# Tagged Questions

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

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### Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?

In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and ...
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### What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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### Are there more entangled states or non-entangled ones?

I'm trying to understand entanglement in terms of scarcity and abundance. Given an arbitrary vector $v$ representing a pure quantum state of, say, dimension 4, i.e. $v \in \mathcal{H}^{\otimes 4}$, ...
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### What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of the ...
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### Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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### Majorana-like representation for mixed symmetric states?

Is there a generalization of the Majorana representation of pure symmetric $n$-qubit states to mixed states (made of pure symmetric $n$-qubit)? By Majorana representation I mean the decomposition of ...
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Berry phase, coming from Schrodinger equation, has well known form in terms of closed integral $$\gamma = \int_C A(\xi) d\xi$$ with Berry connection A(\xi) = i < \psi(\xi) | \partial_{\xi} | \... 1answer 214 views ### Using open system dynamics to define a quantum state Background The density matrix of a closed quantum system with Hilbert space \mathscr H evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ... 4answers 336 views ### Can every density operator be written as an outer product of two vectors? I have a feeling this is a very basic question. I apologize if it is. Using Dirac's notation, can every (mixed) density operator \rho_A of system A be written as the ket-bra (outer) product |a_1 ... 3answers 188 views ### How to connect these two formulations regarding the need for a density matrix in quantum mechanics? I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ... 3answers 256 views ### Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)? I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ... 1answer 129 views ### Eigenvalue of the first-order reduced density matrix (1-RDM) and condensation of bosons It is defined that ... 2answers 324 views ### Is it possible to go from the Master Equation formalism to Heisenberg-Langevin equations If I have derived a master equation (e.g. in the Lindblad form) and solved for the density matrix, \rho(t) I can get the mean value of an operator, A as:  <A> = \mathrm{Tr}A\rho . But ... 1answer 350 views ### How to write a generic density matrix for multi qubit system I was reading the paper device independent outlook on quantum mechanics. The author defines a generic two qubit density matrix as \rho=\frac{1}{4}\left( I \otimes I + \vec{r_{\rho}} \cdot \vec{\...
I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this. For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...