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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Quantum computing, NP complexity [closed]

Hi I have a very limited knowledge of quantum physics and its bothering me trying to understand quantum computing. I want understand how a qubit can return usable data faster then a regular bit, how ...
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About quantum measurement problem, proper or improper mixture?

Generally a quantum measurement is regarded as resulting in a definite outcome due to "state collapse" and the post-measurement state is described as a proper mixture with the ignorance of the ...
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What is the 'area law' in the context of matrix product states?

I am trying to get into the topic of matrix product states by reading this: A practical introduction to tensor networks: Matrix product states and projected entangled pair states. R. Orús. Ann. ...
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Does this quote from my textbook imply that not all states are superpositions?

I read this at a book; The difference between bits and qubits is that a qubit can be in a state other than $|0\rangle$ or $|1\rangle$. It is also possible to form linear combinations of states,...
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Photons have a property from the matter they interact with?

When a photon leaves its source and hits our eye, our brain sees the source of the photon (Like a lightbulb or a star). When a photon is ejected from its source and bounces off of an object we see 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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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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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 $$|\psi\...
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How can I prove following density matrices have same eigenvalues?

I have the following two density operators, the paper I am reading says that these two operators have same eigenvalues $$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1 |+|2\rangle ...
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Can we have a physical interpretation for a time independent Schrodinger equation of this form?

I am interested in a time independent Schrodinger equation of this form. $$F*\psi - \frac{\hbar^2}{2m} \frac{\partial^2{\psi}}{\partial{x^2}} = E\psi$$ Here the product $V\psi$ is replaced by the ...
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Quantum Computation

Is there any rule or technique so that one can design quantum gate operator from matrix operator? Suppose, what will be the quantum gate operator for this matrix operator : $$ \left( \begin{array}{c ...
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Bell State, if Bob applies a Pauli Gate?

After Alice and Bob share a Bell state, Bob applies a Pauli gate to his qubit. What will be the situation of the Bell state? What happens? Then Alice applies the same gate to her qubit – again, what ...
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Can we make a Maxwell's Demon using Quantum Computers?

Although I'm reasonably sure that quantum computing advances will not lead to the ability to construct a machine that globally violates the 2nd law of thermodynamics, it feels like a difficult ...
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$\frac{1}{\sqrt{2}}(1 + i)|0\rangle$ on the Bloch sphere

By definition, a quantum state can be expressed as $$|\psi\rangle = a |0\rangle+b |1\rangle.$$ Here, $a, b\in\mathbb{C}$ and $|a|^2 + |b|^2 = 1$. Now, I would like to take $a = \frac{1}{\sqrt{2}}(1 +...
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What is an incoherent state?

I am reading through a recent paper which speaks frequently of "incoherent states" without ever defining what such a state is. I gather from the context of the paper that it has something to do with ...
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Interference experiment and entanglement with apparatus

Consider a single photon in a Mach-Zehnder interferometer. Considering the photon only, the output state is the sum over both paths $$\vert 1 \rangle + \vert 2 \rangle=\vert \psi \rangle + e^{i\...
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Two definitions of the density matrix?

There seems to be two different definitions of definitions of density matrices in Physics. In Quantum Information we define a the density matrix associated with a wave function $ | \psi \rangle$ as $...
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Numerically finding the energy diagram of the hamiltonian

I'm looking at a collection of three two level systems (qubits) coupled to each other (with known bare state energies and couplings). The hamiltonian is given by $$\mathcal{H}=\sum_{i=1}^3{\omega_ia^\...
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Reference for statistical mechanics from information theoretic view

I am interested in knowing if some one here knows book/notes for statistical mechanics from the information theoretic viewpoint.
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Hilbert Schmidt inner product

I am desperately trying to solve the following problem, and would really appreciate help! Suppose $R$ and $Q$ are two quantum systems with the same Hilbert space $\mathcal{H}$ with $\dim(\mathcal{H})=...
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How to understand the measurement on entangled state in the following cases? [closed]

Assuming an EPR pair AB, event MA is a measurement on A. My questions are: (1) At MB and MB' (depending on where B is located), if we try to describe the state of B (but not measure B yet), what'...
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Theoretically, how does quantum decoherence induce noise?

The decoherence process has allowed us to explain various (classical and decoherence) sources of measurement noise in quantum systems. I intuitively understand this physical concept of decoherence-...
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Separability of density operators on tensor product spaces

Consider a composite system $\mathcal{H}=\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ where $\mathcal{H}_{A}$ and $\mathcal{H}_{B}$ are Hilbert spaces of constituent components (say two qubits). Let $\rho_{...
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Purity of a maximally mixed quantum state

The trace of the square of a density matrix(which is also called the Purity of the quantum state) is (lower)bounded by the inverse of the dimension of the Hilbert space and (upper) bounded by 1. I ...
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Positive Partial Transposition in Fano form

Cite from "Geometry of Quantum States: An Introduction to Quantum Entanglement 1st Edition by Ingemar Bengtsson (Author), Karol Zyczkowski (Author)": "Partial transposition applied on a density ...
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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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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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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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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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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 $\rho^i_A,\rho^...
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When was Electromagnetically Induced Transparency first introduced?

The oldest paper I know regarding this topic was published in 1997 by Stephen E. Harris. But I am not sure if he is the first to introduce this idea. Could you tell me when and by who did introduce ...
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Quantum Bayesianism and contradictory preditions of two agents

In quantum Bayesianism (QBsim) interpretation, the wave function $| \psi \rangle$, or density operator $\hat{\rho} = | \psi \rangle \langle \psi |$, is not objective. It is instead interpreted as the ...
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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: $$U\...
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What does it mean that quantum teleportation can be classically simulated?

Quoting here from Quantum Computation by Nielsen and Chuang : (Gottesman–Knill theorem) Suppose a quantum computation is performed which involves only the following elements: state preparations ...
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A question on partial trace and density matrix computation

Consider a Pure state of a two dimensional system $|\psi\rangle={1\over\sqrt{2}}(|e_1\rangle|e_1\rangle+|e_2\rangle|e_2\rangle)$ where $\{|e_i\rangle\}$ is an orthonormal basis. Could any one just ...
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Meaning of the Reduced Density Operator

I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument. Consider a bipartite system $AB$, ...
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EPR paradox: instantaneous vs very fast?

An EPR quantum experiment can be explained by instantaneous collapse of the wave function regardless of the distance separating a pair of entangled particles. But do we have the certainty that the ...
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Writing down an entanglement in bra-ket notation

I have a relatively complex (for me anyhow) situation which I would like to capture in bra-ket notation, rather than in words. However, I've not been able to find a source which will help me ...
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Mapping a given density matrix to the generalized 2-qubit state

The generalized 2-qubit state is given as: $$ \rho = \frac{1}{4}[ I\otimes I + (m_x\sigma_x + m_y\sigma_y + m_z\sigma_z)\otimes I + I \otimes (n_x\sigma_x + n_y\sigma_y + n_z\sigma_z) + \sum_{ij}...
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Two Qubit problem

A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
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How to choose proper measurement operator?

Let's assume I have two states inside the Bloch sphere, at radial vectors $r_1$ and $r_2$ respectively $(r_1<r_2<1)$. Their angular location is same. These are like: \begin{equation} \rho = \...
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Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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Measurement in many body systems

Any wavefunction for a system of many particles can be decomposed into linear combinations of the direct product of single particle states with respect to a certain observable(single particle basis). ...
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Can a qubit have an imaginary component?

My knowledge of linear algebra is limited and my physics knowledge mostly comes from high school and Youtube so please bear with me. In the equation $$|x\rangle = a|0\rangle+b|1\rangle,$$ I read that ...
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How to solve such a maximal entropy oriented optimization problem?

I am considering such a problem: (1) Given a finite dimensional composite system AB whose initial state is a product state of A and B so that $\rho_{AB}=\rho_A\otimes \rho_B$. (2) Assuming AB ...
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Understanding amplitude amplification in quantum computing

In short, what is the essence of amplitude amplification type of techniques that appear in quantum computing? More precisely, my main questions are, relating them more to Grover's search which ...
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Understanding the delayed choice quantum eraser from a quantum information stand point

A continuation of Understanding the quantum eraser from a quantum information stand point What quantum circuit would correspond to delayed choice? In particular, the decision of whether to not to ...
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Fermi's Golden Rule

Consider a system with countable quantum states. One can define $J_{ij}$ as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\sum_{i} p_{i}...
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Issues with the proof of the no-cloning theorem

The no-cloning theorem states according to Wikipedia that it is impossible to create an identical copy of an arbitrary unknown quantum state. As far as I am aware the theorem is usually proofen ...
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Book question positive square root on quantum operator

On p.86 Section 2.2.4 of the Quantum computation and quantum information book by Nielsen, $M_{o}$ is defined as the positive square root of the positive operator. Is the "positive square root" ...