# Questions tagged [density-operator]

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

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### Density matrix for system and surroundings

In my QM lecture it was claimed that if you have a system with degrees freedom $\vec{s}$ and its surroundings which have degrees of freedom $\vec{u}$ then every density matrix for the combined system ...
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### Classical correlations in bipartite entangled mixed state

I have recently asked somewhat related question and got very illuminating answer. After some thinking however I have realized that (at least) one more point is unclear to me: How can we check ...
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### Deriving or building a Hamiltonian from a Density Matrix

Is it possible to create a Hamiltonian if given a Density Matrix. If you already the the Density Matrix, then is the Partition Function (Z) even needed? This Q is not about physics. Its about an ...
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### Quantum superposition in density matrix formalism

I was thinking about quantum superposition and stumbled into something that made me quite uncomfortable. Consider a qubit with Hamiltonian eigenstates $|0\rangle$ and $|1\rangle$. To each of these ...
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### Calculating the Probability of Measuring One Hydrogen Atom in the Given States

I'm currently enrolled in a statistical mechanics course and am a bit stuck on how to calculate the probabilities of a hydrogen atom in a given state. I'll post the exact question I'm working on and ...
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### Classical and quantum correlations in bipartite system

I would like to know how to answer following questions: Is there classical/quantum correlations in given bipartite pure/mixed state? I have gathered several definitions. Some of them (it seems) ...
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I am attempting to learn a bit more about open quantum systems. Often we derive master equations or Heisenberg-Langevin equations where we have something like \begin{align} \dot{\rho}(t) = \mathcal{...
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### Mathematical formulation of density matrix on hypersurface in 3+1 formalism

Of course we have a notion of qft in curved spacetime, though I'm not sure how one can represent a particle state on curved spacetime without a timelike Killing vector field (i.e. a particle should ...
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### Reconcile a pair of two-qubit boundary-state separability probability analyses

It is now clearly well-established--though formalized proofs are still largely lacking—that the probability, with respect to Hilbert-Schmidt measure, that a generic two-qubit state is separable/...
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### Estimate of trace of powers of density matrix

Given a very generic, lower bounded Hamiltonian, is there a estimate on how $Tr(\rho^{1/k})$ grows as $k>0$ increases? Does this quantity diverge as a function of $N$, the degrees of freedom of the ...
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### Solving the von-Neumann equation explicitly [closed]

The von-Neumann equation reads: $$\frac{d\rho}{dt} = -\frac{i}{\hbar}[H,\rho]$$ The solution: $$\rho(t)=U\rho U^{\dagger}$$ with $U=e^{-\frac{iHt}{\hbar}}$ is easily obtained when starting from the ...
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### Are density matrices symmetric? [closed]

The context is that I want to simplify an expression like $$\mathrm{Trace}[\rho_1 \rho_2 \rho_3] + \mathrm{Trace}[\rho_2 \rho_1 \rho_3]$$ (Note that the second term is not a cyclic permutation of ...
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### Conventions for density matrix and projections

From this link : [http://math.ucr.edu/home/baez/lie/node12.html][1], it is said that, from starting a quantum state, $$\vec{v}=a|\text{up} \rangle+b|\text{down} \rangle,$$ we can define the matrix ...
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### Markovian approximation for teleportation? [closed]

Assume a model including a system with time dependent Hamiltonian ( 3 entangled qubits subject to a noisy reservoir) coupled weakly to a thermal bath. in order to study the time evolution of a ...
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### Deriving a path-integral expression for a thermal density matrix with position-dependent temperature

I've been fiddling with deriving a path-integral expression for a thermal partition function with a position-dependent temperature but I'm not sure how to get started on this. Concretely, I'm trying ...
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### What are unital maps?

In quantum information, one defines an unital map as the one that preserves the identity operator $\epsilon (I) = I$. A popular example is the so-called amplitude damping channel. My question is, ...
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### Does this density matrix represent a density operator of some single qubit state?

$$\rho = \begin{bmatrix} 1/2 & (1+i)/{\sqrt{2}} \\ (1+i)/{\sqrt{2}} & 1/2 \end{bmatrix}$$ Can this matrix represent a a density operator of some single qubit state? I'm a little confused ...
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### What are the range of values of the negativity in quantum mechanics?

The negativity of a quantum state, given by $N(\rho)=\frac{||\rho^{\Gamma_A}||-1}{2}$ where $\rho^{\Gamma_A}$ is the partial transpose with respect to subsystem $A$ of the density matrix of a ...
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### Can the same density matrix represent two (or more) different ensembles?

Given an ensemble i.e, a collection of states and the respective probabilities $\{p_i,|i\rangle\}$, one can uniquely construct the density matrix using $\rho=\sum_ip_i|i\rangle\langle i|$. Is the ...
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### Set of states $\{|\phi_n\rangle\}$ in the density operator $\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$

The set of quantum states $\{|\phi_n\rangle\}$ in the definition of the density operator $$\rho=\sum\limits_n p_n|\phi_n\rangle\langle\phi_n|$$ need not be orthonormal, and need not form a basis. But ...
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### Difference between pure quantum states and coherent quantum states

In the post What is coherence in quantum mechanics? and the answer by udrv in this post it seems to imply that a pure quantum state and coherent quantum state are the same thing since any pure state ...
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### Is it true that $\mathrm{tr}(\rho^n)$ is monotonically decreasing as a function of $n$?

In the case of mixed states density matrix made out of orthogonal vectors this is clear since we have $$\sum_i p_i^n,$$ but what if we use non-orthogonal vectors or a continuous mixture?
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### Is It Meaningful to Talk About Pure vs. Mixed States for (Continuous) Position?

I see a lot written about pure and mixed states regarding state vectors and density matrices/operators that contain a finite number of states/elements. For something like the continuous state vector ...
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### Separability of the outer product of a vector with itself, where the vector is a tensor product of two other vectors

Is it true that $$(|{\psi}\rangle \otimes |{\phi}\rangle)(|{\psi}\rangle \otimes |{\phi}\rangle)^{\dagger} = (|\psi\rangle\langle\psi|)\otimes (|\phi\rangle\langle\phi|)$$ where $^{\dagger}$ is the ...
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### A summation in quantum optics paper

I am going through the paper "Moments of $P$ functions and nonclassical depths of quantum states", which contains the following passage: A. Thermal state The density matrix of the thermal ...
For a spin generic mixed state $\rho$. How should I write $\rho$? $\rho_1 = q_1 |\uparrow\rangle \langle \uparrow| + q_2 |\downarrow\rangle \langle \downarrow|$ or $\rho_2 = q_1 |\uparrow\rangle \... 1answer 134 views ### Density matrix in quantum computation and quantum statistical mechanics What is the difference between the density matrix for quantum statistical mechanics and density matrix for quantum information theory? 1answer 103 views ### Uncertainty relation in mixed states If a system is in a pure state$|\psi\rangle\langle\psi|$we have $$\sigma_A\sigma_B\geq\frac{1}{2}|\langle[A,B]\rangle|.$$ Generalize this and find an uncertainty relation for an arbitrary mixed ... 1answer 344 views ### Time dependent Pauli matrices For an operator$\sigma$(which can be written in terms of Pauli matrices$\sigma_{x/y/z}$), the time evolution can be given by standard quantum rule$\sigma(t) = U^\dagger(t) \sigma U(t)$, where$U(t)...
I have just started learning density matrix and quantum master equations, and I am given a problem set that asks to find the solution to the Lindblad equation with $H$, $L_+$, $L_-$, $L_z$, and \$\rho(...