Questions tagged [quantum-states]

A quantum state is a mathematical entity (abstract geometrical or specific algebraic function) that provides a probability distribution for the outcomes of each possible measurement on a system.

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What is the importance of unitary (in-)equivalent representations?

Say we have two representations of the observables from an abstract $C^*$-algebra $\mathcal A$ on two Hilbert spaces $H_1$ and $H_2$, i.e. consider the maps $\pi_1,\pi_2: \mathcal A \longrightarrow \...
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Is entanglement the only way to get mixed state that is consistent with the Schrödinger equation?

If we treat our entire system (say an electron and a bunch of atoms) quantum mechanically then all possible interactions will be unitary transformations. Thus any state that I describe will always be ...
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Representation of $d$-dim maximally mixed state in different bases

Consider the maximally entangled state in $d$ dimensions, $|\Psi\rangle:= \frac{1}{\sqrt{d}} \sum_{i=0}^{d-1} |i,i\rangle^{AB}$, where $|i\rangle^{AB} := |i\rangle^{A}\otimes|i\rangle^{B}$ and $\{|i\...
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Showing there are infinitely many decompositions of a non-pure state [duplicate]

Consider Problem 2.10 from Ballentine (paraphrased): Show (by constructing an example depending on a continuous parameter) that this can be done in infinitely many ways. I'm not sure how to proceed. ...
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Why symmetry transformations change either the state or the operator but not both. Why?

Why is it assumed that the symmetry transformations change either the state $\psi$ or the operator $O$ but not both simultaneously? For example, if you assume $\psi\to T\psi$, you take $O\to O$ and if ...
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Interpretation of time evolution in Quantum Mechanics

Let a quantum mechanical system, at time $t=0$, be described by: $$ |\psi(0)\rangle = c_1(0) |E_1\rangle + c_2(0) |E_2\rangle \;, $$ here $|E_1\rangle$, $|E_2\rangle$ are energy eigenstates. Now, for ...
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Entanglement Entropy and Entanglement Negativity for pure/mixed separable/entangled state

My question is how is Entanglement Entropy (EE) and Entanglement Negativity (N) related to the combinations of pure/mixed and separable/entangled states? That is for pure separable (PS), pure ...
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Collapse postulate in the density operator formalism [duplicate]

To the extent that the collapse postulate holds, textbooks will almost invariably restrict the discussion to contexts in which states are represented by normalized kets, so that the collapse postulate ...
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What is the most general mathematical structure for representing a state in QM?

In quantum mechanics textbooks which are a little more careful it is common to see it noted that a (pure) quantum state is not a vector $|\psi\rangle$ but rather a ray in Hilbert space, $c|\psi\rangle$...
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If you change the state of one entangled particle will it change the other? [duplicate]

I have seen a bunch of duplicates of this question and I’m sorry if this is a true duplicate, but all the other duplicates have super long and complicated answers that I don’t understand. I just want ...
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Defining initial values of atoms/particles

For a college project I'm simulating the change of magnetization of multiple protons that influence each other. The goal of my project is to provide a good software structure, so my primary focus was ...
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Quantum state in continuous basis [duplicate]

If I have an arbitrary state $|\psi\rangle$ and want to represent it in a continuous basis, for example the position basis in $x$-direction, I will get $$|\psi\rangle = \int dx\, \langle x|\psi\rangle|...
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How to apply Schrödinger equation to superposition with time dependent factors?

The question comes from reading through either of these two papers: https://doi.org/10.1103/PhysRevB.35.3629 https://arxiv.org/abs/1811.05886 The question is on the time dependence of a state like: $$|...
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Non-physical state in tomography

In tomography, we can use Pauli operators to estimate the qubit state, and by performing a substantial number of measurements one can estimate their expectation values. Define the estimates as $\bar\...
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If states cannot be written as superposition of eigenkets of observable, then how do we measure an observable for that state?

Usually, if we have a state $|\psi\rangle$, and have to measure an observable $A$, then all we do is expand $|\psi\rangle$ in terms of the eigenvectors of observable A, and then the probability of ...
9 votes
4 answers
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Why do we choose the Dirac delta function as the eigenstate of position operator?

When we try to find the eigenstates of the position operator, we get that the product of (x-y) and the eigenstate must be zero. It is obvious then that for x different than y, the eigenstate must be ...
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How can eigenstates of a hermitian operator be orthogonal without explicitly defining the inner product?

It's a well known fact that for any hermitian operator, say $H$ (assuming there is no degeneracy), $${\left< a_i \right.\left| a_j \right> \over \sqrt{\left< a_i \right.\left| a_i \right>...
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When spectrum of eigenvalues of Schrodinger equation is continuous or discrete? [duplicate]

There is a point which I do not understand about the Schrödinger equation. I will try to explain the issue. Consider the Schrödinger equation: $\hat H = \frac{ \hat p^2}{2m} + U(\hat x)$ and we are ...
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1 answer
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Quickway to calculate density matrix knowing $[S_{x,y,z}]$

Consider the spin $\frac{1}{2}$ system. A general quantum state could be written as $|\alpha^{(i)}\rangle=c_i|+\rangle+d_i|-\rangle$ and thus we have the density operator $$\rho=\sum_i w_i|\alpha^{(i)}...
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Will photons be entangled in polarisation even when i know their polarisation?

Imagine if i have a KDP crystal (the property of the KDP crystal is, the polarisation of singnal and idler photons that come out by parametric down conversion is orthogonal to pump photon, and both ...
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Quantum Mechanics in practice [closed]

Learning QM for the first time makes me feel like learning set of rules that can describe the quantum phenomena and applying them to predict what would happen to a given quantum state. This makes me ...
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What is adiabatic transfer?

In the context of atomic/quantum states preparation, what does adiabatic transfer mean? I'm currently reading about atom preparation using lasers and they talk about using adiabatic transfer to obtain ...
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What is meant by the measurement of an operator on a state vector

Let $ |\psi\rangle$ be the normalised state vector of a spin 1/2 particle. Let the two function $\psi_\pm (r)$, where $\pm$ correspond to the values $S_z = \pm1/2$, be $$\psi_+ = \langle r,+|\psi \...
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What is a state space in quantum mechanics?

I have begun reading chapter 11 of Zwiebach's "A First Course in String Theory" 2nd edition. Section 11.2 deals with the Heisenberg and Schrodinger pictures. Both pictures will use the same &...
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Confusion with quantum superposition

I have been studying QM and I think doing research on quantum superposition got me more confused about the topic. So I have two interpretation that I came across: A quantum state that is in ...
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Simultaneous transformations on states and observables which leave predictions invariant

Consider (for the sake of simplicity) a finite-dimensional complex Hilbert space $H$. Let $\mathcal O(H)$ and $\mathcal S(H)$ denote the set of all hermitian operators and the set of all density ...
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Quantum mechanics: "Representation" vs. "basis"

I am confused about the difference between the terms "representation" and "basis" of a state or operator. For example, Let us have eigen-kets of Hamiltonian $H$ denoted by $|\phi_n\...
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2 answers
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Question on notation of eigenvectors of position operator in quantum mechanics

From the first postulate of quantum mechanics we known that the vector $|\psi\rangle$ is the mathematical entity that says, intuitively, "in a time $t$, the (state of a) system is a vector". ...
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What does this piece of text mean?

On page 87, section 7.2.3 titled Vacuum matrix elements of Quantum Field Theory and the Standard Model by Matthew Schwartz,the author writes that the vacuum state $|\Omega>$ is annihilated by the ...
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Why quantum mechanical degeneracy is unwanted?

Degeneracy arises when two or more distinguishable quantum states share something same, like energy or angular momentum. Why physics always find for ways to remove this degeneracy? Like external ...
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6 answers
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Why do we need mixed states in quantum mechanics?

I am trying to understand the necessity of density matrices and the notion of "mixed states" in quantum mechanics (I read all the other posts about this, I promise). As far as I understand, ...
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Confusion tight binding model graphene

I think I have a conceptual doubt on the calculation of the matrix elements in momentum space for the tight binding Hamiltonian of graphene. I will break down my question into sections to make it as ...
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Confusion on inner product between quantum states

I think I have a confusion on some basics of quantum mechanics. To explain my problem I constructed this following simple example. Let's consider an infinite 1D system made by two sub lattices $A$ and ...
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How is quantum entanglement understood? [duplicate]

I need enlightening on quantum entanglement. If the entangled pair of particles are, for simplicity's sake, a red and blue ball and I look at one ball and find it to be red then obviously the other ...
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1 answer
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Interpretation of field quantization

In the book on Quantum Field Theory by Peskin and Schroeder, it is explained how the field is promoted to an operator, now my question is that in Quantum Mechanics, operators act on kets, what does ...
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Question about fields and state vectors

$\hbar = 1$ and $c=1$ The question is written on section $2)$ $1)$ Introduction So, when you write Klein-Gordon equation, $(\square + m^2)\phi = 0 \hspace{2mm}(1)$ , you know exactly which type of ...
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Is "high impedance" state analogy with "superposition" state? [closed]

In digital logic (classical bit), there's a state called "1" which is a defined high voltage, for example 2.7 V - 5.0 V. To achieve it we must connect it to VCC. And "0" which is a ...
7 votes
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How to efficiently get the largest probabilities / amplitudes of a quantum state stored as an MPS?

Let's say, that we have the following pure, superposition state $$ |\psi \rangle = \frac{1}{\sqrt{2}}|000001 \rangle + \frac{1}{2}|101101 \rangle + \frac{1}{2}|100100 \rangle $$ stored in the MPS form....
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Creation and annihilation operator applied to non-basis vector

Suppose we are given the vector $$|n_1, n_2, \ldots \rangle \in H^{\otimes n}_s$$ where $H^{\otimes n}_s$ is the $n$-fold symmetric tensor product of a Hilbert space $H$, and $|n_1, n_2, \ldots \...
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What is the relation between purity and ${\rm Tr}(\rho^2)$, for a density matrix? [duplicate]

I would like to understand the equivalence for a state $\psi$ to be pure and its density matrix $\rho=|\psi\rangle\langle\psi|$ having the property $$\operatorname{trace} \rho^2=1.$$ For this I should ...
2 votes
4 answers
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What's the difference between $|x_1+x_2\rangle$ and $|x_1\rangle+|x_2\rangle$?

In quantum mechanics, we very often deal with ket vectors. Usually if two vectors belong to the same vector space, we can add them component wise. But my question is that is it permissible for ket ...
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Thinking QFT in Occupation Number Representation

In this question I want to think about the fields, operators, states, and transformations a bit more explicitly. Therefore, I want to think everything with examples in occupation number ...
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Could one call eigenstates of $ \hat{a} = \hat{x} + i\hat{p}$ coherent states for other potentials than the harmonic oscillator?

Let's say I look at the quantum system of a particle in one dimension, subject to any other potential than the one of the harmonic oscillator, and I define $\hat{a}$ as stated above. I would find the ...
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Orthogonal states evolution

I'm a bit little confused about orthogonality in QM. $<a|b>=0$ what does physically mean? Let's suppose that $<a|b>=0$ and for $t=0$ the system is in state a. Is there a possibility to ...
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On the phase-invariance of vectors in quantum mechanics

One of the postulates of quantum mechanics is that if $\phi$ is a unit vector in some Hilbert space (in the simplest case let's consider $\mathbb{C}$), it describes the same state as $e^{i\theta}\phi$ ...
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Feynman's ammonia molecule

I have been reading Feynman's description of the quantum behaviour of an ammonia molecule. He assumes that the $\rm N$-atom is either pointing up or down as a two-states basis. He then says there is a ...
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4 answers
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Can the wavefunction be inferred from the expectation values of operators?

Preface This question is motivated by $C^*$ type treatments of quantum mechanics where operators (Basically an operator is an object that has a spectrum) are treated as fundamental and states are ...
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Does a complete set of observables tell us everything we can measure about a system in the Heisenberg picture?

Let's say I'm given a two state system that consists of base states $|1 \rangle$ and $|2 \rangle$, those being eigenstates of an hermitean operator $\hat{O}$ that commutes with the hamiltonian, and as ...
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Which interpretation of quantum physics interprets superpositions in the sense of "an object *really* being in two places at once"? [closed]

In popular scientific literature one often reads of "objects being in two places at once" as a verbal way of explaining superposition of states (in the mathematical view of elements of a ...
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Why two energies look same in the relativistic normalization?

I'm reading Peskin's QFT textbook. In this book, to make normalization of momentum eigenstate Lorentz invariant, we define momentum eigenket as $$\left| \mathbf{p} \right> = \sqrt{2E_{\mathbf{p}}} ...

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