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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Entanglement entropy and area law

I am currently reading a review "Area law for the entanglement entropy" by Eisert, Cramer and Plenio (2010). From what I understand: In one dimension, for local gapped models, we have an area law ...
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How many bytes can the observable universe store?

Is the number of states in the Universe countable? What framework could be used to answer the question in the title?
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51 views

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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How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
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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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34 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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1answer
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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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2answers
108 views

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

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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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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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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2answers
105 views

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
60 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
34 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
130 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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3answers
479 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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What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
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1answer
56 views

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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1answer
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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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2answers
154 views

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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1answer
102 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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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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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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1answer
52 views

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
112 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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1answer
58 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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1answer
197 views

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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636 views

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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1answer
102 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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1answer
76 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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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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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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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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144 views

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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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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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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3answers
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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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1answer
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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 ...