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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Entanglement measure to classify topological ordered states
I know long-range entanglement is the essence of nontrivial topological ordered states. (Trivial refers to short range entangled and nontrivial refers to long range.) So, entanglement measure at large ...
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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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Proof of Pauli group preservation by Clifford group conjugation?
A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words:
$C(P_{1} \otimes P_{2})C^{\dagger} = P_{3} \otimes P_{4}$, with $C \in$ Clifford group and ...
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Matrix separability preservation under conjugation?
Someone know any paper about matrix separability preservation under conjugation? A well know result is that Clifford group preserve the Pauli group under conjugation or, in other words:
$C(P_{1} ...
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What is the difference between Quantum teleportation and Radio waves?
Quantum teleportation over 143 kilometres using active feed- forward
What is the difference between Quantum teleportation and radio waves?
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Anybody have example of two-qubit non-Pauli and non-Clifford quantum gate?
A lot of known quantum gates are in the Pauli group (I,X,Z,Y) or in the Clifford group (H,P,Cnot). I need examples of the quantum gates that aren't in this groups. Also, are there are matlab functions ...
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Information relationship to Special Relativity
How do we write mathematically that "information" cannot go faster than light? And along a similar line of thought, how do we relate "information" with special relativity. Lastly, what is the ...
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67 views
Does quantum fingerprinting really argue for the exponential size of wavefunctions?
Does quantum fingerprinting really argue for the exponential size of wavefunctions? Quantum fingerprinting is the idea that an exponentially long classical string can be encoded in a linear number of ...
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107 views
Fast algorithm for maximizing the quantum fidelity
Consider the following optimization problem: Given a quantum state $\sigma$, a constant $b$ and a Hermitian operator $A$, find
$\underset{\rho} \max F(\rho,\sigma)$
subject to $\text{Tr}(\rho ...
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Defining entanglement in subspaces of tensor product
I have asked the question in math.stackexchange, but perhaps it should be more relevant here. Hence I am re-posting it with necessary reediting.
Let $\mathcal{H}=\mathbb{C}^n$ be a Hilbert space. A ...
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200 views
Could someone transmit a signal with equally-tuned Casimir plates across the quantum field?
It seems, one could exploit the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates.
Obviously, relativity would preclude FTL information transfer, ...
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108 views
Can double entanglement preserve correlations?
We have 2 EPR experiments running in parallel, with Alice having one leg of each (a1,a2) and Bob the other leg of each (b1,b2). Thus (a1,b1) are anticorrelated, as are (a2,b2). Thus also (a1,a2) are ...
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Physical meaning of the sign basis in quantum mechanics
If we take a hydrogen atom as qubit, let
$\lvert0\rangle$ = unexcited state
$\lvert1\rangle$ = excited state
then what is the meaning of measuring the qubit value in the sign basis? If the atom may ...
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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 ...
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number of microstates associated with two-level quantum systems
this is a very simple question, but apparently one that has no simple answer, at least from standard quantum mechanics theory
I'm trying to figure the number of simple quantum states (microstates) of ...
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4answers
516 views
Can superdeterminism resolve contextuality, entanglement and Shor's algorithm in quantum mechanics?
Superdeterminism is the idea that the apparent freedom for the choice of experimental apparatuses and their settings are nothing but an illusion. Contextuality is the dependence of the properties of a ...
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179 views
Why do they call it quantum teleportation?
So I have been trying to learn about entanglement and quantum teleportation and from what I've been able to gather so far, the teleportation part seems to be misleading.
At first I thought that the ...
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Entanglement: Is it possible to prepare and reset probabilities to send information?
I'm pretty certain that the answer to the question in the title is a no, but I don't understand why. I have some basic misunderstanding of quantum processes that I’d like clarified in the form of ...
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Entanglement of qubits circuit- Bell states
I know that the quantum circuit $\text{CNOT}\; (H \otimes I)$, where $\text{CNOT}$ is the controlled-not gate and $H$ the Hadamard gate, takes the computational basis of two qubits ...
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State of the entangled particles at the event horizon of black hole
Looking through the article of Samir Mathur http://arxiv.org/abs/0909.1038
he assumes that the entangled particles created at the event horizon have all the state ...
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are pinch-off bubbles valid solutions to general relativity?
are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and ...
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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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3answers
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At what time exactly does decoherence happen? and retrodating
Take a qubit initialized to $|0\rangle$. Apply a Hadamard transform to it. Measure it with an apparatus along the $|0\rangle,\, |1\rangle$ basis. If zero, spare a living cat. If 1, kill the cat. ...
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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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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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Extending mixed states to pure state
Let us consider any pure state $|\psi\rangle\in\mathbb{C^n\otimes C^n\otimes C^n}$. Its reduced bipartite density matrix represent a pure state or mixed state depending on whether $|\psi\rangle$ is ...
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172 views
Schmidt decomposition of coupled oscillators
Consider a system of two coupled oscillators, with Hamiltonian ($\hbar = m = 1$):
\begin{align}
\mathcal{H} = \frac{1}{2}(p_1^2 + \omega_0^2 x_1^2) + \frac{1}{2}(p_2^2 + \omega_0^2 x_2^2) ...
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Separable states of maximum non-classical correlations
Although there is no standard measure of entanglement, the GHZ states
$|GHZ\rangle=\frac{1}{\sqrt{2}}(|0\rangle^{\otimes n}+|1\rangle^{\otimes n})$
are often deemed as maximally entangled states of ...
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2answers
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Bell states entanglement
I'm trying to learn about the Bell state $\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle$. Question 10.1 in Algorithms asks us to show that this cannot be decomposed into the tensor product ...
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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 ...
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155 views
What is the code distance in quantum information theory?
What is the code distance in quantum information theory?
Code distance seems to be a very important concept in fault tolerant
quantum computation and topological quantum computation.
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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 ...
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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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176 views
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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139 views
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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Quantum Compting or DNA computing [closed]
My friend and me are working on DNA computing and on some improvements to it.
Of course, we are working on computing aspects of this branch. So, we have insufficient knowledge about physics and ...
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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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2answers
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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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402 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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1answer
52 views
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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1answer
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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 / quantum information
Is there a computer game using principles of quantum optics or quantum information?
By game I mean not just a simulation or an interactive course, but something than 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 ...
