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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Why schmidt decomposition only holds for two component composite systems?

According to schmidt decomposition any pure state belonging to a composite system $AB$ can be written as $|\psi\rangle = \sum_i \lambda_i |i_A\rangle |i_B\rangle$ where $\lambda_i$ are non negative ...
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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 $\{ ...
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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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Can isotropic states have bound entanglement?

Let us consider the maximally entangled state \begin{equation} |\psi\rangle=\frac{1}{\sqrt{n}}(|0,0\rangle+\cdots+|n-1,n-1\rangle) \end{equation} and construct the pseudo-pure state \begin{equation} ...
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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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which are the non-abelian anyons for universal quantum computation

I am trying to get a list of non-abelian anyons that can be used for universal quantum computation by implementing gates via braiding. I found that Majorana fermions and para-fermions (not sure about ...
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Recommendations for Advanced Books on the Interface between CMT and Quantum Information

I am looking for a book/review article/website which covers applications of condensed matter theory to quantum information. In particular, I am interested in such topics as a mathematical description ...
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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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How can a correlation be teleported?

I am aware of how a qubit can be teleported from party $A$ to party $B$ if both the parties are entangled. Is there a similar way to teleport a correlation? I googled and found Entanglement ...
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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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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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Thought experiment about no-cloning theorem and FTL information

The quantum no-cloning theorem states that one cannot "build" a perfect cloning device for arbitrary quantum systems. There also exists a famous thought experiment where Alice transmits information ...
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How is decoherence due to the environment compatible with the Copenhagen interpretation?

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) How is that compatible with the ...
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How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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Entanglement of Tripartite States

Is there any simple algorithm to determine the entanglement of a tri-partite state? In particular, what is the proof for entanglement of $ |GHZ\rangle $ and $ |W\rangle $ states? $ |GHZ\rangle ...
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Is macroscopic causality an issue in the context of certain quantum experiments?

In order to formulate my question properly I need to explain a few things. Cramer_Herbert Zych_Brukner Reference 1. - John Cramer, Nick Herbert, "An Inquiry into the Possibility of Nonlocal Quantum ...
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Properties of controlled z-rotations

Given n qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which will ...
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What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?

Imagine I write a fusion rule for some anyons on a paper. Then I try to solve pentagon identity and hexagon identity, imagine finally I find out for example Hexagonal equation doesn't have any ...
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How to write a noisy state as a separable operator

Bipartite operators close enough to the identity are separable. But how does one compute the product operator terms of the separable expansion? In particular, if $\left| \Phi \right> = m^{-1/2} ...
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Shape of the state space under different tensor products

I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this). Recall: In a ...
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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 ...
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Is Interpretation of state vectors and density matrices according to Frequentist or Bayesian interpretation of probability?

I asked a question on math stack exchange what does probability mean. I did not know about Frequentist and Bayesian interpretation of probability previously. So according to which interpretation are ...
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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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CNOT gate application to separated qubits

In the case 1 in the picture, it is easy to perform matrix calculations concerning the circuit to obtain a final state. In case 2 however, I am wondering what is a general procedure to calculate it ...
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Heisenberg XXX time evolution operator for three qubits

I've a problem to reproduce the result in equation (4) on page three of this paper: http://arxiv.org/abs/0802.2588. So far I've understood that they apply a Heisenberg XXX interaction between ...
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Taking photos without photons?

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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Should it be obvious that independent quantum states are composed by taking the tensor product?

My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 that the ...
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How to physically prepare a qubit in a certain state?

I earlier asked the question about definition of a qubit. From it I understood that its the experimental setup that actually defines the qubit. But I don't get it's physical realization. How a qubit ...
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Question regarding entanglement

Could the paradoxical nature of entanglement be the result of a change in the nature of quantum properties, or an incomplete understanding of such, instead of non-locality?
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How do you find the projection operator onto an eigenspace if you don't know the eigenvector?

I was working on exercise 2.60 of Nielsen-Chuang which is as follows: Show that $\vec{v}\cdot\vec{\sigma}$ has eigenvalues $\pm 1$, and that the projectors onto the corresponding eigenspaces are ...
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Arrow of Time in Information transfer

I am writing a sci-fi script and need some legitimate theory to back up a central story element (so there's no real world application): Could there be a logically consistent theory supporting the ...
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Why isn't everthing in a superposition state? [duplicate]

I know that a superposition is a state in which there are 50% and 50% (other % also) chances of two things to happen so why am I not in a superposition state? Example, I am at rest and i now choose to ...
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Toric Code and the String-Net Model

What, exactly, makes the toric code a quantum error-correcting code as opposed to any other string-net model? What makes it special? The way I understand it, it's a normal string-net model on a torus, ...
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Why can't a classical bit behave like a qubit?

For example i have a 2 qubits which can have 4 possibilities i.e. 00, 01, 10, 11 so this shows that the 2 qubits can contain four bits of information as they are superpositioned but i think 2 ...
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What is the Philosophy Behind Relational Quantum Mechanics?

I watched this video on Relational Quantum Mechanics yesterday and my brain has been trying to comprehend it since. The interpretation I currently have is this: If an observer O measures the state S ...
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What is the reason for 2 qubits no longer being entangled after interaction with a causality violating qubit?

Background : I was reading the following paper on closed timelike curves ( CTC ) : Quantum Mechanics Near Closed Timelike Curves. The Deutsch consistency equation for CTC is $$\rho_{CTC}=Tr_{CR}( U ...
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Sparse subset of a vector space and entanglement

Could any one tell me concrete mathematical definition of sparse subset of a vector space. I am not understanding this
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Quantum violation of Newton's Third Law? [closed]

From this site: http://www.learning-mind.com/5-thought-provoking-quantum-experiments-showing-that-reality-is-an-illusion/ I gained the knowledge that a group of scientists, upon measuring a tiny ...
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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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Quantum dual-slit experiment via Youtube live streaming (explanation within)?

What will happen with this theoretical setup: A scientist is bored one day and positions his photon detector at the classic dual-slit photon experimental setup. Then he wires the photon detector up to ...
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Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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How does quantum superposition make calculation faster?

In every description of a quantum computer I've seen (that isn't extremely technical), they've been described as computers that use qubits, that use a superposition of 1 and 0 to make processing ...
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BB84 protocol what do they do once they have the key?

In the BB84 protocol Alice and Bob share a key via a method using both quantum and classical channels. I understand how they do this. But I don't understand what they then do with the key? I.e. How do ...
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Question about Hartle and Hawking's universal wavefunction?

My apologies in advance if this question is poorly worded or doesn't make any sense, however I have just finished reading into this theory and it seems as though Hawkings No Boundary Universe is ...
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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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How can quantum entanglement send information?

I don't believe this is a duplication (either that or I didn't understand the answers to the other questions). I understand when sending information via radio waves that the frequency or amplitude is ...
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How does many-worlds interpretation make measurement unitary?

Does many-worlds interpretation of QM make the process of measurement (wavefunction collapse) be an unitary transform? If so, how does it do this? If we have an "object" qubit in state ...
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An analogy for qubits and quantum computing?

I have understood that qubits are special ways to store data where they exist in more than the conventional 2 states. However, I do not understand how they are read, interpreted and manipulated ...
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What is the implication of Schmit decomposition?

According to schmidt decomposition if I have pure state $|\psi\rangle$ in the composite hilbert space $AB$ ( both $A$ and $B$ are hilbert spaces of dimension $n$ ) then it can be writen as ...
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What is coherence in quantum mechanics?

What are coherence and quantum entanglement? Does it mean that two particles are the same? I read this in a book called Physics of the Impossible by Michio Kaku. He says that two particles behave in ...