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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Taking photos without photons? [closed]

I was looking up some science news and I came across this! Blind quantum camera snaps photos of Schrödinger’s cat ...
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Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
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What are typical error rates of quantum computers?

I read in an article that in order to perform error correction on a quantum computer there can only be one error per 10.000 calculations (=unitary transformations). This sounds pretty high but how ...
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Is there any restriction on the ability to measure the full quantum state of a system without inducing backaction?

Suppose an arbitrary quantum system is in the state $ \mid \Psi \rangle $, which may or may not be a function of time. An initially ignorant obsevrer would like to figure out what $ \mid \Psi ...
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Weak measurement and weak value

The concept of weak measurements (and weak values) have become popular in Quantum information community, as I can see quite a few papers in arXiv. Since I am from Mathematical background (and the ...
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Why does a measurement on one qubit force another one into a given state in Simon's algorithm?

This comes from trying to understand the "Simon's algorithm". So we have a set of $2^n$ kets $|x_i >$ one each for $i \in \{0,1\}^n$. Each $x_j \in \{0,1\}^n$. And we have the further constraint ...
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Bounds on dimension of a purification?

Let $\rho \in H_A$ be a density operator, $H_A$ is finite dimensioal, it is well known that $\rho$ has a purification in some larger hilbert space. Let $b$ be the minimum dimension for $H_B$ such ...
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The $n$-th root of the NOT gate

I simply can not find material containing facts about the $n$-th root of the NOT gate and it's realization in Q.M. and also in C.M.. Does anyone have material? A comparison of the $n$-th root NOT ...
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227 views

How to write a generic density matrix for multi qubit system

I was reading the paper device independent outlook on quantum mechanics. The author defines a generic two qubit density matrix as $$ \rho=\frac{1}{4}\left( I \otimes I + \vec{r_{\rho}} \cdot ...
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61 views

What causes continuous errors in a qubit?

I read that due to decoherence a qubit in a superpositon gets destroyed or put into one definite eigenstate. This kind of error seems to occur due to interactions with other stuff like the environment ...
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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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How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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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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Quantum computing can be done via measurement alone, why is this significant?

I read in the Afterword section of Nielsen and Chuang's book Quantum Computation and Quantum Information that A second area of progress has been in understanding of what physical resources are ...
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132 views

Approximating a target operator

I was wondering if anyone knew how the author got to equation 12 on page four of this paper, I will attempt to explain the situation below. Given $C$, a target operator, we wish to create an ...
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60 views

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 is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
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How is measurement on system in a Hilbert space seen?

I am a bit confused about different kinds of measurements on a system in state $W$ where $W$ is the density operator in Hilbert space $H$. A general measurement can be given by POVM's, let ...
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Can a Bell state measurement be described in the Von Neumann measurement scheme?

I have been reading and studying this article recently about non-local weak measurements and quantum erasure. Usually the weak measurement formalism is described using the Von Neumann scheme for ...
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Information and entaglement via determination of the first's system state with interaction

Could we have entangled systems (microscopical or macroscopical) and construct a way of altering the state of one of the two entangled parts (let's say by Alice) via interaction and thus making the ...
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What is the condition for local operations on bipartite entangled state?

I have an entangled state between Alice and Bob $|\psi\rangle_{AB}$ ( both Alice and Bob have states in Hiblert space of dimension $n$ ). Alice and Bob can only perform local meaurements. I assumed ...
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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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Was quantum mechanics made to fit the Bell violations or they just happen to fit them?

Entangled bipartite states can violate the CHSH inequality upto $2\sqrt{2}$ with suitable measurements. Is it that in nature we don't witness violation of CHSH more than this and quantum mechanics ...
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How to apply Controlled-NOT gate?

look at the figure below it is about an example to multiply two qubits by 3 Controlled gate to get the SWAP operation .. I'm trying to follow this step-by-step but I couldn't know how this is ...
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Measuring quantum entanglement in paper by Ma et al [duplicate]

Looking at the links below, could somebody please explain how entanglement between Alice and Bob particles is established/deduced from Victor's choice/measurement? I understand that Alice and Bob can ...
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What is quantum mysticism? [closed]

Most of my questions on stack physics exchange are being commented on as being quantum mystic. The questions I ask are basically related to device independence and how local hidden variable theory ...
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Which bipartite entangled states violate the CHSH maximally?

I am reading the device independent outlook on quantum mechanics. Here the author gives a proof that for two qubit system maximally entangled states violate the CHSH inequality maximally that is upto ...
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Do we have algorithms that are polynomial on a Q-Computer but not poly. on a classical Computer?

I am currently reading “Introduction to Topological Quantum Computation” by J.K. Pachos. In the book the author mentions that Shor’s factoring algorithm is polynomial (with regard to the complexity ...
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What is the meaning of integrating over the state space?

If $\lvert\psi\rangle$ denotes the state space corresponding to a qubit, then what is the meaning of the $$\int d\psi$$ where the integral is over whole state space of a qubit? How do I evaluate it? ...
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40 views

How to calculate fidelity of a specific quantum channel?

Let $\gamma$ be a completely trace preserving operator such that $\gamma(\rho) \to (1-\epsilon)\rho+\epsilon(|\phi\rangle \langle\phi|)$. Here $\rho$ is density matrix of two dimensional hilbert space ...
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What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent ...
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Delayed choice experiment and weak measurements

My questions relate to this recent delayed choice experiment with a helium atom: http://www.nature.com/nphys/journal/vaop/ncurrent/abs/nphys3343.html Is there anyway whatsoever - directly or ...
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384 views

Question on hadamard gate and cnot gate circuit tables

I'm trying to solve this problem for homework: Now show that if the CNOT gate is applied in the Hadamard basis - i.e. apply the Hadamard gate to the inputs and outputs of the CNOT gate - then ...
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Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n\rangle $$ for a given complex number $\alpha$ and where $|n\rangle$ is a ...
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Quantum Teleportation between Entangled Qubits

My question refers to the experiment described in this article: http://www.sciencemag.org/content/345/6196/532.abstract Here's a popular science description: ...
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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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What counts as information?

What counts as information? In e.g. the EPR experiment why is one entangled particle knowing instantaneously the state of the other not counted as 'information'. Edit Following a discussion in the ...
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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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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 ...
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Mermin Inequality

Suppose I want to calculate the maximum of Bell inequality for three parties system. In this case I will have 6 measurement directions (unit vectors). It has been done in the paper PHYSICAL REVIEW A ...
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How asymptotically efficient is quantum state tomography of a flat qubit?

Suppose you receive $n$ copies of a qubit rotated by an unknown angle. That is to say, you're given the state: $$T(\theta) = \left(\sin(\theta) \left|0\right\rangle + \cos(\theta) ...
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What is the entropy of a pure state?

Well, zero of course. Because $S = -\text{tr}(\rho \ln \rho)$ and $\rho$ for a pure state gives zero entropy. But... all quantum states are really pure states right? A mixed state just describes ...
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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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What is the difference between general measurement and projective measurement?

Nielsen and Chuang mention in Quantum Computation and Information that there are two kinds of measurement : general and projective ( and also POVM but that's not what I'm worried about ). General ...
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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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What are the characteristic of a unitary acting on a composite system?

I have a composite system AB, initially the state of the system is $|\psi\rangle_A \otimes |\phi\rangle_B$. $U$ is an operator acting on the composite system. If even after application of the operator ...
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What is Bell Measurement (wrt its use in quantum teleportation)?

Bell measurement is joint quantum-mechanical measurement of two qubits, so that after the measurement the two qubits will be maximally entangled. According to the answer here, this is acceptable ...
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Operational difference between separable, entangled, PPT and NPT states

Given two parties Alice and Bob, a state $\rho_{AB}$ is said to be separable if it can be written as $\rho_{AB}=\sum_i p_i\rho^i_A\otimes\rho^i_B$, with $p_i$ being probabilities and ...
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Why does an anti-unitary operator have to be both left and right anti-unitary?

I am reading about anti-unitary operators from here anti-linear operators. They have defined an anti-unitary operator $$K: |\psi\rangle \to K|\psi\rangle$$ $$K(\alpha|\psi\rangle+\beta|\phi\rangle) ...
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How are anti-unitary operators applied?

I was reading about anti-unitary operators from Wikipedia. They give an example of an anti-unitary operator: were $K$ is complex conjugate operation. $\sigma_y$ is defined with respect to two ...