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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Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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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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52 views

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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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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Why is quantum entanglement considered to be an active link between particles?

From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every ...
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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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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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43 views

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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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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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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202 views

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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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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61 views

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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312 views

How does Landauer's Principle apply in quantum (and generally reversible) computing

I understand that a reversible computer does not dissipate heat through the Landauer's principle whilst running - the memory state at all times is a bijective function of the state at any other time. ...
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419 views

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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152 views

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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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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131 views

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 ...
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39 views

Example of a state which is positive but its partial transpose is not positive

Could any one give me an example of a state whose density matrix is positive semidefinnite but partial transpose is not positive semidefinnite?
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Are there any known physical implementations of quantum gates?

I was wondering if there are any known implementations of a small number of quantum gates that can interact with each other. Certainly we don't have a "complete" set of quantum gates (where ...
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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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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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A universe of a finite but increasing number of states of motion?

A limitation of the geometric models of universe is that space locally is considered as a volume, whilst volume is a part of a selected system of inertia. Wouldn't it be more adequate to consider (the ...
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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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Kraus operator rank

All quantum operations $\mathcal{E}$ on a system of Hilbert space dimension $\mathcal{d}$ can be generated by an operator-sum representation containing at most $\mathcal{d^2}$ elements. Extending ...
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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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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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Where does deleted information go?

I've heard that, in classical and quantum mechanics, the law of conservation of information holds. I always wonder where my deleted files and folders have gone on my computer. It must be somewhere I ...
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60 views

Unitarity and measurement

I used to believed that the wavefunction collapse came from the interaction of the system we want to measure {S} with the measurement apparatus {M} : {S} undergoing a non unitary transformation, but ...
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Is there a lower bound on energy needed to transfer one bit of information?

Let's say we want to transmit information between to stations (points in space). Is there a minimal energy required to transfer a single bit of information, assuming that we tolerate that the bit ...
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What is discrete phase space?

I've been reading a little about the usual, continuous Wigner functions and phase space quasi-distributions in general, and I believe I understand the idea behind them. The Wigner function arises when ...
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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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Uniqueness of representing POVM using projective measurement

$\newcommand\tr{\operatorname{tr}} \newcommand\ket[1]{\lvert#1\rangle} \newcommand\bra[1]{\langle#1\rvert} $[Skip to the conjecture for a self-contained mathematical formulation of the question.] ...
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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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56 views

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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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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91 views

Significance of 'chiral' form for a quibit?

Say I have a qubit with probability amplitude divided evenly among $|0\rangle$ and $|1\rangle$ $$\frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt 2}|1\rangle$$ So it seems that we have a, loosely ...
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Why the original BB84 paper “Quantum cryptography: Public key distribution and coin tossing” has '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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Why do we believe in a “force” driven universe? [closed]

Why do we not believe in the potential for a "unified force field" universe, to the exclusion of the belief in the potential for a mechanical, gear driven universe, if the correct shape for the gear ...
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Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle ...
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Second Qubit Not Flipped in Hadamard Gate

I'm very new to QM and Quantum Computing and I have a likely simple question, It may simply stem from my lack of knowledge of vector calculus. We have a 2-qubit quantum state: $$ \mid\psi\rangle = ...
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These two operators commute…but their eigenvectors aren't all the same. Why?

The Hamiltonian $$H = \left[ \begin{array}{cccc} a & 0 & 0 & -b \\ 0 & 0 & -b & 0\\ 0 & -b & 0 & 0\\ -b & 0 & 0 & -a \end{array} \right] $$ commutes ...
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Is it sensible to speak of the parity operator in 4 dimensional Hilbert space?

So I'm dealing with a system of two qubits, with the hamiltonian given by $$H = \left[ \begin{array}{cccc} a & 0 & -b & 0 \\ 0 & 0 & 0 & -b\\ -b & 0 & 0 & 0\\ 0 ...
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Do Category Theory and/or Quantum Logic add value in physics?

I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
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Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
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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: ...