What is Mixed state: Definition and 40 Discussions

A mixed affective state, formerly known as a mixed-manic or mixed episode, has been defined as a state wherein features unique to both depression and mania—such as episodes of despair, doubt, anguish, rage or homicidal ideation, suicidal ideation, splitting, racing thoughts, sensory overload, pressure of activity, and heightened irritability—occur either simultaneously or in very short succession.
Previously, the diagnostic criteria for both a manic and depressive episode had to be met in a consistent and sustained fashion, with symptoms enduring for at least a week (or any duration if psychiatric hospitalization was required), thereby restricting the official acknowledgement of mixed affective states to only a minority of patients with bipolar I disorder. In current DSM-5 nomenclature, however, a "mixed episode" no longer stands as an episode of illness unto itself; rather, the symptomology specifier "with mixed features" can be applied to any major affective episode (manic, hypomanic, or depressive), meaning that they are now officially recognized in patients with, in addition to bipolar I disorder, bipolar II disorder and, by convention, major depressive disorder. A depressive mixed state in a patient, however, even in the absence of discrete periods of mania or hypomania, effectively rules out unipolar depression.

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  1. T

    I Mixed State Density Matrix

    Hi all, I am having trouble visualizing the matrix representation of the mixed density matrix from the following post (specifically from the accepted answer): https://quantumcomputing.stackexchange.com/questions/21561/swap-test-and-density-matrix-distinguishability That is, for...
  2. G

    I Entangled, mixed state with conditional entropy zero

    Hi. The classical (Shannon) conditional entropy is never negative. It can be written as ##H(Y|X)=H(X,Y)-H(X)## which allows for a quantum generalization using von Neumann entropy. In the case of entangled states, it can become negative. I guess it should be possible to construct an entangled...
  3. Like Tony Stark

    Mixed states and total wave function for three-Fermion-systems

    I've already calculated the total spin of the system in the addition basis: ##\ket{1 \frac{3}{2} \frac{3}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{1 \frac{3}{2} \frac{1}{2}}; \ket{1 \frac{3}{2} \frac{-3}{2}}; \ket{0 \frac{1}{2} \frac{1}{2}}; \ket{0 \frac{1}{2} \frac{-1}{2}}; \ket{1...
  4. MichPod

    I Stern-Gerlach experiment superposition vs mixed state

    Considering SG experiment, it is usually described as if an atom in the end of its path (but before being detected on the screen) is in the superposition state, say, ##|\textsf{spin up}, \textsf{upper path}\rangle+|\textsf{spin down}, \textsf{lower path}\rangle##. Some books (Feynman lectures...
  5. I

    I Mixed states from entangled state

    I'm an undergrad in physics, and have been asking myself the following question recently. Suppose you have a pure quantum state p (von neumann entropy=0), made of 2 sub-states p1 and p2 that are entangled. Because they are entangled, p \neq p1 x p2. Hence the entanglement entropy of p (=0) is...
  6. jk22

    I Averaging Initial & Endstates in Trace Formula

    Basically the question is : since the experiments are repeated and results averaged, should not initial and endstates be mixed states ? So now we should give two density matrices, so how do we average like in the trace formula : ##\langle A\rangle=tr(\rho A)## ? Is it ##\rho=\sum_i...
  7. F

    A How can a mixed state particle absorb a "quanta" of energy?

    Imagine a two-state system, e.g., a single nucleus that can be aligned or anti-aligned with an external magnetic field. If that nucleus is in a "mixed state" at time zero, such that it's wavefunction is 50% up and 50% down at time zero, why can that nucleus absorb a "quanta" of radiofrequency...
  8. AwesomeTrains

    Density matrix for a mixed neutron beam

    Homework Statement A beam of neutrons (moving along the z-direction) consists of an incoherent superposition of two beams that were initially all polarized along the x- and y-direction, respectively. Using the Pauli spin matrices: \sigma_x = \begin{pmatrix} 0 & 1 \\ 1 & 0 \\...
  9. nomadreid

    I Can a Pure State be Interpreted as a Mixed State for a Single Particle?

    A pure state can be interpreted as belonging to a system, but it can also be interpreted as belonging to a single particle (although the resulting probability is in respect to the system), and as I understand it, this is now the preferred interpretation. But in...
  10. sweet springs

    B Is a pure state a kind of mixed states?

    Hi. 1. Does a pure state belong to mixed states \hat{\rho}=\sum_k p_k|\psi_k><\psi_k| where ##p_k=1## for k=i and otherwise 0 ? 2. Does quantum jump by observation work for both mixed and pure states ? Your teachings will be appreciated.
  11. SchroedingersLion

    A Quantum Optics - transition from pure to mixed state

    Hello guys, I am trying to understand the following experiment: 1. Prepare a 2 level atom in state |0> 2. Shine in a Pi/2 pulse --> atom goes to 1/√2 (|0>+|1>) 3. Wait time T 4. Shine in second Pi/2 pulse a) if the state is pure: atom will go to state |1>, p1=1 b) if the state is...
  12. R

    I Actual example of a mixed state not part of entangled state

    A mixed state is when the system is actually in one state or another, but you just don't know which, and you use probabilities to describe your uncertainty. I'm referring to a mixed state of the entire system. I want an actual example. Can you think of some? Note I wasn't describing mixed state...
  13. SchroedingersLion

    I Mixed states vs pure states - physical POV

    Hey guys, I am having issues with understanding the physical nature of pure and mixed states. Maybe you can help me out? 1) A pure state - superposition is a state that consists of different states at the same time. It's like having several waves, each one belonging to an Eigenstate of the...
  14. L

    Partial traces of density operators in the tensor product

    Homework Statement Consider a system formed by particles (1) and (2) of same mass which do not interact among themselves and that are placed in a potential of infinite well type with width a. Let H(1) and H(2) be the individual hamiltonians and denote |\varphi_n(1)\rangle and...
  15. M

    I Qubit mixed state density matrix coordinates on a Bloch ball

    What are the coordinates on the 3D Bloch ball of a qubit's mixed state of the form: ##\rho=p_{00}|0\rangle \langle 0|+p_{01}|0\rangle \langle 1|+p_{10}|1\rangle \langle 0|+p_{11}|1\rangle \langle 1|##
  16. T

    I Is a Qubit in a Quantum Superposition or a Mixed State?

    Is it in a Quantum superposition, and then only in a mixed state when finding the reduced state of a qubit from an entanglement of multiple qubits?
  17. stevendaryl

    I On uniqueness of density matrix description as mixed state

    If you have a density matrix \rho, there is a basis |\psi_j\rangle such that \rho is diagonal in that basis. What are the conditions on \rho such that the basis that diagonalizes it is unique? It's easy enough to work out the answer in the simplest case, of a two-dimensional basis: Then \rho...
  18. B

    I Is Pointer State Eigenstate or Mixed State?

    What really are Pointer States in Zurek stuff? is it an eigenstate or mixed states Zurek seems to be saying that you can reprepare Pointer States even if they are macroscopic. What can you say?
  19. H

    B Still confused about superposition and mixed states

    I am confused about pure state or in mixed states. I've seen several threads on this forum, but I still can't get the grasp of it. I only have very little quantum chemistry to know what these means. So instead, I want to know the answer for specific examples so that I can get an idea. So I...
  20. entropy1

    B Does weak measurement cause mixed state?

    Does a 'weak measurement' on the spin of an electron in a pure state put the electron in a mixed state of the previous state and the state of the measurement axis of the measurement?
  21. kq6up

    I How are Mixed State Ammonia Molecules Separated by an E-Field?

    I am working on a paper about Ammonia masers. It looks like Ammonia molecules are usually found in a superposition of even and odd parity states that are eigenstates of the inversion potential. That is the double well potential of the Nitrogen to tunnel through the Hydrogen plane. If it...
  22. F

    I Difference between superposition and mixed state

    I get that a if we have complete information of the state of the system (i.e. all the possible knowledge we could have about it: the values its observables can take and their corresponding probabilities), then it is a pure state and can be represented by a vector (ket), ##\lvert\psi\rangle## in...
  23. entropy1

    I Density matrices, pure states and mixed states

    I got (very) confused about the concept of states, pure states and mixed states. Is it correct that a linear combination of pure states is another pure state? Can pure (and mixed) states only be expressed in density matrices? Is a pure state expressed in a single density matrix, whereas mixed...
  24. B

    Hydrogen atom in mixed state

    Suppose a single hydrogen atom is in mixed state. Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200 Then energy will be E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV. But there is no spectral line at 8.5 eV.
  25. jk22

    Mixed State Treatment: Eigenvalue Degeneracy

    Suppose i have an eigenvalue which is two fold degenerate-. Is it possible to have a density matrix formulation for the following : there is a continuum of states considered namely every state in the eigenspace. How would it be written : $$\sum_{\lambda}\int \rho (\lambda,\alpha)|\lambda...
  26. S.Daedalus

    A firewall confusion related to disentangling the vacuum

    So while reading some old threads/blog posts on the black hole firewall paradox, it occurred to me that I had some residual confusion regarding why firewalls (supposedly) form at all. IIUC, the argument is that usually, the vacuum is a highly entangled state, and that disentangling it (in order...
  27. Larry Pendarvis

    Is it possible to distinguish between pure and mixed states?

    Is it possible, in principle, for an experiment to distinguish between an ensemble of pure states and an ensemble of mixed states? If so, how? In particular, I am thinking of an ensemble of particles whose spin has been measured, one at a time, on the "Vertical" axis. The ensemble consists of...
  28. S

    Pure state, mixed state and measurement

    Hello guys, Homework Statement the problem goes as follows: "Which measurement should you do on a statistical ensemble of qubits in order to distinguish between the pure state |Ψ>= cos(θ)|0> + sin(θ)|1> and the mixed state ρ=cos^2(θ)|0><0| + sin^2(θ)|1><1| " Homework Equations I am not...
  29. X

    Trace and its square of mixed state density operator using integral

    Homework Statement I want to show that tr\left(\hat{\rho}_{mixed}\right)=1 tr\left(\hat{\rho}_{mixed}^{2}\right)<1 when \hat{\rho}_{mixed}=\frac{1}{2\pi}\int_{0}^{2\pi}d \alpha \hat{\rho}(\psi) Homework Equations tr\left(\psi\right)= \sum_{n}\langle n|\psi|n\rangle...
  30. K

    Schrödinger's cat, pure or mixed state?

    The usual description of Schrödinger's cat is that after being placed in the box, Schrödinger's cat in a superposition state of being alive and dead. Sometimes, I see this written as: \mid \Psi \rangle=\frac{1}{\sqrt{2}}(\mid alive \rangle+\mid dead \rangle) This is representing a particular...
  31. K

    Mixed state vs. pure state

    In quantum mechanics, regarding light (photon), how to tell that a wavefunction is in a pure state or mixed state? I am learning these stuffs for my first time. I have attempted to answer that question but I am not sure: a wavefunction can be wrtitten as a linear combination of linear...
  32. R

    Decoherence, Coherence, Pure State, Mixed State

    Hi, I'm confused by subtle differences between the concept. Let's take the example of a Schrodinger Cat. Supposed you could make a box that can isolate anything inside from say gravity, microwave radiation, is in 0 kelvin, etc. or let's just accept (for sake of discussion) that a box can totally...
  33. K

    Mixed State Eigenfuntion Equations

    H(a1u1 + a2u2) = a1E1 u1 + a2 E2u2 H is the Hamiltonian energy operator, a1 and a2 are normalisation constants, u1 and u2 are wave functions, E1 and E2 are the eigenvalues. Is it possible to calculate the values of E1 and E2 from the above equation if everything else is given? It should be...
  34. D

    Mixed State QM: Unpacking the Non-Diagonal Density Matrix

    what do the non-diagonal components of a density matrix tell us about the mixed state we are in?
  35. P

    Calculating Uncertainty in a Quantum Oscillator Mixed State

    Homework Statement Consider a quantum oscillator in a mixed state described by the density operator \rho = \frac{1}{2}( |\alpha><\alpha| + |-\alpha><-\alpha| ) . Calculate \Delta (\hat{X}^2)_1 and \Delta (\hat{X}^2)_2 in this case. Where X1 and X2 are the dimensionless position and...
  36. M

    Is a Pseudo-Wavefunction Really a Mixed State?

    Hello, I'm studying pseudopotentials right now, and I had an epiphany that the pseudo-wavefunction is really mixed-state of the original Hamiltonian. Has anyone ever thought about a pseudo-wavefunction that way? Just curious. modey3
  37. T

    Mixed Quantum States: Definition, Uses & Homework

    I have a book on quantum computation that explains the concept of a mixed quantum state. The definition is pretty plain, you just have a boring probability distribution over a set of quantum states. What I would like to know is why we need mixed states. How are they represented physically in...
  38. D

    Difference between Mixed State and Superposition

    What is the difference between a mixed state and a superposition?
  39. S

    About mixed state and pure state

    I don't have any problems dealing with mechanical calculations(I think), but yet I have some conceptual problems with mixed state(= statistical mixture?) and pure state in QM. - pure state : |Φ> = 1/sqrt2 ( |↑> + |↓> ) - mixed state : ρ = 1/2 ( |↑><↑| + |↑><↑| ) What is the difference...
  40. T

    What is a Pure State and Mixed State?

    What is a pure state and a mixed state?