_{eg})$$ $$v=\frac{1}{2i}(\rho_{eg}-\rho_{ge})$$ $$w=\frac{1}{2}(\rho_{gg}-\rho_{ee})$$ Where $\rho$ is the density matrix for a two ...
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How does pulse duration and shape affect the rotation of a quantum state?

If I have some quantum state $|\psi>$ and I apply a pulse to this to rotate it by 90 degrees, the model would normally assume a rectangular pulse. However, realistically, the pulse will probably ...
45 views

A shaped pulse as a sum of rectangular pulses

I have a pulse with lineshape $L(ω)=\frac{1}{π}\frac{\frac{1}{2}Γ}{((ω−ω_0)^2+(\frac{1}{2}Γ)^2)}$ in the frequency domain where $\Gamma$ is the pulse width and $\omega_0$ is the resonant frequency ...
155 views

Visual representation of quantum state/phase

Is there a known good way to visualize a quantum state, composed of the sum of eigenstates, with a phase rotating on each state. I am looking for a way to keep up with the state and the phase. In a ...
52 views

Virtual energy level in the Bloch sphere representation

How the Bloch vector would evolve, if the electron makes a transition to a virtual energy level (placed below the excited state of our two-level atom), as it does in all sorts of phenomena in ...
2k views

How to calculate the bloch vector of a mixed state qubit

As I understand there are pure state and mixed state qubits. Pure states can be computed by $$|\psi\rangle = \cos(\theta/2)|0\rangle + \exp(i \phi) \sin(\theta/2)|1\rangle .$$ Simple enough. You need ...
94 views

Does an stereographical projection of a physical plane have any physical meaning?

Mathematically, an arbitrary 2D plane can be mapped onto a sphere by stereographical projection. Each line on the plane is equivalent to each line on the sphere. If the sphere rotates under the $SO(3)$...
578 views

Spin-1 representation in the Bloch sphere

I am working now with spin-1 where I have instead of states $|{+1}\rangle$ and $|{-1}\rangle$, as for in spin-1/2 case, I have $|{+1}\rangle$, $|0\rangle$ and $|{-1}\rangle$. How can I check the ...
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Minimal decoherence for a 3 levels system

In the case of a two level system driven by a monochromatic excitation, a minimal amount of decoherence results from the finite lifetime of the excited state. In the optical bloch equations, the ...
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Probabilities of sequential measurments of spin 1/2 particle

I'm interested in checking why my working for the following problem does not agree with the expected result. In a section describing Bell's Inequality, the following sequence of measurments is ...
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Rotations of spin eigenstates in QM

If you have a state $| \psi \rangle = | \uparrow \rangle$ which is the spin eignstate of the spin operator $\hat{S}_z = \frac{\hbar}{2} \hat{\sigma}_{z}$ then if you view this state as a vector in the ...
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Is there a way to represent a 3 qubit system using 3 Bloch Spheres?

I am relatively new to the Quantum Computing world and was wondering if representing a 3 qubit system using 3 Bloch Spheres feasible and if so what would the correct way to do it? I understand a ...