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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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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Shor's Algorithm: Why throw away the f(x)?
I'm having a little trouble understanding Shor's algorithm - namely, why do we throw away the result f(x) that we get after applying the F gate? Isn't that the answer we need?
My notation:
...
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Representations of Pauli matrices involving outer product of qubit states
Let $| 0 \rangle$ and $| 1 \rangle $ be the states of qubit. Let $\hat{\sigma_x}$, $\hat{\sigma_y}$, $\hat{\sigma_z}$ be Pauli matrices:
$$
\hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ ...
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Quantum Coin Flipping Protocol
$\newcommand{\ket}[1]{\left|#1\right>}$
I have the next protocol:
$A$ tosses a fair coin $a\in \{0,1\}$, if $a=0$, $A$ sends to $B$ $\ket{\psi_0}=\ket0$, if $a=1$ $A$ sends to $B$, ...
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Faster-than-light communication using Alcubierre warp drive metric around a single qubit?
The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
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States diagonal in the tensor product of Bell states.
Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition ...
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131 views
Can spatial coherence be maintained in fiber optic cables over time?
I am doing research with a double slit experiment, using a beam splitter and 2 lengths of fiber optic cable, whose ends brought close together form the effective double slit. I notice that the ...
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Functional relations for Kochen-Specker proofs
Many proofs of the Kochen-Specker theorem use some form of the following argument (from Mermin's "Simple Unified Form for the major No-Hidden-Variables Theorems" )
[I]f some functional relation
...
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105 views
Multiqubit state tomography by performing measurement in the same basis
For a $n$-qubit state $\rho$ we perform all projective measurement consisting of one-particle measurements in the same basis, that is,
$$p_{i_1i_2\ldots i_n}(\theta,\varphi) = \text{Tr}\left \{ \rho ...
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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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67 views
Shape of the state space under different tensor products
I am currently studying generalized probabilistic theories. Let me roughly recall how such a theory looks like (you can skip this and go to "My question" if you are familiar with this).
Recall: In a ...
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Is the universe a quantum computer - is light speed barrier a computational constraint [duplicate]
Possible Duplicate:
Is the universe a quantum computer - is light speed barrier a computational constraint
Cross-posting this question, since physics.stackexchange has not provided any ...
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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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930 views
Is the universe a quantum computer - is light speed barrier a computational constraint
There is currently a debate ongoing on leading maths blog Gödel’s Lost Letter, between Gil Kalai and Aram Harrow, with the former arguing that building a quantum computer may not be possible due to ...
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253 views
Does no-cloning theorem implies a no-comparison theorem?
I was reading about no cloning theorem and it arose a thought experiment, if there were a way of compare quantum states (for being equal) then you could build a pseudocloning machine that searches for ...
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585 views
Ignorance in statistical mechanics
Consider this penny on my desc. It is a particular piece of metal,
well described by statistical mechanics, which assigns to it a state,
namely the density matrix $\rho_0=\frac{1}{Z}e^{-\beta H}$ ...
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1answer
46 views
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
813 views
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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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 ...
4
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1answer
58 views
Spatial and polarizing beam splitters in a graphical calculus
Suppose I have four wires, and I tensor product them together
$A \otimes B \otimes C \otimes D$
I pass $A \otimes B$ through a spatial beam splitter
$Spl: A \otimes B \rightarrow A^\prime \otimes ...
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1answer
178 views
Matlab package: graphical calculus for quantum operations (esp. linear optics)
I need a matlab package that will make my life easier. I have quantum circuits with optical beam splitters, polarizing beam splitters and photodetectors. These circuits are getting very complicated ...
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Quantum information science references
I was hoping you guys could recommend reading material on Quantum Information Science. First off, here's my background.
Personally, I started reading Ballentine's Quantum Mechanics and I found it be ...
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Many body quantum states analyzed as probabilistic sequences
Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in ...
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POVMs that do not require enlargement of the Hilbert space
The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
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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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2answers
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Can quantum measurement process be thought of as a sieve?
Consider an observable represented by the Hermitian operator
$$A=\sum_{a'}a' |a'\rangle \langle a'|.$$
As I read on Sakurai's textbook, the process of measuring $A$ throws a system ...
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451 views
Quantum Computing, Qubit Creation/Entanglement
I am currently a high school student researching quantum computing. I was referred to this site by Google and a friend. Currently I am researching the qubit part of quantum computing. My question is ...
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1answer
75 views
Number of conditions for a two-particle state to be decomposable
Suppose we have a general two-particle state $ \Phi (x_1, x_2 ) = \sum_{n_1,n_2} \phi_{n_1,n_2}(x_1,x_2)|n_1,n_2> $, where $n_1$ can be any of $n$ possible states, and $n_2$ can be any of $m$ ...
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Hilbert-Schmidt basis for many qubits - reference
Every density matrix of $n$ qubits can be written in the following way
$$\hat{\rho}=\frac{1}{2^n}\sum_{i_1,i_2,\ldots,i_n=0}^3 t_{i_1i_2\ldots i_n} ...
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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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565 views
Simplified partial trace of two operators
If I have two operators A and B living in the Composite Hilbert Space $H_I \bigotimes H_{II} $ and I want to take the partial trace of $C=AB$ over the subspace $H_I$, i.e., $Tr_I[AB]$, is there any ...
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Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)
In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
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What Shannon channel capacity bound is associated to two coupled spins?
The question asked is:
What is the Shannon channel capacity $C$ that is naturally associated to the two-spin quantum Hamiltonian $H = \boldsymbol{L\cdot S}$?
This question arises with a view ...
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State of Matrix Product States
What is a good summary of the results about the correspondence between matrix product states (MPS) or projected entangled pair states (PEPS) and the ground states of local Hamiltonians? Specifically, ...
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Decoherence and measurement in NMR
It seems that the Bloch equations, or a suitable generalization thereof, are enough to phenomenologically model the measurement process in NMR. Has anyone attempted a fully quantum mechanical model ...
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129 views
What proof techniques have failed for solving the SIC-POVM problem and what new insights have been gleaned from them?
The SIC-POVM problem is remarkably easy to state given that it has not yet been solved. It goes like this. With dim($\mathcal H$) $=d$, find states $|\psi_k\rangle\in\mathcal H$, $k=1,\ldots,d^2$ ...
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1answer
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Explicit construction for unitary extensions of CPTP maps?
Given a completely positive and trace preserving map $\Phi : \textrm{L}(\mathcal{H})\to\textrm{L}(\mathcal{G})$, it is clear by the Kraus representation theorem that there exist $A_k \in ...
12
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1answer
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What is the Holevo-Schumacher-Westmoreland capacity of a Pauli channel?
Suppose you are given an $n$-qubit quantum channel defined as $\mathcal{E}(\rho) = \sum_{i} p_i X_i \rho X_i^\dagger$, where $X_i$ denotes an $n$-fold tensor product of Pauli matrices and $\{p_i\}$ is ...
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2answers
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Relevance of SIC-POVMs to quantum information
What is the real relevance of SIC-POVMs (symmetric informationally complete POVMs) to concrete tasks in quantum information theory? A lot of work has been put into giving explicit constructions, and ...
13
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2answers
157 views
A resource theory of quantum discord?
Local Operations and Classical Communication (LOCC) is the classic paradigm for studying entanglement. These are things that are `cheap' and unable to produce entanglement as a resource for a quantum ...
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2answers
371 views
How do I calculate the position on the Bloch sphere of a quantum gate with a given diagonal matrix?
In quantum computation there are several principal quantum gates that have corresponding matrix representations. One of these is the Z gate, whose matrix is $\left[\begin{smallmatrix} 1 & 0 \\ 0 ...
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Quantum entanglement faster than speed of light?
recently i was watching a video on quantum computing where the narrators describes that quantum entanglement information travels faster than light!
Is it really possible for anything to move faster ...
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An entropy of the Wigner function
Is there an entropy that one can use for the Wigner quasi-probability distribution?
(In the sense of a phase-space probability distribution, not - just von Neumann entropy.)
One cannot simply use ...
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What is the use of a Universal-NOT gate?
The universal-NOT gate in quantum computing is an operation which maps every point on the Bloch sphere to its antipodal point (see Buzek et al, Phys. Rev. A 60, R2626–R2629). In general, a single ...
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113 views
Information Retrieval
This question is motivated by the issue of information retrieval from black holes, but it is essentially a question about quantum information.
It is widely believed (in certain circles) that the ...
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2answers
604 views
What is postselection?
I was reading some questions here.
I couldn't understand what it means by postselection.
What is postselection? What is its use/significance? Where did it came from?
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Is Tsirelson's Bound the only constraint on these quantum correlations?
Alice and Bob are each in possession of one half of a maximally entangled pair of particles. Alice can make either of two observations, $A_1$ or $A_2$. Bob can make either of two observations, $B_1$ ...
