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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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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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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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 ...
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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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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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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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Are universally valid possibilistic theories possible?

This is a spin-off of the following question: Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence? Given that Thomas ...
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Entropy increase vs Conservation of information (QM)

Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of ...
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Quantum information references

I was hoping you guys could recommend reading material on quantum information. First off, here's my background. Personally, I started reading Ballentine's Quantum Mechanics and I found it be a very ...
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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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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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45 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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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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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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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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Significance of 'chiral' form for a qubit?

Say I have a qubit with probability amplitude divided evenly among $|0\rangle$ and $|1\rangle$ $$\frac{1}{\sqrt 2}|0\rangle + \frac{1}{\sqrt 2}|1\rangle$$ So it seems that we have a, loosely ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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1answer
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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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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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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 ...