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.
30
votes
3answers
319 views
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 ...
23
votes
8answers
4k views
Why quantum entanglement is considered to be active link between particles?
From everything I've read about quantum mechanics and quantum entanglement phenomena it's unobvious for me, why quantum entanglement is considered to be active link. I.e. it's stated every time that ...
23
votes
2answers
3k views
What can the D-Wave quantum computer do?
The media are reporting the commercially sold 128-bit quantum computer from D-Wave
http://news.google.com/news?ned=us&hl=us&q=d-wave+quantum&cf=all&scoring=n
which of course ...
21
votes
4answers
262 views
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 ...
19
votes
1answer
280 views
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, ...
18
votes
3answers
1k views
Why are von Neumann Algebras important in quantum physics?
At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important ...
18
votes
1answer
288 views
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 ...
17
votes
2answers
91 views
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 ...
17
votes
10answers
1k views
What is spontaneous symmetry breaking in QUANTUM systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous ...
17
votes
7answers
625 views
Is there a symmetry associated to the conservation of information?
Conservation of information seems to be a deep physical principle.
For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.
We may wonder if there is an underlying ...
16
votes
1answer
136 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 $|\psi_k\rangle\in\mathcal H$, $k=1,\ldots,d^2$ ...
15
votes
3answers
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 ...
15
votes
2answers
120 views
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 ...
14
votes
6answers
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 ...
13
votes
5answers
494 views
Do quantum states contain exponentially more information than classical states?
Do quantum states contain exponentially more information than classical states? It might seem so at first sight, but what about in light of this talk?
13
votes
2answers
158 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 ...
13
votes
1answer
109 views
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, ...
13
votes
2answers
400 views
What does the sum of two qubits tell about their correlations?
How much can I learn about correlations between two quits by measuring
the sum of their values? What is the best way to formalize such a
question?
Below is my original, longer formulation of ...
12
votes
6answers
1k views
Is Shor's algorithm a demonstration of the many worlds interpretation?
David Deutsch is very fond of pointing out Shor's integer factorization algorithm is a demonstration of the many worlds interpretation. As he often asked, where else did all the exponentially many ...
12
votes
1answer
82 views
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 ...
12
votes
1answer
56 views
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
votes
2answers
68 views
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 ...
12
votes
3answers
936 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 ...
12
votes
0answers
213 views
Bell polytopes with nontrivial symmetries
Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
11
votes
5answers
701 views
Is there such a thing as “Action at a distance”?
What ever happened to "action at a distance" in entangled quantum states, i.e. the Einstein-Rosen-Podolsky (EPR) paradox? I thought they argued that in principle one could communicate faster than ...
11
votes
3answers
133 views
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 ...
11
votes
1answer
82 views
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}$, ...
10
votes
4answers
589 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}$ ...
10
votes
2answers
413 views
Interpretation of “superqubits”
Two very intriguing papers recently appeared on the arXiv, claiming that one can use "superqubits" -- a supersymmetric generalization of qubits -- to violate the Bell inequality by more than standard ...
10
votes
2answers
827 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 ...
10
votes
2answers
527 views
Unambiguous distinguishing of quantum states by local measurement
Let's have two orthogonal n-particle quantum states: $|\psi \rangle$ and $|\phi \rangle$. In theory it is always possible to make an unambiguous measurement.
However, things get complicated when one ...
9
votes
5answers
1k views
Do Category Theory and/or Quantum Logic add value in physics?
I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just ...
9
votes
7answers
1k views
How many bits are needed to simulate the universe?
This is not the same as: How many bytes can the observable universe store?
The Bekenstein bound tells us how many bits of data can be stored in a space. Using this value, we can determine the ...
9
votes
1answer
45 views
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 ...
9
votes
3answers
135 views
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} ...
9
votes
2answers
661 views
How much is quantum computation changing the interpretation of quantum theory, and, if at all, how?
At the beginning of quantum computation, David Deutsch made a strong claim that the Many Worlds interpretation of quantum theory was at the foundation of his ability to do what he did. There was a lot ...
9
votes
2answers
307 views
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 $\rho$ ...
9
votes
1answer
41 views
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
...
9
votes
3answers
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 ...
8
votes
3answers
37 views
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?
...
8
votes
3answers
752 views
Is “analog” quantum-computation not useful?
I understand what a qubit-based quantum computer by the current definition is and how they are constructed. I read another thread where someone suggested encoding a computation into a dual-slit ...
8
votes
3answers
535 views
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 ...
8
votes
1answer
255 views
Which qubit states are accessible with linear optics operations?
Given a quantum state of $n$ qubits, and being restricted to linear optics (that is, the output annihilation operators are linear combinations of the input annihilation operators):
Which states are ...
8
votes
2answers
152 views
Is there a simple way to express the 2ⁿ+1 mutually unbiased bases for n qubits?
The title says it. An explanation for only 2 qubits would already be interesting, since I already have difficulties to find the 5 MUBs in this simple case.
8
votes
3answers
254 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 ...
8
votes
1answer
329 views
Are there any applications of quantum information theory to physics?
Are there any applications of quantum information theory to physics?
8
votes
1answer
87 views
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 ...
8
votes
1answer
73 views
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 ...
7
votes
8answers
618 views
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 ...
7
votes
3answers
37 views
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 ...
