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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Group theory and quantum optics

This is a question about application of group theory to physics. The starting point is the group $SU(n)$. I have a representation $R$ of $SU(n)$ that takes values on the unitary group on an infinite ...
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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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When using quantum regression theorem to get the correlation function,like in the below system, why it appears sin and cos in the function? [on hold]

In this four-level single atom interact with classic field system, when using quantum regression theorem, the derivation of the density matrix and the annihilator operator are used: Then use ...
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What is the significance of trigonometric angles in quantum mechanics? [closed]

So, I've been doing a lot of research about quantum mechanics and quantum computing, and I found a paper detailing speed limits for quantum circuits. I'm not understanding what the data means. The ...
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When an unitary operator is a quantum gate?

Quantum gates we use like X, Y, Z, H, CNOT, etc. are all unitary. When an arbitary unitary operator can be considered as a quantum gate?
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Physical significance of Williamson parameters

I am trying to read some of the quantum mechanical problems from a mathematical point of view, and came to the following problem. Let us consider a $n$ mode quantum Gaussian state (which is in ...
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32 views

Can changing representation change the meaning of density operator?

I had posted a question What is the actual meaning of the density operator?. After that I understood that if I have the expression of a density operator $$\rho=\sum_{i=1}^{i=k}p_i|\psi_i\rangle ...
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2answers
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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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45 views

If perfect maximal entanglement is never true, does a remainder invalidate the monogamy of entanglement?

If something is only very nearly (and/or observed to be) maximally entangled, does that remainder allow for a menage trois of hybrid correlation (as it relates to AMPS)?
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Is “maximal entanglement” ever perfectly true?

Can two aggregate sets of entangled particles ever be (observed to be) maximally entangled? The thought experiment by Leonard Susskind for ER=EPR assumes, in principle, you can take segregate ...
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Can one representation of a projector operator be re-arranged to get another?

I have a vector space $V$ and a subspace of $V$, $W$. Let $P$ be the projection operator for subspace $W$. Also let the dimension of $W$ be $d$. Also I have two orthonormal basis $(a_1,a_2,...a_d)$ ...
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how to arrive at first-order correlation function with the above master equation?

My question arose when I was reading a paper called " Multi-photon Blockade of the dressing of the dressed states'. This is the states this paper used: This is the master equation this paper has ...
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Is there any method to solve the many particle stationary scattering problem like the one for the single particle problem?

The stationary scattering problem by a potential barrier lies in every textbook of quantum mechanics, in which the scattering amplitudes for the single particle wave can be obtained by solving the ...
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2answers
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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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1answer
56 views

Prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy

I'm trying to prove that $-\log{d} \leq H(A|B) \leq \log{d}$ for von Neumann entropy. Now, for this to make sense I should give some definitions. System $A$ lives in Hilbert space ...
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1answer
31 views

A question about entanglement of formation and decomposition

In the answer of this question, the last paragraph says that If you know one decomposition which is optimal for Entanglement of Formation for a given state $\rho$, you can obtain the optimal ...
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2answers
126 views

What does density operator being same for two sytems tells us?

Yesterday I asked a question. I got it that if a density operator is given as $$\rho=\sum_{i=1}^{i=k}p_i|\psi_i\rangle \langle\psi_i| \tag{1}$$ then it means that the system is one of the states ...
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1answer
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Finding all decompositions of mixed states

Some quantities, such as the entanglement of formation, are defined using a quantity that is minimized over all possible decompositions of a mixed state. A closed form can be found for this in some ...
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465 views

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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1answer
41 views

I don't understand the no-communication theorem

I don't understand the no-communication theorem. Okay, first I'll say the bit I do understand about it: if Alice and Bob both have two atoms, such that Alice's atom 1 is entangled with Bob's atom 1, ...
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71 views

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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2answers
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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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2answers
132 views

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 ...
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1answer
97 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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Transition rate of two level system subjected to noise

(this question is simpler than its length implies. I did this on purpose to provide a nice complete development for future readers) The setup Suppose we have a two-level quantum system with ...
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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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1answer
39 views

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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72 views

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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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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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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1answer
41 views

How does observer affects the wave-particle nature ? (and related questions: part 2)

Following comments I split my question in to two parts which are independent. The questions are about double slit experiment with an observer(s). Suppose electrons are being used in the experiment ...
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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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56 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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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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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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1answer
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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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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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1answer
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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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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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154 views

What's the Cause of Quantum Entanglement? [duplicate]

What is the cause of quantum entanglement? When two particles become entangled what property of them basically changes as to establish a link between them and how the information is exchanged between ...
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5answers
596 views

Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in ...
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1answer
43 views

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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1answer
88 views

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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2answers
123 views

“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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1answer
64 views

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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27 views

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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How is decoherence due to the environment compatible with the Copenhagen interpretation?

Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) How is that compatible with the ...
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1answer
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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 ...