# Tagged Questions

The density operator describes a quantum system in an (in general mixed) state.

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### Density operator - Coherence relativ to a different basis

Consider the density matrix of the pure state $\left|\psi\right>$. Relativ to the basis, whose eigenvector is $\left|\psi\right>$, there are no coherences. Do a basis transformation and show ...
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### Examples of Matrix Product State(s)

Matrix product states(MPS) is a way of representing a (many-body) wavefunction. The method has been described in, https://arxiv.org/abs/1008.3477 However, would it be possible to see a concrete ...
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### How can we define the distance for a pair quantum states in phase space?

In condensed matter physics, we know that two degenerate ferromagnetic ground states $|\uparrow\uparrow ...\uparrow \rangle$ and $|\downarrow\downarrow...\downarrow\rangle$ are far from each other in ...
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### Reduced Density operator in matrix form

I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac ...
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### Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics

I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ...
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### If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
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### Dirac notation - trace of product of (bipartite) density matrices

I'm getting confused by the Dirac notation. Suppose I have the following two objects. $$\rho = \sum_k p_k (\rho_A \otimes \rho_B) = \sum_k p_k |k \rangle \langle k | \otimes |k\rangle \langle k | ,$$...
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### Questions involving seperable states

I'm reading Mark Wilde's book Quantum Information Theory, and I'm stuck on two parts. I'm unable to prove: The state $\sum_{z} p_{Z}(z) \; \rho_z \; \otimes \sigma_z$, where $\rho_z$ and $\sigma_z$ ...
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### Equivalence condition of lindblad operators

So from Nielsen and Chuang th. 8.2 we know the equivalence condition of Kraus operators (quantum operation) What is the equivalence condition of lindblad operators of master equation?
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### Undergraduate quantum book treating density operators, mixed states, and entanglement [duplicate]

I'm working on a project on quantum measurement theory - in particular, relating to the quantum Zeno effect - over the summer. Right now, I'm in the process of doing background readings that'd enable ...
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### What is an incoherent state?

I am reading through a recent paper which speaks frequently of "incoherent states" without ever defining what such a state is. I gather from the context of the paper that it has something to do with ...
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### Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? [closed]

Does Unitary operator take a pure state to a pure state or can it take a pure state to a mixed state? I think so but why? I assume the Unitary operator acts on a pure state only.
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### Diagonalisation: Schmidt vs eigenvalue - when to use which?

In physics we encounter diagonalisation of matrices or operators in a variety of areas. But there are different kinds, the main two being Schmidt decomposition and eigenvalue diagonalisation. The two ...
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### A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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### What is the qualitative difference between quantum superpostion and mixed states? [duplicate]

As I understand it, if one has a complete knowledge of the state of a quantum system (insofar as one knows the statistical distributions of all the observables associated with the state) then one can ...
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### Quantum computing entanglement dimensions question

While trying to understand the basics of how quantum computers work, I recently read this statement. "...consider that single-qubit states can be represented by a point inside a sphere in 3-...
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