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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Calculating states of entangled and disentangled qubits

I'm writing a quantum computer simulator (about 8 qubits) and I know most of the basics (i.e. how to calculate the effect of a quantum gate on a qubit). But I have hit a wall. Is it possible, with ...
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What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Neilsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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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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The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
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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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161 views

Importance of zero and non-zero eigenvalues of density matrix

What can we say about the quantum state from the number of zero and non-zero eigenvalues of the corresponding density matrix? Anything related to entanglement or any other properties? Does they vary ...
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62 views

Quantum cloning of orthonormal states

If I understand correctly, for two orthonormal states $\left|\psi_1\right\rangle$ and $\left|\psi_2\right\rangle$ in the Hilbert space H, there must exist a unitary transformation $U$, such that: ...
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Why does the BB84 paper “Quantum cryptography: Public key distribution and coin tossing” have a 'withdrawn' status?

The original paper proposing quantum key distribution protocol (now known as BB84): Charles H. Bennett, Gilles Brassard, Quantum cryptography: Public key distribution and coin tossing seems to ...
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Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
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187 views

Quantum teleportation and no-communication theorem

According to the Wikipedia article for the No-communication theorem: In very rough terms, the theorem describes a situation that is analogous to two people, each with a radio receiver, listening ...
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Resource cost and noise effects in quantum teleportation of multible (entangled) qbits

Suppose you have n qubits that are in an unknown state (may be entangled, etc). Can you teleport this state by teleporting each qubit individually (using a Bell state and a classical channel)? If ...
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Probabilities of pure states and density operators

According to my skript: A pure state is a ray: $\quad$ $\{λψ\}$, where $ψ ∈ \mathcal H$, $||ψ|| =1$ fixed and $λ ∈ \mathbb C$, $|λ| = 1$. Pure states are uniquely given by 1-dimensional orthogonal ...
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Quantum vs classical degrees of freedom

It is sometimes stated that any classical underpinnings (rightly non-local) of a general quantum system are unrealistic or unphysical because these require exponentially more information to store what ...
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How do we know that photon entanglement isn't the result of the photons's states being predetermined?

I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language ...
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Proving (instead of discovering) the laws of quantum mechanics

A single toss of a fair coin cannot be predicted. But if we observe a large number of tosses, we can prove mathematically the law that roughly half of them will show up heads. The movements of ...
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62 views

What is trivial and non-trivial gate in computing?

My question seems like it should be posted in Computer Engineering section, but below is how I found this word. I was reading the textbook: Quantum Computation And Quantum Information - by Michael A. ...
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Sufficient criterion for su(2) invariant spin-1*spin_s bipartite density matrix

SU(2) invariant spin-1 and spin-S bipartite density matrix is given by $\rho ^{1,S}=\frac1{3*(2S+1)}[1+\alpha {S^A_i\times S^B_i}+\beta S^A_{ij}\times S^B_{ij}]$, i j varies from ...
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Best book for learning Quantum Communication [duplicate]

I am new in Quantum physics. I want to do my BSc thesis on Quantum Communication. My major is Communication. So I want to learn fast. I have little idea about quantum computing. So please suggest me ...
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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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How “fundamental” is quantum information/computation?

I am wondering how fundamental the study of quantum information theory and computation is, in the sense of contributing to our understanding of the basic laws of nature. Will quantum information ...
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Are superoperators (CPTPM) equal if they are equal on all density operators?

$\DeclareMathOperator\tr{tr} $Is the following statement true? Conjecture: Let $\cal E_1,\cal E_2$ be completely positive trace-preserving maps (quantum superoperators). Assume that for any positive ...
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Equivalence classes in a Hilbert space

I'm reading something about quantum information/quantum computing theory, and I've run into a wall. I know what is meant by an equivalence class and how something can be partitioned into equivalence ...
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Quantum memories: What are they?

Searching the literature for the term "quantum memory" seems to bring up results from two different communities. On the one hand there are quantum opticians, who see a quantum memory as something ...
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Eigen value, matrix, Quantum game

In this paper, on the page 5 http://math.ucsd.edu/~dmeyer/research/publications/qstrat/qstrat.pdf in the second paragraph: his first action puts the penny into a simultaneous eigenvalue 1 eigenstate ...
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Quantum mechanics: compatible observables

I am confused about something. If (all what I will write are operators) $x$ is compatible with $p_y$ that means they have the same eigenvectors. However, $x$ is compatible with $y$ which means they ...
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What are density matrices and how do they work?

I have looked in Stack Exchange about density matrices but haven't found any answers. What are density matrices and how do they work? What are they used for? (Also, please tell me what is wrong with ...
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“Entangled photons never show interference in the total pattern without coincidence count” implies FTL

In my previous question, the most defended objection to the gedankenexperiment was that "Entangled photons never show interference in the total pattern without coincidence count". Here I show another ...
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What is the principle behind the use of one LASER for optical pumping of Rubidium in presence of magnetic field?

How can we use a single LASER for optical pumping of rubidium in the presence of magnetic field as the zeeman levels are degenerate in the presence of magnetic field and how to decide upon the ...
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How to entangle two particles? [duplicate]

After learning about quantum entanglement I wanted to know, what is the simplest way to entangle two particles in a lab?
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What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of ...
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Quantum Games/Superiority of quantum strategies over probabilistic

In the paper Multi-Player Quantum Games by Hayden and Benjamin, there is a 3-player game in Fig 2.c where Probabilistic Classical players do better then Quantum players. What does the words "do ...
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What are the practical consequences of “approximate” quantum cloning with a stimulated emission cloning machine?

Say I build some stimulated emission-based cloning machine for photons (e.g. some active laser medium). Alternatively I could do cloning via interference, e.g. a linearly polarized photon could be ...
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Density matrix of a single qubit as a function of its Stokes Parameters

$\newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\prom}[1]{\langle{#1}\rangle} \newcommand{\matrixel}[3]{\bra{#1}{#2}\ket{#3}}$ How can I prove ...
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Projection operators in a direct product space

The things I'm pretty sure I understand: Let's say I have a single particle hamiltonian $H$ represented by a $2$x$2$ matrix, so it has two eigenstates $|\lambda_1\rangle$ and $|\lambda_2\rangle$. I ...
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Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
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Strange definition of a two-level system by the Bloch vector

A two-level system can be described by a density operator involving the Bloch vector $$ \vec{r}; \quad r_x = Tr(\rho X); \quad r_y = Tr(\rho Y); \quad r_z = Tr(\rho Z) $$ as $$ \rho = \frac{I + ...
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SciFi Stasis Field and the Quantum Zeno Effect

The Quantum Zeno Effect concerns the use of repeated measurement of a particle to prevent the time evolution of the wave function, and hence "freeze" it in the observed state. A Stasis Field is a ...
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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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Probabilities with a qubit

A two-state quantum system has orthonormal energy eigenstates ψ1 and ψ2, with energy eigenvalues E1 and E2 = E1 + ∆E (∆E > 0). These energy eigenstates form a complete set of wavefunctions for the ...
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Number of States and Required Info for Bits vs Qubits

So with classical bits, if you have 2 bits, there are 4 possible outcomes that are possible. To determine these states, you only need 2 pieces of info, the state of each bit. With 3 bits, you can have ...
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Change in Shannon entropy of a quantum circuit of Hadamard gate and a loop

The following Q&A about reversible computing is available here. It has listed a number of practical scenarios where a reversible circuit can still be dissipating heat. Let's assume that none of ...
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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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How to find the required rotation on the Bloch sphere, knowing the start and end

I'm trying to figure out the following situation. Say we have a Bloch sphere with $|g\rangle$ on the positive z-axis and $|e\rangle$ on the negative z-axis. The state is initially in $|g\rangle$, but ...
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How to construct this oracle quantum gate?

I was reading the paper Quantum Computational Complexity in the Presence of Closed Timelike Curves. In this the author mentions that following quantum oracle gate which operates on $n+1$ qubits, can ...
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What is the motivation for the definition of concurrence in quantum information?

What is the motivation for the definition of concurrence in quantum information? On the surface, the definition looks pretty ad hoc. The definition is often given for the case of 2 qubits only. What ...
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Can the concurrence be calculated in terms of the entanglement of formation?

Can the concurrence be calculated in terms of the entanglement of formation? If I somehow know the entanglement of formation, $E_F$ for two mixed qubits, where \begin{equation} E_F = -x \log x - ...
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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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State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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Design a quantum circuit from a matrix

I have unitary matrix and I would find the quantum circuit associated. There are 3 qubits input so it's a 8x8 matrix but it's not a simple operation. The number of gates is not specified. Is there a ...