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 “code” in “toric code”?

When I first heard people talking about using Kitaev's toric code to do topological quantum computation, I was thinking how many lines does the toric code have. Then I was told that the "code" really ...
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How can you distinguish between projections of quantum states?

Consider this problem in quantum cryptography: We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which ...
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Are there any connections between James–Stein estimator and quantum mechanics?

Very nice statement from wiki: When three or more unrelated parameters are measured, their total MSE can be reduced by using a combined estimator such as the James–Stein estimator; whereas when ...
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What is the difference between quantum cryptography and quantum teleportation?

Generate two entangled photons, send one to a message sender and the other to the intended receiver. Both the sender and the receiver recover the same piece of quantum information from the photons, ...
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Quantum communication

Is it possible to get two atoms to opposite quantum states of one another so when I change the state of first one, the state of the other one changes too? Is it possible to move them to another place ...
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Given entanglement, why is it permissible to consider the quantum state of subsystems?

Quantum entanglement is the norm, is it not? All that exists in reality is the wave function of the whole universe, true? So how come we can blithely talk about the quantum state of subsystems if ...
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Did anyone claim that quantum theory meant lasers would never work

I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many ...
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How to deterministically distinguish the following quantum states?

(1) How to deterministically distinguish the following quantum states: $$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle$$, ...
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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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864 views

Entanglement spectrum

What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
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Again about all-win lottery

I suggest the following thought experiment that describes a machine which makes everybody happy. Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal ...
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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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Building some measurement appratus that distinguish between two mixtures

We have a measurement $M$ that distinguishs between $\rho_1$ and $\rho_0$, if it has three possible answers 1,2,3 and whenever it answers something different than 3 it's correct. $M$ succeeds with ...
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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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Looking for description of Helstrom's measurement

I hope someone can help me find the page or chapter where Helstrom discusses his famous measurement for distinguishing between two mixtures in the textbook Quantum Detection and Estimation Theory. ...
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Computer game with quantum optics/ information

Is there a computer game using principles of quantum optics or quantum information? By game I don't mean just a simulation or an interactive course, but something that can be played in an enjoyable ...
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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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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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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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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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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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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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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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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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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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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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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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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 ...
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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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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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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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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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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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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 ...