0
votes
1answer
43 views

Low rank entangled states

In some recent works, I got the information that low rank mixed states need not be bound entangled. In particular, for the system $3\otimes 3$ there is no bound entangled states. Can anyone tell me ...
2
votes
0answers
38 views

What is known about the trace of two copies of a channel / four copies of an isometry

Let $\mathcal{E} : \mathcal{L}(A) \to \mathcal{L}(B)$ be a completely positive trace preserving map. By the Choi–Jamiołkowski isomorphism there is an isometry $J : A \to B \otimes C$ such that ...
11
votes
1answer
230 views

Can Werner states have bound entanglement?

Let us consider the maximally entangled state \begin{equation} |\psi\rangle=\frac{1}{\sqrt{n}}(|0,0\rangle+\cdots+|n-1,n-1\rangle) \end{equation} and construct the pseudo-pure state \begin{equation} ...
1
vote
0answers
65 views

Experimental realization of Quantum Teleportation of Spin, not polarization, not ions or atoms

I've looked everywhere in databases my school provides, to google searches, to the questions asked in physics forums, and here. As I understand, the original QT (quantum teleportation) protocol ...
4
votes
2answers
364 views

Quantum Mechanics in terms of *-algebras

I'm currently trying to find my way into the geometric description of Quantum Mechanics. I therefor started reading: Geometry of state spaces. In: Entanglement and Decoherence (A. Buchleitner et ...
4
votes
0answers
77 views

Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n ...
3
votes
1answer
131 views

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 ...
2
votes
0answers
81 views

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. ...
6
votes
1answer
91 views

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 ...
9
votes
1answer
60 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 ...
5
votes
7answers
651 views

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 ...
8
votes
1answer
85 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 ...
9
votes
3answers
235 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} ...
6
votes
1answer
435 views

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 ...