# Tagged Questions

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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### What does conditional probability mean in case of two party system where no-signalling holds?

Background to the problem: I have two parties ( spatially separated ) $A$ and $B$ each having a set of measurements $M_A$ and $M_B$ respectively, and set of outcomes $m_A$ and $m_B$ respectively. Let ...
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### Is a zero-energy universe necessarily also a zero-information universe?

The universe needs to be near zero energy to not crumple in on itself. Under the same logic, does it also need to have near zero information content to prevent the passage of time from burning it to ...
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### How to see validity of no signalling principles in case of entangled parties?

From what I understood the density operator $\rho$ is a mathematical tool which tells us about the probabilities of getting a particular output after measurement. I have two parties entangled with ...
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### Bloch representation. Why Pauli operators?

Why do I know that a general qubit state can be written as $$\rho = \frac 1 2 \big(\mathbb 1 +\vec r \vec \sigma\big)\;\text ?$$ It is clear that the factor of $1/2$ comes from $\text{tr}\rho=1$. ...
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### Quantum coherence and decoherence

In Quantum Mechanics coherent states are defined as eigenstates to some annihilation operator. Afaik this notion is due to Roy Glauber. Now, I just read that if you have a spin-state for example, ...
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### Is the spin and charge of an atom a quantum or classical concept?

I have no idea whether these properties of an atom fall under quantum or classical physics, or perhaps both. Some clarification would be helpful.
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### Thermodynamics for Dummies: Entropy and temperature

I do not study physics and I have never had a course in thermodynamics. I have no idea what it is about, but I am currently taking a course where we had something about entropy. Would be great if ...
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### What is Getting in the Way of Testing D-Wave?

I know there are other questions i.e. Do quantum computers manufactured by D-Wave Systems, Inc. work? , What can the D-Wave quantum computer do? , etc. But I can't seem to find my answer. What is ...
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### Jump Method and the Lindblad Equation

I am studying the time evolution of a density matrix using the Lindblad equation. My initial density matrix is $\rho(0)=|\alpha\rangle\langle\alpha|$, where $|\alpha\rangle$ is a coherent state. Then ...
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### How to derive quantum Fourier transform from discrete Fourier transform (DFT)?

I am interested in Shor's algorithm, and I am reading several papers that related to the quantum Fourier transform (QFT). I know the there is a difference between the output of QFT and DFT (DFT). ...
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### Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
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### Physical Interpretation of the Bloch vector

In the expression of the density matrix of a (Electron-Spin) Qubit $$\rho=\frac{1}{2}(I + x \sigma_x + y \sigma_y + z \sigma_z)$$ where $\tau=(x,y,z)$ is unit vector in the Bloch sphere, which is ...
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### What does “decompositions of a mixed state” mean?

I came across an expression for Entanglement of formation for a mixed state $$E_F(\rho_{AB}) = \text{min}\sum_i p_i S(\rho^i_B)\leq S(\rho_B)$$ where minimum is taken over all the decompositions of ...
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### rotation of a state in Bell basis

Suppose I have a state in Bell basis. For example \rho = \begin{pmatrix} \rho_{11} &0 & 0 & \rho_{14} \\ 0 &\rho_{22} & \rho_{23} & 0 \\ 0 &\rho_{32} &...
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### Undergraduate quantum book treating density operators, mixed states, and entanglement [duplicate]

I'm working on a project on quantum measurement theory - in particular, relating to the quantum Zeno effect - over the summer. Right now, I'm in the process of doing background readings that'd enable ...
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### What processes create or destroy information?

From a classical standpoint, it seems pretty clear that information can be easily lost. If you knock over a bookshelf and the books fall out, it seems like their initial order on the shelf cannot be ...
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### What is the difference between the atomic resonance frequency and the Rabi frequency?

I've been trying to work my way through the solution to the optical bloch equations for a two-level atom system which is being driven by a laser. One thing that has been confusing me is the difference ...
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### Hamiltonian of a quantum harmonic oscillator

On page 286-287 of Nielsen Chuang's Quantum Information and Quantum Computation (10th edition) book, the Hamiltonian for a quantum harmonic oscillator is approximated as $H=a^\dagger a.$ What are the ...
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### Proof of Uhlmann Theorem [closed]

In p228, Chapter 9 of Mark Wilde's text , in the course of proving Uhlmann's theorem for quantum fidelity, it claims \sum_{i,j} <i|^R <i|^A (U^R \otimes (\sqrt{\rho}\sqrt{\sigma})^A) |j>^R |...
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### What is entanglement entropy? and all those stories about counting [closed]

In Quantum mechanics entanglement is a concept that informs us about nature of states. It is a statement about non-product states, thus correlations. This is my rather foolish view of entanglement(...
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### Deriving a POVM from a projective measurement

I understand how to show that every POVM is equivalent to a projective measurement on a larger Hilbert space, but I don't understand why the converse is true. The vast majority of explanations of ...
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### How to define a 'clone' of a mixed state?

State clone of a pure state is clear. But how to define a clone of a mixed state? For example, for a proper mixed state A, $\tfrac12(|0\rangle\langle 0|+|1\rangle\langle 1|)$, if there is a clone of ...
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### Reduced density operator of a maximally entangled state

Is the reduced density operator of a maximally entangled pure state always maximally mixed (trace being half)? I test it on 4 bell state and this claim is true. I wonder why and can the degree of ...
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### Measuring Qubits in Entangled State

If two people (Alice and Bob) are given a state $|\phi^+\rangle = \frac{1}{\sqrt2}(|00\rangle + |11\rangle)$ from a list of states, then Alice can read the first qubit, see if it is 0 or 1, and send ...
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### Definition of the “support” of the reduced density matrix

Some of the papers in condensed matter physics use the word "support" (space). For example, the following papers use the support especially for the reduced density matrix. http://journals.aps.org/prb/...
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### Why can arbitrary two qubit density matrices be expressed in this form? [duplicate]

In the paper "Violating Bell inequality by mixed spin 1/2 states: necessary and sufficient condition" (http://www.sciencedirect.com/science/article/pii/037596019500214N#) by three Horodecki siblings, ...
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### What is known about Renyi entropy of a probability density function?

I see most discussions about Renyi entropy to be using either of these two kinds of definitions, for $\alpha > 0, \alpha \neq 1$ $H_{\alpha}(p_i)=\frac{1}{1-\alpha}\log \sum p_i^{\alpha}$ for a ...
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### Is device independence and non local games only studied for cryptography purposes?

I started reading device independent approach on quantum mechanics from here Device Independent Outlook on QM. I am still a beginner in this field, but out of interest I just browse papers related to ...
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### Why reduced density operator being same is necessary sufficient for no signalling?

Problem Statement : Two parties $A$ ( Alice ) and $B$ ( Bob ) ( in order ) share an entangled pair $\frac{1}{\sqrt{3}}(|00\rangle+|01\rangle +|11\rangle)$. Bob does a measurement in basis \$\{ |0\...