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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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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116 views

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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151 views

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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56 views

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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45 views

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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45 views

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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104 views

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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63 views

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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1answer
70 views

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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24 views

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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182 views

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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3answers
220 views

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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1answer
67 views

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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1answer
56 views

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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27 views

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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43 views

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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298 views

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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1answer
167 views

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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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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35 views

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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94 views

How can quantum entanglement send information?

I don't believe this is a duplication (either that or I didn't understand the answers to the other questions). I understand when sending information via radio waves that the frequency or amplitude is ...
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3answers
197 views

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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1answer
60 views

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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1answer
28 views

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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157 views

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 ...
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1answer
45 views

Why does a quantum cloner imply superluminal communication

I am wondering why superluminal communication would be possible if a quantum cloner would exist? The common argument (FLASH) goes as follows: Alice and Bob share the Bell state $$ |\psi^-\rangle = ...
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40 views

Have there been any experiments that have demonstrated a quantum error correcting code?

Has quantum error correction been demonstrated? I know that classical error correction has been demonstrated by [1], they correct a single bit flip error, but has anyone been able to detect and ...
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1answer
50 views

Distinguishing density operators with the same diagonal elements

If I have two sources of qubits and one source produces the density matrix: $$\rho_1 = \begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix}$$ and the other source produces: $$\rho_2 = ...
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1answer
77 views

Phase shift of the displacement operator

According to my professor, the displacement operator $D(α)=e^{\alpha a^†−α^*a}$ can be written, "with a simple phase shift", as $D(α)=e^{i\alpha(a^†+a)}$ which he then proceeds to write as ...
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1answer
44 views

Properties of controlled z-rotations

Given n qubit gate of the form c-z-z-z... (shorthand for c-z between qubit 1 and 2 followed by c-z between 1 and 3 and so on up to n qubits) it seems to be possible to find local unitaries which will ...
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159 views

How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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123 views

What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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1answer
44 views

The Simon's Algorithm, confusing equation

I'm approaching the Simon's Algorithm and have troubles with understanding a logic in an introduction. Above the eq. 6.5.4 they introduce that set S which has 2 elements. As far as I understand, ...
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120 views

About long range entanglement [closed]

“topologically non-trivial” ground states have long-range entanglement. Is this possible to process the quantum information with help of the studies in topological non-trivial ground states for ...
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1answer
57 views

Is a quantum channel well behaved under a perturbation of its Choi matrix?

Every completely positive trace preserving quantum channel can be associated with a unique quantum state. Supposing one perturbs the quantum state into a new state. Is there some sense in which one ...
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2answers
109 views

Definition of Fermion [closed]

Recently, I encounter a problem about the definition of Fermion operator. In our standard textbooks, the Fermions are defined by their exchange/braiding property, that is, if a minus sign appears by ...
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1answer
80 views

Are there any known continuous (non-lattice) quantum error correction codes?

I come from a hep-th background, but I have noticed that quantum information is becoming increasingly common in discussions of AdS/CFT and black hole information, and so I've begun thinking about it ...
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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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1answer
49 views

Would a pair of independent quantum coin tosses be perfectly anti-correlated?

Background Suppose we attach a button to an electronic flip flop such that an LED will toggle when we press the button with 50% probability, where the source of the randomness is a quantum event, ...
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1answer
39 views

Wigner-Yanase skew information [closed]

I am reading Eric Carlen's paper on Trace Inequalities and Quantum Entropy. I am currently reading about the Wigner-Yanase skew information which is defined as: $$I_{WY}(\rho)=-\frac{1}{2} ...
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2answers
293 views

What is the difference between a bit and a qubit?

I am Computer Science student and learning about quantum computing. But, I have a problem in understanding Bit and Qubit relationship. A bit with 2 bits = 4 states 00,01,10,11--- 1 state at a time. ...
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1answer
119 views

Quantum coherence and decoherence

In Quantum Mechanics coherent states are defined as eigenstates to some annihilation operator. Afaik this notion is due to Roy Glauber. Now, I just read that if you have a spin-state for example, ...
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57 views

explaining qubits to beginning CS students

&I have 15 minutes as a guest lecturer to explain the notion of quantum computing to CS students in a Theory of Computation class. There is a lot of information on the web, e.g., ...
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Could a travelling quantum object transport an on-board monitor to restitute information later? [closed]

Could a pair of identical "automated observers" such as a camera inside a capsule, be made to travel slowly along different paths, and then be recovered to play back a film of its on-board ...
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230 views

Finding the matrix representation of a superoperator

I am trying to express superoperator (e.g. the Liouvillian) as matrices and am having a hard time finding a way to do this. For instance, given the Pauli matrix $\sigma_y$, how do I find the matrix ...
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189 views

How are the field operator and quantum state after a beam splitter and a polarizing beam splitter individually?

How are the field operator $\hat{a}$, $\hat{a}^\dagger$ and the quantum state (like coherent state $|\alpha>$, Fock state $|n>$) changed after a beam splitter and a polarizing beam splitter ...
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82 views

Ternary dimensioned density matrix

I am currently reading this paper: Entropy Inequalities by Araki and Lieb (project Euclid link). And I am not able to understand one step: $${\rm Tr}^{123}\left(\rho^{12}\rho^{23}\right)={\rm ...
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74 views

Query about the proof why non-orthogonal states cannot be reliably distinguished

I have a query regarding the proof given in the book by Nielsen and Chuang on why two non-orthogonal states cannot be perfectly distinguished. The proof is given on page 87 of the 10th edition; here ...