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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How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?
I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation.
Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution ...
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QFT in Quantum Computing and Control Theory?
Is QFT being applied to quantum computing and control theory?
I took yesteryear a basic course on quantum computing and if I remember correctly we didn't touch on any QFT (though I think that if it ...
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75 views
Quantum gates Hadamard before a toffoli gate
After applying a Hadamard gate so that the state splits into either $|1\rangle+|0\rangle$ or $|0\rangle-|1\rangle$ what happens when applying a ccnot (toffoli) gate, this flips a third qbit if the ...
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Quantum gate: Phase shift
I dont undestand how to apply a phase shift gate to a qubit. By example how to map $|\psi_0\rangle = \cos (30^\circ) |0\rangle + \sin (30^\circ) |1\rangle$ to $|\psi_1\rangle = \cos(-15^\circ) ...
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100 views
How to measure a qubit in a random basis
Let a two dimensional system be in the state $\phi=|0\rangle\langle0|$, for any basis $M$ spanned by the orthogonal vectors $|\psi_0\rangle,|\psi_1\rangle$, we can measure $\phi$ in basis $M$ and ...
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143 views
Can the concurrence be calculated in terms of the entanglement of formation?
If I somehow know the entanglement of formation, $E_F$ for two mixed qubits, where
\begin{equation}
E_F = -x \log x - (1-x) \log (1-x),
\end{equation}
where $x = (1+\sqrt{1-\mathcal{C}^2})/2$ and ...
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1answer
63 views
mixture of maximally mixed and maximally entangled state
Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the ...
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190 views
Quantum Teleportation Fidelity
I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
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84 views
POVM advantage in state discrimination
Suppose we are given the task of discriminating, with minimum error, between a set of states $\{|\psi_1\rangle,|\psi_2\rangle,\ldots,|\psi_N\rangle\}$. In other words, we are given an unknown state ...
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3answers
174 views
Is a quantum system mandatory for generating true random sequence?
Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
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2answers
490 views
How to apply a Hadamard gate?
How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
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How is a Rydberg Blockade Radius defined?
Rydberg blockade is a phenomena in 3 or more level systems of Rydberg dressed atoms.
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Quantum circuit simulation software [closed]
Would anyone be able to recommend some software that you can use to simulate a quantum circuit? Something someone created to easily be able to create nice looking quantum circuits and quickly ...
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1answer
63 views
Which similar properties must objects have to sustain quantum entanglement?
Quantum entanglement occurs when particles such as photons, electrons,
molecules as large as buckyballs, and even small diamonds
interact physically and then become separated; the type of ...
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2answers
153 views
Constructing a Toffoli gate with 2-and 1-qubit gates?
I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how ...
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1answer
141 views
Two Qubit problem
A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
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1answer
50 views
Reversible gates
Is it possible to make any gate reversible merely by retaining the input bits in the
output and introducing ancilla bits as necessary? That is, given an irreversible
gate with $k$ inputs and $l$ ...
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3answers
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Is “entanglement” unique to quantum systems?
My text shows (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. ...
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22 views
Finding all marked element by Grover search(not in superposition)
Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, ...
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1answer
120 views
Quantum Circuit, example of the Bernstein-Vazirani problem
This question is regarding the quantum circuit in the picture below.
Suppose we have the set up below, where U performs the operation $U:\mid x \rangle \mid y \rangle \rightarrow \mid x \rangle\mid y ...
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54 views
Equivalence of simple formulations of qubit entanglement
I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement.
One definition states that (1) the bits of a ...
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1answer
108 views
Entanglement and conservation
Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum ...
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1answer
163 views
Quantum circuit, two control not gates
Consider the quantum circuit in the picture below:
We have a Hadamard gate followed by a CNOT gate, this puts the 2nd & 3rd state in the bell state $\beta_{00}=\frac{1}{\sqrt2}(\mid 00\rangle ...
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211 views
Computing with qubits [closed]
We have a qubit in the state $|\psi \rangle= √3/2 |0\rangle + 1/2 |1\rangle$, which we want to measure in the $cos \theta\ |\theta\rangle + sin \theta |1\rangle, sin \theta |\theta\rangle - cos θ ...
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OAM states in communications [duplicate]
Possible Duplicate:
OAM states for wireless communications
Can someone give me an overview of how OAM states are used in communications?
Using Orbital Angular Momentum States seems like a ...
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1answer
76 views
Tracing out an observable vs integrating over unitaries
Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define
$\displaystyle O_B = ...
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1answer
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What is the motivation for the definition of concurrence in quantum information?
What is the motivation for the definition of concurrence in quantum information? On the surface, the definition looks pretty ad hoc.
The definition is often given for the case of 2 qubits only. What ...
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2answers
287 views
Convert state Vectors to Bloch Sphere angles
I think this question is a bit low brow for the forum. I want to take a state vector $ \alpha |0\rangle + \beta |1\rangle $ to the two bloch angles. What's the best way? I tried to just factor out ...
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1answer
211 views
Quantum dimension in topological entanglement entropy
In 2D the entanglement entropy of a simply connected region goes like
\begin{align}
S_L \to \alpha L - \gamma + \cdots,
\end{align}
where $\gamma$ is the topological entanglement entropy.
$\gamma$ is ...
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110 views
What is a Hilbert space filter?
In a recent paper,
Side-Channel-Free Quantum Key Distribution, by Samuel L. Braunstein and Stefano Pirandola. Phys. Rev. Lett. 108, 130502 (2012). doi:10.1103/PhysRevLett.108.130502, ...
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1answer
162 views
partial trace with sparse matrices
Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space.
For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
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What is the physical difference between states and unital completely positive maps?
Mathematically, completely positive maps on C*-algebras generalize positive linear functionals in that every positive linear functional on a C*-algebra $A$ is a completely positive map of $A$ into ...
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Geometric picture behind quantum expanders
A $(d,\lambda)$-quantum expander is a distribution $\nu$ over the unitary group $\mathcal{U}(d)$ with the property that: a) $|\mathrm{supp} \ \nu| =d$, b) $\Vert \mathbb{E}_{U \sim \nu} U \otimes ...
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using a unitary matrix to transpose
A unitary matrix U is a matrix such that the conjugate transpose of U, when multiplied on the right with U, yields identity. My question is, is it possible to obtain the transpose of any density ...
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1answer
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States diagonal in the tensor product of Bell states.
Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition ...
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Functional relations for Kochen-Specker proofs
Many proofs of the Kochen-Specker theorem use some form of the following argument (from Mermin's "Simple Unified Form for the major No-Hidden-Variables Theorems" )
[I]f some functional relation
...
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6answers
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Multiqubit state tomography by performing measurement in the same basis
For a $n$-qubit state $\rho$ we perform all projective measurement consisting of one-particle measurements in the same basis, that is,
$$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
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1answer
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Monte Carlo integration over space of quantum states
I am currently facing the problem of calculating integrals that take the general form
$\int_{R} P(\sigma)d\sigma$
where $P(\sigma)$ is a probability density over the space of mixed quantum states, ...
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1answer
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Unknown quantum state with promise of classical data
I am trying to solve a problem in the measurement and identification of quantum states with a promise as to what states it could be. Here is the problem. Imagine a system that produces qubits in ...
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2answers
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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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3answers
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Constructing a CP map with some decaying property
Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is ...
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Quantum Computing Power Advantages
Currently, the world's fastest supercomputer runs at 17.59 Petaflops, which consumes 9 megawatts of electricity. A qubit-based quantum computer has the potential to operate much more quickly for some ...
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Depolarizing threshold for CSS codes
Many years ago, when CSS codes were first invented, the error threshold of p=0.11 was found when bit and phase flips are independent. Has a threshold yet been found for the case of depolarizing noise?
...
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658 views
How many qubits does it take to specify an event in spacetime?
The title says it all.
My understanding is that a qubit is a superposition of $|0\rangle$ and $|1\rangle$, i.e. the answer to a binary question. So I imagine that specifying an event in spacetime ...
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2answers
710 views
Faster-than-light communication using Alcubierre warp drive metric around a single qubit?
The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
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Non-destructive measurement of qbits
Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says:
"The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
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CHSH violation and entanglement of quantum states
How is the violation of the usual CHSH inequality by a quantum state related to the entanglement of that quantum state?
Say we know that exist Hermitian and unitary operators $A_{0}$, $A_{1}$, ...
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Operator norm directly from phase space representation of photonic quantum operator
I'm interested in calculating the operator norm of a Hermitian operator, say $B$, acting on the Hilbert space of square integrable functions. The context is I have an optical system in all its ...
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1answer
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Accurate quantum state estimation via “Keeping the experimentalist honest”
Bob has a black-box, with the label "V-Wade", which he has been promised prepares a qubit which he would like to know the state of. He asks Alice, who happens also to be an experimental physicist, to ...
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Controlled-measurement of a quantum register
Given a state vector $\left[\alpha,\beta,\gamma,\delta\right]$ which is not known a priori, does there exist an operation, which I will call "controlled-measurement", which results in the ensemble
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