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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How is Q superposition in Q information different from a classical dice?

Let's consider a dice with 1 or -1 on its faces, opposites faces adding up to 0. The point of this post is to relate the quantum coherence of a single qubit to something "weird", i.e., incapable of ...
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What state is a qubit system in if it is measured by someone, but we do not know the measurement?

Suppose there is a qubit Q in the state $$ \lvert+\rangle = \frac{1}{\sqrt2}(\lvert 0\rangle+ \lvert 1\rangle) $$ Now somebody makes a computational basis measurement on Q, but we do not learn the ...
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Eigenvalues of density operator under quantum channel

Consider a 2x2 density operator $\rho$ with eigenvalues $\lambda_{1},\lambda_{2}$ (where $\lambda_{1}\geq\lambda_{2}$) evolving into a 4x4 density operator $\rho'$ (with eigenvalues ...
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Relation between Von Neumann entropy (and other entanglement measures) and thermodynamical entropy

Suppose I have a bipartite system (with Hilbert space $H = H_a \times H_b$) and the following state: $$\sigma = \sum_{n} \frac{e^{-\beta E_n}}{Z} \rho_n$$ where $Z = \sum_n e^{- \beta E_n}$ and ...
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How powerful would a quantum computer need to be to break RSA encrytion codes?

First off, just to reassure everybody, I have no motive other than pure curiosity for asking this question. I don't want my bank account hacked any more than you want the same done to yours. My ...
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What does density operator being same for two sytems tells us?

Yesterday I asked a question. I got it that if a density operator is given as $$\rho=\sum_{i=1}^{i=k}p_i|\psi_i\rangle \langle\psi_i| \tag{1}$$ then it means that the system is one of the states ...
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470 views

I don't understand the no-communication theorem

I don't understand the no-communication theorem. Okay, first I'll say the bit I do understand about it: if Alice and Bob both have two atoms, such that Alice's atom 1 is entangled with Bob's atom 1, ...
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Qubit projections

Given the qubit: $$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$ What is the corresponding point on the extended complex plane and Bloch sphere? How to perform calculations and get the point representing ...
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359 views

Purpose of Grover's algorithm?

How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm? So can you give me a ...
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How to measure a qubit in a random basis

Let a two dimensional system be in the state $\phi=|0\rangle\langle0|$, for any basis $M$ spanned by the orthogonal vectors $|\psi_0\rangle,|\psi_1\rangle$, we can measure $\phi$ in basis $M$ and ...
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Quantum communication

Is it possible to get two atoms to opposite quantum states of one another so when I change the state of first one, the state of the other one changes too? Is it possible to move them to another place ...
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Quantum circuit and Witness preserving amplification for QMA

My question is about the witness preserving amplification scheme for QMA proposed by Marriott and Watrous in 2005 (see http://arxiv.org/abs/cs/0506068 and ...
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What's wrong with my Quantum Early Warning System (Thought Experiment) [closed]

I'm a lay physics enthusiast and I came up with a thought experiment that I can't fully wrap my head around: Alice and Bob are worried about an impending attack by the dreaded Xenomorphs, so they ...
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How do we take the limit of this quantum operation?

I am wondering how to take the following limit: \begin{align} L= \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} dy \, \left(1 - \frac{1}{\sqrt{ \pi} \sigma } ...
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Understanding measurement based quantum computing

I am currently reading M. A. Nielsen's review on Cluster-state Quantum Computation (Nielsen, Michael A. "Cluster-state quantum computation." Reports on Mathematical Physics 57.1 (2006): 147-161.). ...
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The black hole paradox

I recently read in the news that Stephen Hawking claims to have solved the Black Hole Information paradox. I researched a bit about the paradox and the research that Stephen Hawking did to solve it. ...
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Can someone explain why this QM FTL communication setup is wrong?

So I thought I understood the double-slit experiment and EPR paradox until this setup occured to me. It combines EPR entanglement with "which-way" double slit setups. I know it must be wrong, but I ...
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How to understand the three state descriptions from 3 observers of such a system?

Assuming an EPR pair $\psi_{AB}=|00>+|11>$ and three observers Alice, Bob and Charlie, who can communicate with each other but they do not do it for the time being. Alice with a qubit $|0>$ ...
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Is there a definition of relative Renyi entropy?

Is there a Renyi entropy analogue of ``$H(X \vert Y)$" ? If yes then is there any known meaning to that? Googling around I found a few different notions, equation 18 here, ...
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Long distance entanglement maintenance for quantum teleportation

Quantum teleportation starts out with an EPR pair being distributed among Alice and Bob i.e. one qubit goes to Alice and the other goes to Bob. The problem that I see in this scenario is the state of ...
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How to take partial trace?

$L$ is a linear operator acting on hilbert space $V$ of dimension $n$, $L: V \to V$. The trace of a linear operator is defined as sum of diagonal entries of any matrix representation in same input ...
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Can All 4-D column matrices be given as tensor product of 2-D column matrices?

I am familiar with entanglement concept. But it feels bit weird to me that all possibilities of a system in a $4$-dimensional vector space cannot be given as tensor product of two $2$-dimensional ...
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Spin in magnetic field and eigenvalues

We have some arbitrary quantum state, lets say $$\vert\Psi\rangle=\alpha_{1}\vert\uparrow\rangle+\alpha_{2}\vert\downarrow\rangle= \begin{pmatrix} \alpha_{1} \\ \alpha_{2} \\ \end{pmatrix}$$. And ...
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Prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy

I'm trying to prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy. Now, for this to make sense I should give some definitions. System $A$ lives in Hilbert space ...
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Connection between quantum error correction and entropic quantities

Can the requirement of a quantum code to be error correcting be expressed in terms of a relation involving only entropic quantities (von neumann entropy, mutual information etc)? For example, a lot ...
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How is it that Quantum entanglement does not let you transmit infomation?

when I was first introduced to entanglement I was told that "it is a phenomena that allows information to be transmitted faster than light", however, as I kept reading up on it, this seemed to be an ...
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Is there non-trivial multipartite entanglement not witnessed by the spectra of reduced states?

A lot of analysis of multipartite entanglement is based on examining the spectra of various reduced states. (E.g. area laws.) Of course one generally needs not just the $N$ local states of each ...
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why non orthogonal states are indistinguishable?

I want to know what does it mean by distinguishable quantum state from Mathematics perspective I mean mathematically. As a non physics background student could any one explain me why non orthogonal ...
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Simple Mach-Zehnder Interferometer with Polarizing Beam Splitters

I am wondering which state leaves the simple interferometer below. The beam splitters are polarizing beam splitters (PBS) which transmit vertical polarization and reflect horizontal polarization. Say ...
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Maximum density that we can store information

I was informed that: There is a maximum density at which we can store information. For a sphere with surface area A, the maximum information that can be contained within is equivalent to the ...
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Superimposed state vs. zero amplitude state

Two equal amplitude wave pulses approaching each other through some medium such as a string may form a region of zero amplitude when they overlap completely. At this point, the location of overlap is ...
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Alice sends random states in a channel, what Bob receives?

Suppose Alice prepares $\rho_x$ with probabilities $p_x$ and sends it to Bob. I would say this is the same thing as "Alice prepares $\rho = \sum_x p_x \rho_x$ and sends it to Bob", but Preskill's ...
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A good book for Quantum Cryptography

I am interested in Quantum Information and Cryptography in particular. I have gone through Nielsen's text and Preskill's notes . Can someone suggest me some good text for Quantum Cryptography ? I ...
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Is boson sampling a problem in 'continuous variable' quantum information?

When people generally speak of quantum information in the context of continuous variables, what is generally meant is that observables, like position/momentum or the field quadratures of quantum ...
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CNOT gate broken in 2 different quantum simulators? Or am I wrong?

My understanding is that the control qubit in a controlled-not gate remains unchanged after the controlled-not operation is performed on a target-qubit (so the Pauli-X gate is performed only on the ...
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Super-dense coding protocol with a key

I have this assignment: Show that super-dense coding protocol with the key in the state $\frac{|00⟩⟨00|+|11⟩⟨11|}{2}$ is equivalent (in a sense of transmission rate and security) with ...
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Purposes of QEC stabilizers

I am going through the idea of stabilizer formalism. Defined what is a Pauli group $P_n$ and its properties, we describe a stabilizer set $S$ as: $$S\subset P_n$$ The stabilizer set establishes ...
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Sinusoidaly Driven Two-Level System (TLS)

I'm trying to solve the driven Two-Level System (TLS or qubit) question using a Fourier transform of the Schrodinger equation (SHE), but I'm getting stuck on solving the equation. Given Hamiltonian ...
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318 views

Why does this state have a Schmidt rank of 1?

A system is entangled if and only if the Schmidt rank is greater than 1. Why does this ...
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Constructing a Toffoli gate with 2-and 1-qubit gates?

I'm looking through Nielsen & Chuang's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't ...
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873 views

Quantum Circuit, example of the Bernstein-Vazirani problem

This question is regarding the quantum circuit in the picture below. Suppose we have the set up below, where U performs the operation $U:\mid x \rangle \mid y \rangle \rightarrow \mid x \rangle\mid y ...
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Non-destructive measurement of qbits

Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says: "The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
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Why must quantum logic gates be linear operators?

Why must quantum logic gates be linear operators? I mean, is it just a consequence of quantum mechanics postulates?
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Schmidt decomposition of coupled oscillators

Consider a system of two coupled oscillators, with Hamiltonian ($\hbar = m = 1$): \begin{align} \mathcal{H} = \frac{1}{2}(p_1^2 + \omega_0^2 x_1^2) + \frac{1}{2}(p_2^2 + \omega_0^2 x_2^2) ...
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790 views

Simplified partial trace of two operators

If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any ...
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Can Quantum Measurement Be Detected After The Fact?

My question is simple and has a crude drawing associated with it. I was watching some videos of the quantum erasure experiments and being a computer scientist have researched quantum encryption ...
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What is the significance of the imaginary unit in Deutsch gate?

What is the significance of the imaginary unit $i$ in Deutsch gate? Is this controlled $R_x(\pi\alpha)$ still universal without the imaginary unit $i$?
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Purification of Gaussian states

Let us consider an $n$-mode Gaussian state $\rho_g$ (mixed state) in the Bosonic Fock space $\Gamma(\mathbb{C}^n)$. My question is, can we have a purification of $\rho_g$ which is itself Gaussian? ...
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Superposition in Quantum Mechanics

First of all, let $V$ be a vector space over the field $\mathbb{F}$. It is possible then to show, by Zorn's Lemma that there is a basis for $V$. The main point is that although basis are quite ...
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are there known fundamental limits of quantum computer scaling?

Quantum computers provide exponential speedup relative to classical computers. However, it is empirical fact that increasing of number of qubits makes the the computer harder and harder to keep ...