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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Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
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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 ...
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Is this statement about quantum mechanics valid?

In Philosophy of Language by William G. Lycan, there are the lines: Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
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Can superdeterminism resolve contextuality, entanglement and Shor's algorithm in quantum mechanics?

Superdeterminism is the idea that the apparent freedom for the choice of experimental apparatuses and their settings are nothing but an illusion. Contextuality is the dependence of the properties of a ...
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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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Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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The definition of entropy in quantum mechanics

I have seen entropy with several different definitions. Like Von Neumann entropy and Rényi entropy, etc. So I am curious why there are so many different definitions in quantum mechanics while only ...
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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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The role of context in information theory

Consider Hofstaedter’s jukebox analogy: A jukebox that contains only one record, but many different record players, each of which interprets that one record in a different way to produce an entirely ...
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How can you distinguish between projections of quantum states?

Consider this problem in quantum cryptography: We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which ...
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The complementary variable to the qubit and spin-1/2

The qubit is a big topic of quantum information theory. A qubit is a single quantum bit. Physical examples of qubits include the spin-1/2 of an electron, for example, see page 39 of Preskill: ...
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How can projection operators be expressed in form $\frac{1}{d} (I + \sum_i r_i \lambda_i)$?

How can projection operator be expressed in form $\frac{1}{d} (I + \sum_i r_i \lambda_i)$? I was reading a paper and found out that the density matrix in $d$-dimensional Hilbert Space can be ...
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Quantum Teleportation Fidelity

I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
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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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Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
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Why is quantum entanglement so important?

Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
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Quantum cryptography: encryptions

I am studying quantum cryptography and I have a very basic question. Suppose A and B share a secret key k, where k=0 or 1. A wants to send one qubit to B. What A does is, if k=1, she 'flips' the qubit ...
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Understanding a Physics Paper on Quantum Teleportation of Continuous variables

The paper I am trying to understand is here: http://pra.aps.org/abstract/PRA/v49/i2/p1473_1 The paper describes the quantum teleportation protocol in a general case with continuous dynamical ...
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What are the benefits of quantum information “teleportation”?

I read occasionally popular science articles and from time to time encounter issues about quantum information teleportation. (this one for example http://www.physorg.com/news193551675.html) So far I ...
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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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Finding the matrix representation of a superoperator

I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this. For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...
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Measuring non-commuting observable at once

Given an Hilbert space $H$ (finite dimensional for sake of clarity), and two non-commuting operators $$A = \sum_a a |a\rangle\langle a|$$ and $$B=\sum_a b |b\rangle\langle b|,$$ is it possible to find ...
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Stimulated emission and No cloning theorem

I have a little trouble with the simulated emission. I know of the no-cloning theorem which states that it is not possible to duplicate any state. One the other hand, I know about the stimulated ...
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A (mundane) CS analogy for quantum teleportation

From my limited understanding of quantum entanglement, it seems like qubits act the same way as pseudo-random-number-generators (except as far as we can tell, these ones really are random). When you ...
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How do I calculate the position on the Bloch sphere of a quantum gate with a given diagonal matrix?

In quantum computation there are several principal quantum gates that have corresponding matrix representations. One of these is the Z gate, whose matrix is $\left[\begin{smallmatrix} 1 & 0 \\ 0 ...
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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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Can reduced density matrices of sub systems of an entangled composite system be different?

In a 4-dimensional hilbert space, only 4 entangled states( normalized ) are possible ( if I am not wrong ), the bell basis. In each of the state in bell basis the reduced density matrix is ...
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Quantum Entanglement and BB84 protocol

Can Quantum entanglement can be used to strengthen the security or increase the efficiency of communication via the BB84 protocol? If so, how?
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Inner products containing the tensor product of two operators

The book Nielsen & Chuang "Quantum Computation and Quantum Information" presents the concept of tensor products as follows. Suppose we have the vectors $|v\rangle$ and $|w\rangle$ which exist in ...
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Partial measurement (destructive) collapses |1> to |0>

In the following QScript program: ...
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A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
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(thought) experiment re: Bell's Theorem and Schrodinger's cat

I apologize if this question is naive. I am wondering about what would happen with the following experiment. Start with a standard Bell's Theorem setup: We have two quibits entangled in a particular ...
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Intuition behind Hamiltonian

I am reading this paper by Das et al. which converts Deutsch's algorithm into an adiabatic quantum algorithm. I don't get the intuition behind the initial and final Hamiltonians. If defines the ...
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Canonical form of GHZ and W state

What is the Schmidt decomposition of the tripartite states$|GHZ\rangle=\frac{1}{\sqrt 2}[|000\rangle+|111\rangle]$ or $|W\rangle=\frac{1}{\sqrt 3}[|001\rangle+|010\rangle+|100\rangle]$? Are these same ...
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Classical vs qubits: Superposition

Since a quantum information lecture today I have been wondering what does it really mean for a state to be in superposition? Is this something that is answerable? This is what we learnt (or what I ...
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Entanglement: Is it possible to prepare and reset probabilities to send information?

I'm pretty certain that the answer to the question in the title is a no, but I don't understand why. I have some basic misunderstanding of quantum processes that I’d like clarified in the form of ...
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Can PEPS explain the holographic principle in quantum gravity?

Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the ...
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How are the PPT criterion and Bell's inequality different?

Bell (1964) writes that if we assume an equivalent classical hidden variable distribution for a two-qubit state then the expectation value of the product of two observables $A$ and $B$ can be written ...
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Are there any known continuous (non-lattice) quantum error correction codes?

I come from a hep-th background, but I have noticed that quantum information is becoming increasingly common in discussions of AdS/CFT and black hole information, and so I've begun thinking about it ...
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Proving the unitary relation of ensemble decompositions

In my class it was told that ensemble decompositions of a density operator $\rho$ are not unique, but that the ones that exist are related by a unitary operator. I'm trying to prove this, but I get ...
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Solution of dynamics of density matrix

Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda ...
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mixture of maximally mixed and maximally entangled state

Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the ...
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Reversible gates

Is it possible to make any gate reversible merely by retaining the input bits in the output and introducing ancilla bits as necessary? That is, given an irreversible gate with $k$ inputs and $l$ ...
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System with no entanglement but consuming quantum discord

I have come across an article which talks about quantum discord (Observing the operational significance of discord consumption. M. Gu et al. Nature Physics 8, 671–675 (2012) doi:10.1038/nphys2376), ...
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Entanglement measure to classify topological ordered states

I know long-range entanglement is the essence of nontrivial topological ordered states. (Trivial refers to short range entangled and nontrivial refers to long range.) So, entanglement measure at large ...
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Defining entanglement in subspaces of tensor product

I have asked the question in math.stackexchange, but perhaps it should be more relevant here. Hence I am re-posting it with necessary reediting. Let $\mathcal{H}=\mathbb{C}^n$ be a Hilbert space. A ...
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Can spatial coherence be maintained in fiber optic cables over time?

I am doing research with a double slit experiment, using a beam splitter and 2 lengths of fiber optic cable, whose ends brought close together form the effective double slit. I notice that the ...
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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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Deutsch's Algorithm. Unitary Transform $U_f$

I'm studying Deutsch's algorithm and I keep coming across the phrase along the lines of "There is a unitary transform (a sequence of quantum gates) $U_f$ that transforms the state $|x\rangle |y\rangle ...
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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 ...