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)

5
votes
1answer
149 views

What are qubits made of in Wen's string-net theory?

In Prof. Xiaogang Wen's theory, photons and electrons are described as quasi-particles appeared as a result of the existence of the string-net liquid, which is the topological order of the qubits that ...
5
votes
2answers
342 views

using a unitary matrix to transpose

A unitary matrix U is a matrix such that the conjugate transpose of U, when multiplied on the right with U, yields identity. My question is, is it possible to obtain the transpose of any density ...
5
votes
1answer
130 views

Fast algorithm for maximizing the quantum fidelity

Consider the following optimization problem: Given a quantum state $\sigma$, a constant $b$ and a Hermitian operator $A$, find $\underset{\rho} \max F(\rho,\sigma)$ subject to $\text{Tr}(\rho ...
5
votes
3answers
36 views

Constructing a CP map with some decaying property

Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
5
votes
2answers
150 views

Can quantum measurement process be thought of as a sieve?

Consider an observable represented by the Hermitian operator $$A=\sum_{a'}a' |a'\rangle \langle a'|.$$ As I read on Sakurai's textbook, the process of measuring $A$ throws a system ...
5
votes
1answer
196 views

Is Tsirelson's Bound the only constraint on these quantum correlations?

Alice and Bob are each in possession of one half of a maximally entangled pair of particles. Alice can make either of two observations, $A_1$ or $A_2$. Bob can make either of two observations, $B_1$ ...
5
votes
1answer
166 views

Can entanglement be explained as a consequence of conservation laws?

This article at NewScientist magazine (subscription required) describes entangling photons by passing them through a half silvered mirror. ...
5
votes
1answer
262 views

Matlab package: graphical calculus for quantum operations (esp. linear optics)

I need a matlab package that will make my life easier. I have quantum circuits with optical beam splitters, polarizing beam splitters and photodetectors. These circuits are getting very complicated ...
5
votes
1answer
228 views

What is the code distance in quantum information theory?

What is the code distance in quantum information theory? Code distance seems to be a very important concept in fault tolerant quantum computation and topological quantum computation.
5
votes
2answers
206 views

Toric Code and Random Bond Ising Model

It was established by Dennis, Kitaev et al. that the 2D Toric Code can be mapped to a 2D Random Bond Ising Model. The original derivation was given in the paper "Topological quantum memory" which ...
5
votes
1answer
108 views

Tracing out an observable vs integrating over unitaries

Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define $\displaystyle O_B = ...
5
votes
1answer
348 views

What is the motivation for the definition of concurrence in quantum information?

What is the motivation for the definition of concurrence in quantum information? On the surface, the definition looks pretty ad hoc. The definition is often given for the case of 2 qubits only. What ...
5
votes
2answers
219 views

Hayden-Preskill informational mirrors and decryption

I do have a question about an assumption made in the very interesting Hayden-Preskill paper of black holes as informational mirrors. Alice throws her top secret quantum diary which is $k$ qubits long ...
5
votes
3answers
670 views

Conservation of energy in quantum teleportation

Consider the quantum state teleportation protocol of Bennett et. al. How does one prove that this protocol would never violate the conservation of energy? At the face of it, it doesn't seem to be ...
5
votes
0answers
86 views

What are the prerequisites to study topological quantum computation/topological phases of the matter? [closed]

I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if ...
5
votes
0answers
108 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
5
votes
1answer
79 views

When is an operator subspace the span of Kraus operators?

Let $A$ and $B$ be finite dimensional Hilbert spaces, and let $\mathcal{L}(A \to B)$ be the space of linear operators from $A$ to $B$. Say that a subspace $K \subseteq \mathcal{L}(A \to B)$ is a span ...
4
votes
4answers
600 views

Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
4
votes
3answers
783 views

Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
4
votes
3answers
472 views

number of microstates associated with two-level quantum systems

this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory I'm trying to figure the number of simple quantum states (microstates) of ...
4
votes
3answers
404 views

How could a particle be isolated to avoid decoherence?

The question aims to this issue : if there is some technological arrangement (or action) to take over the particle/system in order to keep it in a coherent state, then the field, (force or whatever) ...
4
votes
2answers
103 views

Tensor product of Hadamard Operators

The Hadamard Operator on one qubit is: \begin{align*} H = \tfrac{1}{\sqrt{2}}\left[\,\left(\color{darkgreen}{|0\rangle + |1\rangle}\right)\color{darkblue}{\langle ...
4
votes
3answers
219 views

What's wrong with this faster-than-light gedankenexperiment?

It is common wisdom - and mathematically proven - that quantum entanglement cannot be used to bypass the relativistic speed limit and transfer information faster than light. So there must be something ...
4
votes
3answers
280 views

Extending mixed states to pure state

Let us consider any pure state $|\psi\rangle\in\mathbb{C^n\otimes C^n\otimes C^n}$. Its reduced bipartite density matrix represent a pure state or mixed state depending on whether $|\psi\rangle$ is ...
4
votes
2answers
131 views

Why does quantum cryptography give us uncrackable codes?

Why does quantum cryptography give us uncrackable codes? What makes it 'uncrackable'? Articles in for example pop science magazines always claim QC produces uncrackable coded, however I highly doubt ...
4
votes
1answer
759 views

How many states can a n qubit quantum computer store?

A classical computer composed of '0' or '1' transistors stores $2^n$ states. Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
4
votes
7answers
468 views

Information relationship to Special Relativity

How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...
4
votes
2answers
167 views

On Bell inequality and bound entangled states

I have recently seen some presentation slides of Michał Horodecki (slide number 77) in which he discussed the following conjecture. Bound entangled states satisfy all Bell inequalities The ...
4
votes
2answers
589 views

Again about all-win lottery

I suggest the following thought experiment that describes a machine which makes everybody happy. Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal ...
4
votes
1answer
153 views

Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
4
votes
2answers
110 views

Approaches to Fault tolerant quantum computation

What are the various approaches to fault tolerant quantum computation ? Two examples are 1. topological quantum computation which uses topological phases in quantum states (2-Dimensional for ...
4
votes
1answer
61 views

Can entanglement with an inaccessible system be useful?

Quantum phenomena in bipartite pure state systems like teleportation are pretty well understood. What I'm interested in is the following situation: Alice, Bob and Charlie hold some general tripartite ...
4
votes
1answer
1k views

Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
4
votes
1answer
494 views

Entanglement of qubits circuit- Bell states

I know that the quantum circuit $\text{CNOT}\; (H \otimes I)$, where $\text{CNOT}$ is the controlled-not gate and $H$ the Hadamard gate, takes the computational basis of two qubits ...
4
votes
1answer
75 views

Spatial and polarizing beam splitters in a graphical calculus

Suppose I have four wires, and I tensor product them together $A \otimes B \otimes C \otimes D$ I pass $A \otimes B$ through a spatial beam splitter $Spl: A \otimes B \rightarrow A^\prime \otimes ...
4
votes
1answer
895 views

Representations of Pauli matrices involving outer product of qubit states

Let $| 0 \rangle$ and $| 1 \rangle $ be the states of qubit. Let $\hat{\sigma_x}$, $\hat{\sigma_y}$, $\hat{\sigma_z}$ be Pauli matrices: $$ \hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ ...
4
votes
2answers
411 views

Extending the idea of superdense coding

I was reading through the superdense coding protocol, that lets A convey two classical bits to B by sending one qubit (assuming B sends A a qubit beforehand). So B creates a 2-qubit state and sends ...
4
votes
2answers
368 views

Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
4
votes
2answers
480 views

Physical meaning of the sign basis in quantum mechanics

If we take a hydrogen atom as qubit, let $\lvert0\rangle$ = unexcited state $\lvert1\rangle$ = excited state then what is the meaning of measuring the qubit value in the sign basis? If the atom may ...
4
votes
2answers
254 views

Can the concurrence be calculated in terms of the entanglement of formation?

If I somehow know the entanglement of formation, $E_F$ for two mixed qubits, where \begin{equation} E_F = -x \log x - (1-x) \log (1-x), \end{equation} where $x = (1+\sqrt{1-\mathcal{C}^2})/2$ and ...
4
votes
1answer
119 views

Couder-Fort Oil Bath Experiments and Quantum Entanglement Phenomena

The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit ...
4
votes
1answer
845 views

Bloch-sphere-like representation of two-qubit density operators

The Bloch sphere is an excellent way to visualize the state-space available to a single qubit, both for pure and mixed states. Aside from its connection to physical orientation of spin in a spin-1/2 ...
4
votes
1answer
384 views

Constructing a maximally entangled qutrit state from $n$ Bell states

I've read that maximally entangled qubit states are a good "unit" of bipartite entanglement since it is possible to create any other entangled state from them using local operations and classical ...
4
votes
2answers
152 views

Can I parameterize the state of a quantum system given reduced density matrices describing its subparts?

As the simplest example, consider a set of two qubits where the reduced density matrix of each qubit is known. If the two qubits are not entangled, the overall state would be given by the tensor ...
4
votes
3answers
273 views

Thought experiment using quantum entanglement in position and its effects

Consider we have two atoms $a$ and $b$. They are entangled with each other in position and momentum, with some wavefuction describing them in position space that is $\Psi(x_a, x_b)$. This ...
4
votes
1answer
156 views

Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( ...
4
votes
1answer
76 views

Local decoherence and entropy

Consider a quantum system consisting of two subsystems, $A$ and $B$. Let $\rho$ be the density matrix of the whole system $A\cup B$. Let $|\alpha\rangle$, $\alpha = 1,2\cdots d_B$, be the states of ...
4
votes
2answers
159 views

CHSH Inequality: why $\pi/8$?

I understand the mechanism how CHSH Inequality works. One thing bugs me is why $\pi/8$. I can also take $\pi/100$ for example and $\cos^2(\pi/100)> \cos^2(\pi/8)$ so much better probability and ...
4
votes
1answer
77 views

Limits of superdense coding

Holevo's theorem says that no more than n bits can be stored (and retrieved) in n qubits. Indeed, allowing error can't improve this either -- the probability of retrieving the correct information is ...
4
votes
2answers
308 views

How do you come up with a POVM?

This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me. Say you have a physical quantity $E$ that can take values 1, 2, 3 ...