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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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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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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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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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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36 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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243 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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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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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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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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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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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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23 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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135 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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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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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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34 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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26 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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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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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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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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35 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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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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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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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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60 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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44 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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Conjugate of unknown qubit?

I have seen this problem somewhere on stack exchange, but I have a separate question. Given a qubit which is unknown say $\alpha|0\rangle +\beta|1\rangle $ ( $\alpha, \beta$ are unknown ) is there a ...
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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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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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75 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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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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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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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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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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61 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 ...
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Is there a unitary, linear bijection between (1) Maximally Entangled and (2) Factorizable States?

Pretty much as the title says. I am interested in the two particle system, each particle having two dimensional quantum states; naturally if there is a generalisation I'd be interested in that too. ...
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Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
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Superimposed hydrogen electron states

I have been following an Edx.org course on Quantum Computing. The Prof. has started with a Hydrogen atom qubit, assuming that the electron can only be in the ground state and the first excited state. ...
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How does one devise a Grover quantum oracle despite the no-cloning theorem?

I think I have misunderstood Grover's quantum search algorithm, and would appreciate clarification. From what I understand, the Oracle operator takes an index register of qubits $|x\rangle$ (that ...
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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 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 ...