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.

learn more… | top users | synonyms (1)

0
votes
0answers
4 views

Invariance of a maximally entangled state under unitary operation $U \otimes U^\dagger$

Apparently the (d-dimensional) maximally entangled state, $|E \rangle = \sum_{i} |ii\rangle /\sqrt{d}$ is invariant under operations of the form $U \otimes U^\dagger$. I want to prove this result, ...
0
votes
1answer
25 views

Why do quantum gates have to be reversible?

One possible reason I have come up with is that we are modeling quantum gates by unitary matrices. And since unitary operations are reversible we have to be able reverse the operation in the physical ...
9
votes
1answer
124 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 ...
6
votes
0answers
57 views

What's the intuition behind the Choi-Jamiolkowski isomorphism?

What is the intuition behind the Choi-Jamiolkowski isomorphism? It says that with every superoperator $\mathbb{E}$ we can associate a state given by a density matrix $$ J(\mathbb{E}) = (\mathbb{E} \...
-2
votes
2answers
59 views

How do Rabi oscillations act on the relative phase of state kets

Suppose we have a system with a lower state $\left|{\downarrow}\right\rangle$ and and upper state $\left|{\uparrow}\right\rangle$, coupled by a pulsed electromagnetic field. I thought that from an ...
0
votes
1answer
23 views

What is the maximum limit for concurrence for a multiparticle state derived from a symmetric hamiltonian? [on hold]

What is the limit for the Entanglement of a multi particle state? Say I have N spins and a symmetric Hamiltonian. Is it 1 or more? Is there a limit at all? I thought it would be 1, since that value ...
8
votes
3answers
2k views

What is a completely positive map *physically*?

I am sure this question is really stupid, but I could not refrain from asking it in this forum. This can be considered as a continuation of this question. ...
1
vote
0answers
44 views

What is a maximally entangled state? Or better, what really is entanglement entropy?

I was trying to understand the concept of entanglement entropy and for that I was studying the density operator formalism in the context of a bipartite quantum system. In some references, people ...
0
votes
1answer
53 views

When should parameters be replaced while changing basis? [on hold]

I have the following equality: $$a\lvert 00\rangle + b\lvert 11\rangle = a\lvert ++\rangle + b\lvert --\rangle$$ for any $a,b \in C$ that satisfy the normalization condition. For $a = \frac{1}{\...
1
vote
1answer
56 views

Trouble understanding Nielsen & Chuang exercise

I am probably just stuck on something very simple, but I'm having trouble understanding a premise of Exercise 10.40 in Nielsen & Chuang. The full details of the exercise are not important for my ...
-3
votes
1answer
49 views

Simplest way to store a quantum superposition temporarily [on hold]

My understanding of the Schroedinger's Cat experiment is that, while it's an amusing thought experiment, the cat would not actually be in a superposition of states because it's just too massive an ...
0
votes
0answers
51 views

Entanglement of bi- and tripartite pure and mixed states

since I'm not sure on how to find out whether a system is entangled or not I thought about examples that could clarify the whole thing. first example: system is in the state $\rho=1/2 (| 000 \rangle \...
-2
votes
0answers
26 views

Imaginary part in calculation [closed]

I want to simulate (I use mathematica) a matrix that has imaginary number. Given the matrix, $$A = \begin{pmatrix} e^{2I+3}Sin{(2\Pi t)} & e^{I (\Pi)}Cos{(2\Pi t)} \\ Cos{(2\Pi t)} & -e^{...
0
votes
2answers
43 views

Calculating the product state capacity of the quantum depolarizing channel

This is homework, so just let me know if I'm on the right track or where I went wrong, please. So, we are asked to compute the product state capacity $$C_1(T) = \max_{\{p_j,\,\vert \psi_j\rangle\}}\...
0
votes
1answer
18 views

Inverting squeezing and displacement operators

This question is about inverting the product of squeezing operator and a displacement operator in the following way: I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$. Where $...
0
votes
1answer
44 views

How can I measure the security of Quantum Key Distribution (QKD)?

QKD protocol is a technique that allow two parties to share common secret key for cryptographic purpose and defined as being secure, by definition. But I am still wondering how can we measure that QKD ...
0
votes
1answer
33 views

CNOT sandwiched by hadamards

I'm having trouble understanding why I'm getting the wrong answer when simplifying a quantum circuit: The relevant matrices are \begin{align*} H = \frac{1}{\sqrt{2}}\left[\begin{matrix} 1 & 1 \...
2
votes
2answers
54 views

Quantum Logic Gates

In classical computation, a bit can have the value of either 1 or 0 and one can apply a logic gate to this bit. As far as I understand, in classical computation, no matter what gate is used, the value ...
1
vote
1answer
56 views

$\frac{1}{\sqrt{2}}(1 + i)|0\rangle$ on the Bloch sphere

By definition, a quantum state can be expressed as $$|\psi\rangle = a |0\rangle+b |1\rangle.$$ Here, $a, b\in\mathbb{C}$ and $|a|^2 + |b|^2 = 1$. Now, I would like to take $a = \frac{1}{\sqrt{2}}(1 +...
1
vote
0answers
31 views

How difficult is it to construct the time inverse of a state? [closed]

This is a vague question, but I hope it can have some sort of answer. Given an isolated state, classical or quantum, of finite size, how difficult is it to actually produce a state that is the time-...
3
votes
4answers
178 views

How would my life be different without quantum entanglement? [closed]

What would happen if for some reason quantum entanglement were suddenly turned off? By "turned off", let's say that every entangled state is immediately replaced with a separable (but still ...
0
votes
3answers
58 views

Relation between coherent states [closed]

Suppose $\left|\alpha\right\rangle$ and $\left|-\alpha\right\rangle$ be two coherent states. Is there any relation between them or are they completely different coherent states?
1
vote
1answer
451 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,...
1
vote
2answers
46 views

Measuring polarization - problem with understanding

Let's assume that we have 2 polarizing filters. First with vertical (1) orientation and second with horizontal (0). I want to measure probability that photon passes through those 2 filters. I have: $...
0
votes
1answer
112 views

How to calculate fidelity of a specific quantum channel?

Let $\gamma$ be a completely trace preserving operator such that $\gamma(\rho) \to (1-\epsilon)\rho+\epsilon(|\phi\rangle \langle\phi|)$. Here $\rho$ is density matrix of two dimensional hilbert space ...
0
votes
1answer
55 views

How to prove that quantum computers can't solve problems outside PSPACE quickly?

What are general methods to prove that certain complexity class is not proper superset of PSPACE class, and how to apply them in quantum case (for BQP class, for example).
1
vote
1answer
25 views

Effect of the translation operator affected by spin?

I'm reading an introductory review on quantum walks and at some point it incorporates spin into the translation operator in a way that I don't follow. Initially it states that the translation by ...
0
votes
2answers
83 views

Is it possible to reverse engineer quantum computer?

Case: I give you a "live" box with quantum signals going through it (while performing calculations) and which contains quantum logic gates. You don't know exact internal structure of box, but you're ...
49
votes
11answers
7k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
10
votes
3answers
147 views

No-Cloning and Uncertainty: Connections or Misconception

In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
6
votes
3answers
206 views

To what extent is it true that quantum computation cannot be simulated on classical computers, and how can we prove it?

I have read several times, for example in chapter 3 of Computer-aided-design Methods for Emerging Quantum Computing Technologies by David Dov Yehuda Feinstein (PhD thesis, Southern Methodist ...
3
votes
2answers
265 views

Can spatial coherence be maintained in fiber optic cables over time?

I am doing research with a double slit experiment, using a beam splitter and 2 lengths of fiber optic cable, whose ends brought close together form the effective double slit. I notice that the ...
4
votes
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 ...
1
vote
1answer
120 views

Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
14
votes
7answers
1k views

Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ for a given complex number $\alpha$ and where $|n\rangle$ is a ...
0
votes
3answers
68 views

Quantum computer able to compute non-computable elements? [closed]

I just recently read the journal article (below) about the Orchestrated Objective Reduction theory put forth by Roger Penrose and Stuart Hammeroff. According to this theory, the phenomenon of '...
0
votes
1answer
45 views

Can quantum computer provide random or just pseudo-random number, or none of both? [closed]

Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
1
vote
1answer
45 views

Entangled qubit measurement

I came across this while reading lecture notes and I have no idea how they got the $M_0$ and $M_1$. The way I see it, the matrix $U$ is a block matrix: $$ \left[ \begin{array}{ c c } P &...
1
vote
0answers
20 views

Quantum Discord and entropy

I'm trying to understand certain aspects of Quantum Discord. The idea is that a quantum system might have non-classical correlations despite it not being in an EPR-like state. So the discord is ...
2
votes
0answers
44 views

dependence of braiding matrix element on the fusion product of anyons

In the case of Majorana fermions (MFs), one knows that if one braids MF $a$ with MF $b,$ then braiding matrix element $R^{c}_{ab}$ depends on the state $c$ which is the fusion outcome of $a$ and $b$. ...
0
votes
1answer
52 views

Is Schmidt Decomposition well defined for periodic matrix product representation(MPS)?

We are able to perform Schmidt decomposition for open-boundary MPSs with dimension of boundary bond $m_0 = 1$, $|\psi\rangle=\sum w_{a_l}|a_l\rangle_L|a_l\rangle_R$. Because we can make $|a_l\rangle_{...
12
votes
1answer
330 views

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 ...
2
votes
1answer
52 views

Is there a theorem which specifies the state (with energy $E$) with maximum entanglement? [closed]

Does there exist any theorem in quantum information which states that the particular state with energy $E$ is the state with maximum entanglement (or discord) among all possible state with the same ...
0
votes
0answers
38 views

Decomposition of the Time-Evolution Operator: Translationally Invariant MPO

Hello everyone myself Sudipto. Currently I'm learning the matrix product state technique in order to simulate 1d spin system and study different properties of the system form quantum information ...
-1
votes
0answers
64 views

Is there a fundamental picture for 'the speed of light'?

I am curious about the profound reason for the concept of 'the speed of light'. My considerations are: (1) It's related with the structure of spacetime (for example in Penrose's twistor plan),so ...
4
votes
2answers
135 views

What is the black hole information paradox really? [closed]

Preliminaries What is the black hole information paradox really? Is it a sophisticated way to ponder and debate the existence of an operator on the boundary that can tease out the interior of a ...
2
votes
3answers
61 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\...
1
vote
2answers
465 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
3
votes
1answer
53 views

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) \...
0
votes
1answer
58 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 + |...