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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When should parameters be replaced while changing basis?

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}{\...
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45 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 ...
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44 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 \...
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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 ...
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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\}}\...
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2answers
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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 ...
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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 $...
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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 +...
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32 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 \...
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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^{...
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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-...
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4answers
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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 ...
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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?
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How to get this one qubit evolution operator in Bloch sphere? [closed]

I can't find have to get matrix equation (13) in this paper: http://arxiv.org/abs/1401.2495 if any body knows how he has derived this matrix please share it in details.
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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: $...
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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 ...
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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 ...
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2answers
47 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 ...
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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).
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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 ...
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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 '...
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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.
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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 ...
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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 &...
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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 ...
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51 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_{...
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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 ...
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1answer
43 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 ...
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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 ...
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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 ...
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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\...
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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 + |...
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61 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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1answer
46 views

Want to measure entanglement of the state [closed]

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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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
60 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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58 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 ...
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231 views

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

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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1answer
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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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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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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 ...
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1answer
70 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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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 ...
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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
137 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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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 ...
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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 ...
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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 ...
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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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1answer
49 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 ...