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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Is this theory about Universe and information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...
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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 ...
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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) ...
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Entanglement of Mixed Quantum State

As per Wikipedia: Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot ...
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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 ...
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What is the next step beyond quantum computation?

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...
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Is there a unitary, linear bijection between (1) Maximally Entangled and (2) Factorizable States?

Pretty much as the title says. I am interested in the two particle system, each particle having two dimensional quantum states; naturally if there is a generalisation I'd be interested in that too. ...
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Dimension of separable state

Please can you help me to understand how the dimension of the set of separable states is $\dim \cal H_1 + \dim \cal H_2$? This is the relevant passage: So far, we have assumed implicitly that the ...
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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 ...
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How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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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 ...
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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 ...
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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 ...
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What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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How many states are there in the observable universe

If we took a single instant and considered all possible states of all energy and matter do we have any bounds on how much that would be? Would that number be related to information?
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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 ...
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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 ...
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734 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 ...
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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 ...
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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 \\ ...
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Does squeezing a vacuum state produces photons?

A squeezed vacuum state is produced by applying a squeezing operator $S$ on the vacuum state $|0 \rangle$: \begin{eqnarray} S | 0 \rangle = \sum_n C_n |n \rangle \end{eqnarray} My question is, from ...
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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. ...
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Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
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Mathematically challenging areas in Quantum information theory and quantum cryptography

I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
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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 ...
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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 ...
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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 ...
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Can the concurrence be calculated in terms of the entanglement of formation?

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 - ...
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How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
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Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...
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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 ...
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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 ...
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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 ...
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Why does the BB84 paper “Quantum cryptography: Public key distribution and coin tossing” have a 'withdrawn' status?

The original paper proposing quantum key distribution protocol (now known as BB84): Charles H. Bennett, Gilles Brassard, Quantum cryptography: Public key distribution and coin tossing seems to ...
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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 ...
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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}( ...
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104 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 ...
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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 ...
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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 ...
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492 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 ...
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Mixed state after measurement

I'm looking at Section 2.4.1 of Nielsen and Chuang's Quantum Computation and Quantum Information were they derive the density operator versions of the evolution and measurement postulates of quantum ...
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Situation after Saini & Stojkovic's paper on unitarity in gravitational collapse and non-formation of black holes?

In their paper, Anshul Saini and Dejan Stojkovic [1] claimed that by calculations it is possible to demonstrate that in a gravitational collapse of a disk, an event horizon is never made for a far ...
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Group theory and quantum optics

This is a question about application of group theory to physics. The starting point is the group $SU(n)$. I have a representation $R$ of $SU(n)$ that takes values on the unitary group on an infinite ...
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Eigenvalue of the adiabatic Hamiltonian of Farhi's three qubit 2-SAT problem

I was trying to reproduce example 3.3 of Quantum Computation by Adiabatic Evolution by Edward Farhi et. al. This is an adiabatic algorithm to solve an instance of three qubits 2-SAT problem. I think ...
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How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
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Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
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Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $$|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n ...
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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 ...
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Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...