# 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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### Measurement in many body systems

Any wavefunction for a system of many particles can be decomposed into linear combinations of the direct product of single particle states with respect to a certain observable(single particle basis). ...
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### Size of the quotient of normalizer by the stabilizer in the Pauli group [closed]

Let $P_n$ be the Pauli group on the $n$-qubit and $S$ be a stabilizer subgroup of it. Let $N$ be the normalizer of $S$ in $P_n$. In p. 69 of Lidar & Brun, Quantum Error Correction, it mentioned ...
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### In quantum weak measurement, what kind of theory replace Copenhagen interpretation?

Here, I denote the initial states of device and quantum system as $|\Phi_\textrm{in}\rangle$ and $|\Psi_\textrm{in}\rangle$. The measurement interval is $[t_i,t_f]$, after measurement, the device and ...
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### Questions involving seperable states

I'm reading Mark Wilde's book Quantum Information Theory, and I'm stuck on two parts. I'm unable to prove: The state $\sum_{z} p_{Z}(z) \; \rho_z \; \otimes \sigma_z$, where $\rho_z$ and $\sigma_z$ ...
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### Gaining intuition over Hamiltonian for qubit systems

A typical Hamiltonian for a two state system with some driving field can be written as $$H=J(t)\sigma_z+h\sigma_x$$ This represents a qubit system driven along a single axis. On the other hand we ...
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### Heisenberg Representation of Quantum Computers explain observable transformations

The Heisenberg Representation of Quantum Computers (Daniel Gottesman) http://arxiv.org/abs/quant-ph/9807006 Suppose we have a quantum computer in the state $|\psi\rangle$, and we apply the ...
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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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### Complexity of quantum simulation

Richard Feynman showed that Quantum simulation on a Turing machine will have an exponential slowdown. If that is so, does this put quantum simulation outside of P (complexity class)? I thought quantum ...
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### Exact solution of Qubit Decoherence using Transfer Matrix

I'm going through a particular paper on decoherence: Exact Solution of Qubit Decoherence models by a transfer matrix method I'm having trouble understanding a particular step in the mathematics ...
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### How is the lifetime of a symmetric and antisymmetric state determined by its constituents

In the context of quantum mechanics, there is the concept of so called symmetric and antisymmetric states, which can have multiple constituents. A type of hybridized state, if you will. To keep the ...
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### A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
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### If we can't clone quantum states, then how does stimulated emission work? [duplicate]

So we know we cannot fully copy a quantum state. But doesn't stimulated emission does just that? Say, a photon in a particular qubit state $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$ passes ...
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### What is the qualitative difference between quantum superpostion and mixed states? [duplicate]

As I understand it, if one has a complete knowledge of the state of a quantum system (insofar as one knows the statistical distributions of all the observables associated with the state) then one can ...
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### Measurement on two Qubits

Assuming I have two Qubits, i.e. a four-dim. Hilbert space. In the following, I choose the basis {|11>,|10>,|01>,|00>}. I want to have a look on the non-diagonal part <11|$\rho$|00>. How can I ...
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### Is there a quantum computing model accounting for uncertainty of a qubit state?

Any physical quantum computer would have a limit on the fidelity with which it can create qubit superposition states. If we're trying to create $|\Psi\rangle = c_0|0\rangle + c_1|1\rangle$, the ...
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### Trace of an observable [closed]

If $X$ and $Y$ are two observables and $\rho$ is a density operator, is it true that for every complex number $z$ the quantity $$\mathrm{tr}[\rho (X+zY)^*(X+zY)]$$ is non-negative?
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### Holevo Information and Quantum Mutual Information

This question is about the difference between Quantum Mutual Information and Holevo Information of quantum channels. From http://arxiv.org/pdf/1004.2495.pdf equation 7 we know that the sum of quantum ...
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### What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
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### Measuring qubit as the presence or absence of a particle [closed]

My background is not physics so forgive the confusion. If we use photon polarization as qubits, I can understand that the angle is in a superposition between 0 and 90 degrees. But we can also use ...
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### Can a non-entangled qubit be teleported by entangling it?

Let's say I have a qubit that is not entangled in state $\psi$. I want to teleport this qubit by entangling it with another qubit but still getting $\psi$ back in the end. Is this possible, or would ...
I am trying to get an intuitive idea of how the No-Cloning theorem affects Quantum computation. My understanding is that given a qubit $Q$ in superposition \$Q_0 \left| 0 \right> + Q_1 \left| 1 \...