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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Entropy of a state subject to the action of a set of random unitaries

Suppose that we have a known set of unitaries $U_1,...,U_n$ randomly selected from the Haar measure and suppose that each unitary is applied with probability $\frac{1}{n}$ to some input state $\rho$ ...
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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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Are there any applications of quantum information theory to physics?

Are there any applications of quantum information theory to physics?
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Does quantum collapse involve a loss of information? Does it require energy as suggested by the Landauer Limit?

I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called ...
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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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Can quantum annealing be used for factorization?

It is known that there is a famous quantum factorization algorithm by Peter Shor. The algorithm is thought to be suitable only for quantum gate computer. But can a an adiabatic quantum computer ...
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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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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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Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in ...
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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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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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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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Informational capacity of qubits and photons

How much information is contained in one qubit? A qubit is defined in Wikipedia as $a\left|0\right> +b\left|1\right>$, where a and b are complex numbers subject to $a^2 + b^2 = 1$. One complex ...
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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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Positivity in the Pauli/Bloch/coherence vector representation

Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is $$ x_k = {\rm Tr}(\rho \sigma_k), $$ ...
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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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Is a weak measurement the same as an unsharp measurement or POVM?

This is prompted by the strong claims made in Science 332, 1170 (2011) to have observed trajectories of photons, "something all of our textbooks and professors had always told us was impossible". I'm ...
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Hamilton operator in absence of causal order?

I hope, this question isn't too broad or vague. In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
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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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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 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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Are coherent states of light 'classical' or 'quantum'?

Coherent states of light, defined as $$|\alpha\rangle=e^{-\frac{|\alpha|^2}{2}}\sum_{n=0}^\infty \frac{\alpha^n}{n!}|n\rangle$$ for a given complex number $\alpha$ and where $|n\rangle$ is a Fock ...
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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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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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No-cloning theorem with 3 particles

I know how to demonstrate that it is not possible to make a unitary operator so that $|a\rangle|0\rangle$ turns into $|a\rangle|a\rangle$ , but is it possible to have $|a\rangle|0\rangle|0\rangle ...
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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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Is there any problem a quantum finite state machine can do faster than a classical finite state machine?

All of the quantum algorithms I've seen so far require a turing-complete quantum computer, at least as far as I can tell. Are there any quantum algorithms that require only a quantum finite automaton? ...
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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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Why are there only perfectly anti-correlated quantum states, not perfectly correlated?

The singlet state of two qubits is anticorrelated in every basis. For example, in the Pauli bases, it can be expressed, $\frac{1}{\sqrt{2}} ( | 01 \rangle - | 10 \rangle) = \frac{1}{\sqrt{2}} ( | +- ...
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Recent breakthroughs in quantum computing?

Can anyone explain to me why we have had no major breakthroughs in the theory of quantum computation in the past 15 years? Shor's algorithm set the standard, since then we've had Grover's algorithm ...
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Probabilistic quantum cloning

I have a question with regard to probabilistic quantum cloning - see for example http://prl.aps.org/abstract/PRL/v80/i22/p4999_1. It does seems like I can use the proof for no-cloning theorem to ...
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Areas of computer science required for quantum computing

What knowledge of computer science should I have, to be able to pursue research in quantum computing. I am a Physics undergrad and would take three core courses in QM, before the completion of my ...
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How many stabilised qubits have been achieved in Quantum Computing?

The latest I read is 3 but that was in Oct. With Lene Hau of Harvard's "frozen light" and with quantum donuts, newer strategies for stabilization are appearing, but the problem of keeping the qubit in ...
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Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
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Is there a formalism for talking about diagonality/commutativity of operators with respect to an overcomplete basis?

Consider a density matrix of a free particle in non-relativistic quantum mechanics. Nice, quasi-classical particles will be well-approximated by a wavepacket or a mixture of wavepackets. The ...
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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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Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
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What is a completely positive map *physically*?

I am sure this question is really stupid, but I could not refrain from asking it in this forum. This can be considered as a continuation of this question. ...
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How many states can a n qubit quantum computer store?

A classical computer composed of '0' or '1' transistors stores $2^n$ states. Is it true that a quantum computer composed of '0' or '1' or '0 & 1' qubits stores $3^n$ states?
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Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
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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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Quantum Computing and Animal Navigation

Someone sent me this link to a talk by Prof. Klaus Schulten from the University of Illinois: (my emphasis) Quantum Computing and Animal Navigation Quantum computing is all the rage nowadays. ...
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Why is $\theta \over 2$ used for a Bloch sphere instead of $\theta$?

I'm a beginner in studying quantum info, and I'm a little confused about the representation of a qubit with a Bloch Sphere. Wikipedia says that we can use $$\lvert\Psi\rangle=\cos\frac{\theta}{2} ...
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What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold?

The assumptions are: Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons The idea is simply to have Alice and Bob perform the ...
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Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
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Is microcausality *necessary* for no-signaling?

There are proofs in the literature that QFT including microcausality is sufficient for it not to be possible to send signals by making quantum mechanical measurements associated with regions of ...
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Is the subadditivity of quantum entropy valid in the infinite-dimensional case?

Does the subadditivity (and strong subadditivity) of quantum entropy hold for infinite dimensional quantum systems as well? Unfortunately the books in my hand give proof for finite dimensional cases ...
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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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Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...