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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Need help with which books I should buy [duplicate]

I need some help with witch books i should read. I would like to study science, physics, quantum physcics, astrophysics and all other kind of physics. Hit me with the best books inside of thoes ...
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Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
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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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What is Absorption Grating

I came across the word "absorption grating" in a review article. I googled it tried to find out what it means but couldn't. Could you explain it to me?
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How would a quantum computer receive input from a classical computer?

One of the potential applications of a quantum computer would be as a coprocessor to a classical computing system, much in the same way as a graphics processing unit (GPU) performs specialized ...
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Shor's quantum error correction code with unknown basis [migrated]

$\newcommand{\ket}[1]{\lvert #1 \rangle}$I've met a problem in quantum secret sharing which involves the use of a quantum error-correction code. (let's make it simple to be the 9-qubit Shor code) In ...
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Quantum computing records (entangled qubits)

What is the current record number of entagled qubits and how has this number been increased? The latest result on stack exchange, which is 3 years old, reports 14 via this post: How many stabilised ...
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What is the definition of a qubit and a copy/clone of a qubit?

A qubit with state $|\psi \rangle =\alpha|0\rangle + \beta|1\rangle$ is defined as : if we have infinite copies of $|\psi \rangle$ and measure them all in the basis $\{|0\rangle,|1\rangle\}$ then ...
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Amount of entanglement in terms of greatest eigen value for hermitian matrices?

I was reading the paper No Universal Qubit Flipper. In this the paper they show inability to create a universal flipping machine. The method they follow is they take an entangled state between Alice ...
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Situation after Saini & Stojkovic's paper on unitarity in gravitational collapse and non-formation of black holes?

In their paper, Anshul Saini and Dejan Stojkovic [1] claimed that by calculations it is possible to demonstrate that in a gravitational collapse of a disk, an event horizon is never made for a far ...
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How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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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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Bloch representation. Why Pauli operators?

Why do I know that a general qubit state can be written as $$ \rho = \frac 1 2 \big(\mathbb 1 +\vec r \vec \sigma\big)\;\text ? $$ It is clear that the factor of $1/2$ comes from $\text{tr}\rho=1$. ...
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Are measurement results only orthogonal?

Are all measurement operators on a quantum mechanical system defined by a Hilbert space, such that all possible post-measurement states are orthogonal? For example measuring a qubit in some ...
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Precisely when is a matrix representation of Hermitian operator also Hermitian?

I asked a question on math exchange Are properties of linear operators reflected in matrix representations with different output and input basis?. In that question I asked: if I had a Hermitian ...
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Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
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243 views

Why does replacing bra and ket basis vectors by their row and column representations give the wrong matrix representation in a non-orthogonal basis?

I have a Hermitian operator (for a 2D Hilbert space) given by $$H=|\psi\rangle \langle \psi|+|\phi\rangle \langle \phi|$$ where $|\psi\rangle$ and $|\phi\rangle$ are normalized but not necessarily ...
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Is there a simple expression for the coherent information of a Pauli channel?

The coherent information of a channel $\Lambda$, with complementary channel $\Lambda_c$ is defined as: $I(\Lambda)=max_{\rho} \{ S(\Lambda[\rho])-S(\Lambda_c[\rho])\}$ I have noticed that it seems ...
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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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Why is $\theta \over 2$ used for a Bloch sphere instead of $\theta$?

I'm a beginner in studying quantum info, and I'm a little confused about the representation of a qubit with a Bloch Sphere. Wikipedia says that we can use $$\lvert\Psi\rangle=\cos\frac{\theta}{2} ...
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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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Is entanglement a classical phenomena?

If I have an entangled state shared between two parties Alice and Bob $$\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle....(1)$$ then the reduced density operator of Alice's side is ...
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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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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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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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Spin in magnetic field and eigenvalues

We have some arbitrary quantum state, lets say $$\vert\Psi\rangle=\alpha_{1}\vert\uparrow\rangle+\alpha_{2}\vert\downarrow\rangle= \begin{pmatrix} \alpha_{1} \\ \alpha_{2} \\ \end{pmatrix}$$. And ...
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How is CNOT operation realized physically?

I think I understood very well how operations on one qubit are done - if qubit is electron, we just apply magnetic field in direction we want to make spin precess (unitary operations on single qubit). ...
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commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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Can All 4-D column matrices be given as tensor product of 2-D column matrices?

I am familiar with entanglement concept. But it feels bit weird to me that all possibilities of a system in a $4$-dimensional vector space cannot be given as tensor product of two $2$-dimensional ...
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Unitarity and measurement

I used to believe 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 the universe a quantum computer - is light speed barrier a computational constraint

There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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Entanglement entropy in (1+1)d field theory with dynamical critical exponent $z>1$

It was well known that for (1+1)d CFT(z=1) case, we can use the tool of conformal map to derive the formula of entanglement entropy for a finite interval: S ~ $c \log L$. L is the length of the ...
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Can single maximal fraction be increased by one-party local operation?

For a quantum channel $\Lambda$, the corresponding bipartite state is $\rho=(I\otimes\Lambda)(|\Phi\rangle\langle\Phi|)$, where $|\Phi\rangle=\frac{1}{\sqrt{n}}\sum_{i}|ii\rangle$. The maximal ...
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Binomial expansion of non-commutative operators

I would like to determine the general expansion of $(A+B)^n$, where $[A,B]\neq0$, i.e. A and B are two generally no-commutative operators. How could I express this in terms of summations of the ...
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What sort of operations can be applied on a Hilbert spaces?

I was reading the paper No Universal Flipper for Quantum States. In this paper they have tried to prove by contradiction that a universal flipping machine cannot exist. By flipping I mean if I have a ...
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Is the quantum NOT operation similar to the classical NOT operation?

$\renewcommand{ket}[1]{\left| #1 \right\rangle}$ Classical NOT operation Suppose I had an interval $S = [a,b]\in\Bbb{R}$, then $$\mathrm{NOT}(S) = (-\infty,a) \cup (b,\infty)$$ Quantum NOT operation ...
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Double slit experiment where the “particle” is a macroscopic capsule with people inside

I understand that the double slit experiment (i.e. the creation of interference pattern) holds also when the "particle" is not just a single particle but any item, experimentally proven even for a C60 ...
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SU(3) interferometry with qutrits

It is well known that a two-mode interferometer can be described in terms of $SU(2)$ group Smerzi. I wonder if something symilar exists for three mode interferometer and qutrit states ? Not only ...
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Why won't this quantum communication work

I'm sure I'm failing to understand something here. Could someone please explain why this would not work? Preparation: Select two complementary properties, X and Y, and a measurement function for X ...
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Entanglement of Mixed Quantum State

As per Wikipedia: Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot ...
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Verifying quantum states

Suppose Alice creates a secret n-qubit state $\lvert \psi \rangle$ from a description $d$, and gives the states to Bob. (Bob doesn't know $d$ ) Bob who doesn't trust the channel, wants to verify if ...
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Entanglement distillation - Interpreting a protocol

I have a general question regarding the interpretation of a enganglement distillation protocol. In general you have a set of entanglet qubit pairs in a Werner-state. Point of matter of this is that I ...
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What is the difference between maximally entangled and maximally mixed states?

To my understanding, mixed states is composed of various states with their corresponding probabilities, but what is the actual difference between maximally mixed states and maximally entangled states? ...
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What are the Eigenstates in a Flux Qubit?

By reading Wikipedia I get that the two Eigenstates of a Flux Qubit are clockwise or counter-clockwise circulating current. This is somehow intuitive, as my current-generated H-Field compensates the ...
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Quantum computer simulators [closed]

What are good, free, open source, GUI-based quantum computer simulators? I remember there used to be a Java-based one that was very good, but it doesn't seem to be online anymore, or it's relocated.
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Why is the matrix representation in the same basis not same for a density operator?

I have a $\rho : V \to V$ density operator of a $n$ dimensional space $V$ and $\{i\}=\{i_1,i_2..i_n\}$ is an orthonormal basis of this space. The density operator is defined as $$\rho=\sum ...
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What is the actual meaning of the density operator?

I am not able to understand the definition of the density operator. I know that if $V$ is a vector space and if I have $k$ states belonging to this vector space, say $|\psi_{i}\rangle$ for $1\le i\le ...
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Condition for quantum error correction based on encoded states

I am trying to understand the properties of quantum error correcting codes. Consider a quantum code on a lattice, with the property that a given region $R$ is correctable (for any error localized to ...
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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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Quantum Error Correction: Surface code vs. color code

Recently, two groups working on quantum computers published results on quantum error correction. The first was Rainer Blatt's group, who used trapped ions to perform a topologically encoded qubit ...