Quantum information is the study of the informational content of quantum states. The most common object of study is the "qubit", the information in a two-state quantum system such as spin-1/2 or photon polarization.

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On LOCC operations

I am trying to learn quantum information theory. Suppose we have a bipartite (as well as multi-partite) quantum system $H_A \otimes H_B$. What is a LOCC map $\phi: \mathcal{B}(H_A \otimes H_B) \...
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30 views

How to do partial trace of three qubit? [on hold]

Good day, $\|A\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|B\rangle=\left(\dfrac{i_0}{j_1}\right)$, $\|C\rangle=\left(\frac{i_0}{j_1}\right)$, For 2-qubit systems, the $\|AB\rangle\langle AB|$, ...
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1answer
76 views

Significance when fidelity of a quantum state or density matrix is 0 or 0.5? [closed]

What is the significance when fidelity of a quantum state or density matrix with the original quantum state or density matrix is 0 or 0.5? Which point indicates the state being completely decohered, ...
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1answer
43 views

State vector after quantum eraser

Suppose I have a particle in a two-slit setup. At the slits, it's in state $|\psi\rangle = |x_1\rangle + |x_2\rangle$ I entangle it with some detector: $|\psi'\rangle = |x_1\rangle|d_1\rangle + |...
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3answers
39 views

Two qubits system in polar co-ordinates

I know that I can write a single qubit state in terms of polar co-ordinates $(r,\theta,\phi)$ on a Bloch sphere. \begin{equation} \rho = \begin{pmatrix} \frac{1+r \cos\theta}{2} &\frac{r \exp(-i\...
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0answers
35 views

Building a solid foundation for Quantum Information [on hold]

For the student with a keen interest in Quantum Information, what would be a sound course/set of prerequisites(possibly along with a few good resources) in Math, Physics, Computer Science, Electronics ...
8
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1answer
117 views

are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is the ...
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31 views

Interpreting conical intersection in quantum adiabatic evolution

Recently, I have studied a particular quantum adiabatic algorithm. When I plot the eigenvalues of the ground and first excited state against normalized time $s$, there appears a conical intersection. ...
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1answer
58 views

How to choose proper measurement operator?

Let's assume I have two states inside the Bloch sphere, at radial vectors $r_1$ and $r_2$ respectively $(r_1<r_2<1)$. Their angular location is same. These are like: \begin{equation} \rho = \...
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0answers
223 views

Intuition behind transforming a Hamiltonian expressed in momentum representation in eigenbasis [on hold]

This question is a supplement to a previous question on the same paper. In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve ...
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6answers
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Is there something behind non-commuting observables?

Consider a quantum system described by the Hilbert space $\mathcal{H}$ and consider $A,B\in \mathcal{L}(\mathcal{H},\mathcal{H})$ to be observables. If those observables do not commute there's no ...
3
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1answer
418 views

Double slit experiment and entanglement [duplicate]

Just wondering, what would happen in this experiment. In the experiment you would first have two entangled particles. Then you fire one of the particles, lets say "Particle A", at a double slit ...
0
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1answer
42 views

Want to measure entanglement of the state [on hold]

Good day, I want to measure the state with concurrence and negativity. I do local unitary transformation with represented by $U\in SU(4)$ (Lie group). After the transformation (rotation of angle) ...
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2answers
87 views

Measurement in many body systems

Any wavefunction for a system of many particles can be decomposed into linear combinations of the direct product of single particle states with respect to a certain observable(single particle basis). ...
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0answers
40 views

Proof of Tridecompositional Uniqueness Theorem (Elby and Bub, 1994)

I'm looking for a proof of the Tridecompositional Uniqueness Theorem (Elby and Bub, 1994). Could someone help me? References: Maximilian Schlosshauer, arXiv:quant-ph/0312059; p.12-13. A. Elby &...
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1answer
55 views

rotation of a state in Bell basis

Suppose I have a state in Bell basis. For example \begin{equation} \rho = \begin{pmatrix} \rho_{11} &0 & 0 & \rho_{14} \\ 0 &\rho_{22} & \rho_{23} & 0 \\ 0 &\rho_{32} &...
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1answer
51 views

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 ...
3
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1answer
117 views

Replacing fermionic operators with their Fourier transform and boundary conditions

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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0answers
57 views

Does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with these two Hamiltonians? [closed]

This is supplementary to a previous question. It was answered in that question why the operator $\prod^n_{j=1}\sigma^{(j)}_x$ commutes with the adiabatic Hamiltonian $(1-s) \sum^n_{j=1}(1-\sigma^{(j)}...
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1answer
39 views

Representing Graphs in Entangled States [closed]

Are there ways to represent a graph G=(V,E) in an entangled state of a system of qubits ? and is there a way to forget the labels of the nodes so as to use the representation as a template to check ...
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1answer
441 views

Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between 2&4,...
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4answers
779 views

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 ...
3
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1answer
133 views

Is it possible to build a logical theory in QM based on quantum logic? [closed]

Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ...
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2answers
103 views

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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53 views

Why is there a state which is annihilated by two different operators with same absolute Fourier index?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposed a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
2
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1answer
67 views

Are the 'clock' and 'shift' operators used in Qudit codes physically realizable?

I've recently started doing some reading on the subject of qudit codes. In particular, i'm interested in the frequently used clock and shift operators. Can these operators be physically realized? Or,...
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0answers
59 views

Confused about the substitution of the fermionic operators with their Fourier transform in an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
3
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0answers
33 views

Implication of non-positive tripartite information

Hayden et al 2011 showed that tripartite information is non-positive given Ryu-Takanayagi formula. (For definition of tripartite information, see for instance section 4.4 of this paper) Is there ...
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1answer
110 views

Has Jaynes' argument for quantum mechanics as a possible theory of inference been debunked?

To my understanding, there is currently no scientific consensus on which interpretation of quantum physics is the correct one, if any. The most famous one, perhaps for historical reasons, is the ...
3
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1answer
219 views

In quantum weak measurement, what kind of theory replace Copenhagen interpretation?

Here, I denote the initial states of device and quantum system as $|\Phi_\textrm{in}\rangle$ and $|\Psi_\textrm{in}\rangle$. The measurement interval is $[t_i,t_f]$, after measurement, the device and ...
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1answer
48 views

Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
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1answer
28 views

Boundary value condition used during Jordan-Wigner transformation for a $1 D$ Ising chain

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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0answers
36 views

Why does the Quantum Approximate Optimization Algorithm work?

I am trying to understand the structure of the QAOA algorithm (see here) which is seen as one of the candidates to demonstrate early quantum supremacy. Yet Farhi, Goldstone and Gutmann only describe ...
0
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1answer
33 views

Reasoning behind taking the Fourier transform of the fermionic operators for a circular $1$D spin chain [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
4
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1answer
86 views

Ground state of an adiabatic Hamiltonian as an eigenstate of the total spin

I am going through Quantum Adiabatic Evolution Algorithms with Different Paths by Farhi et al. Here, the authors propose to add a special term to the adiabatic Hamiltonian so that the path of the ...
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2answers
75 views

What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
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2answers
57 views

What kind of product is $\prod^n_{j=1}\sigma^{(j)}_x$?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
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25 views

Separable and entangled states under unitary transformation

Show that a separable state remains separable under a local unitary transformation. Similarly, an entangled state cannot be turned into a separable state by means of a local unitary transformation....
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5answers
371 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| \...
1
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1answer
40 views

Size of the quotient of normalizer by the stabilizer in the Pauli group [closed]

Let $P_n$ be the Pauli group on the $n$-qubit and $S$ be a stabilizer subgroup of it. Let $N$ be the normalizer of $S$ in $P_n$. In p. 69 of Lidar & Brun, Quantum Error Correction, it mentioned ...
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36 views

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 $\sigma_z$ ...
2
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1answer
74 views

Why does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with this adiabatic Hamiltonian? [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
0
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0answers
59 views

easy thought experiment for quantum Maxwell demon

I am learning QM,and when I learn tunneling I think of Maxwell demon (I have no thermodynamics backgrounds) Here it goes: There is a potential barrier sitting at x=0 (the whole experiment is 1D) ...
6
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1answer
122 views

Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
0
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1answer
83 views

The minimal knowledge required for theoretical research in Quantum computing & AMO physics [duplicate]

I'm a senior undergraduate student and I have chosen my future Ph.D research area in {Quantum Computing}$\bigcap${AMO physics} (e.g. design a new experimental realization of QC or propose a new way to ...
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1answer
82 views

Quantum cloning of orthonormal states

If I understand correctly, for two orthonormal states $\left|\psi_1\right\rangle$ and $\left|\psi_2\right\rangle$ in the Hilbert space H, there must exist a unitary transformation $U$, such that: $$U\...