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.

learn more… | top users | synonyms (1)

2
votes
1answer
304 views

Quantum algorithm for checking if element exists

I am currently having hard times while facing an interesting idea, which could speed up many present quantum algorithms, but I am not sure whether my thought is not misleading, or more precisely, ...
2
votes
1answer
99 views

What's wrong with my Quantum Early Warning System (Thought Experiment) [closed]

I'm a lay physics enthusiast and I came up with a thought experiment that I can't fully wrap my head around: Alice and Bob are worried about an impending attack by the dreaded Xenomorphs, so they ...
1
vote
1answer
115 views

Deriving a POVM from a projective measurement

I understand how to show that every POVM is equivalent to a projective measurement on a larger Hilbert space, but I don't understand why the converse is true. The vast majority of explanations of ...
1
vote
1answer
110 views

How to understand the measurement on entangled state in the following cases? [closed]

Assuming an EPR pair AB, event MA is a measurement on A. My questions are: (1) At MB and MB' (depending on where B is located), if we try to describe the state of B (but not measure B yet), what'...
3
votes
2answers
59 views

What is $\gamma$ in the qutrit?

We know that the qubit is defined as follows $$\lvert\psi\rangle = \alpha\lvert 0\rangle + \beta\lvert 1\rangle$$ where $\alpha, \beta \in \mathbb{C}$. We can also rewrite the state of the qubit using ...
0
votes
1answer
91 views

Which information is “destroyed” when a qubit is read?

A quantum bit is a unit vector in $C^2$. That is, a four dimensional unit vector. A computational basis is a pair of orthogonal vectors in $C^2$ that you choose - say, [0, 1] and [1, 0]. So the ...
1
vote
1answer
190 views

Fermi's Golden Rule

Consider a system with countable quantum states. One can define $J_{ij}$ as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\sum_{i} p_{i}...
2
votes
0answers
57 views

Is density matrix really a description of 'state'? [closed]

Generally a density matrix is in fact a description of a set of equivalent (experimentally indistinguishable in linear QM) states. So there is no 1-to-1 correspondence between density matrix and '...
0
votes
2answers
77 views

Is in all 'superluminal signaling' setups, entanglement involved? [closed]

Nonlinear extension of QM may lead to the 'superluminal signaling' so that it seems to violate the finite speed limit. I am wondering if it's true that in all such kind of 'superluminal' setups, ...
1
vote
0answers
41 views

How to understand the instant state collapse in all references?

When a subsystem A of an EPR pair AB is measured, it's usually said that the state of B collapse instantly, and also this is true for all observers according to relativistic quantum information. ...
9
votes
1answer
124 views

are locally unique pure quantum states also ground states of some local hamiltonian?

Let $H=\sum_i H_i$ be some k-local hamiltonian with a unique ground state $|\psi>$. Then it is easily shown that $|\psi>$ is k-locally distinguishable from any other state $|\psi'>$. Is the ...
3
votes
1answer
84 views

Superposition State in Coin Toss

I was reading the following lines from Quantum Computation and Quantum Information by Nielsen and Chuang on page 278 of chapter 7. A coin has two states and makes a good bit but a poor qubit ...
1
vote
1answer
45 views

How to define a 'clone' of a mixed state?

State clone of a pure state is clear. But how to define a clone of a mixed state? For example, for a proper mixed state A, $\tfrac12(|0\rangle\langle 0|+|1\rangle\langle 1|)$, if there is a clone of ...
1
vote
1answer
91 views

About quantum measurement problem, proper or improper mixture?

Generally a quantum measurement is regarded as resulting in a definite outcome due to "state collapse" and the post-measurement state is described as a proper mixture with the ignorance of the ...
0
votes
1answer
98 views

The minimal knowledge required for theoretical research in Quantum computing & AMO physics [duplicate]

I'm a senior undergraduate student and I have chosen my future Ph.D research area in {Quantum Computing}$\bigcap${AMO physics} (e.g. design a new experimental realization of QC or propose a new way to ...
3
votes
3answers
116 views

How much can we compute with one single qubit?

This might be a little stupid question, but I was just talking with some friends who are working in neuroscience and I tried to explain them quantum computing. When I explained them the bloch sphere ...
3
votes
1answer
59 views

Quantum entanglement and superdense encoding etc

Is the following a somewhat correct analogy for what these phenomenae are? Imagine a box of thousands of apples where exactly half of each apple is red and the other half is green. Each apple is ...
3
votes
1answer
99 views

Infinite bits to describe a qubit

In the Quantum Computation book by Nielsen and Chuang, the authors write in the context of quantum teleportation "Even if she (Alice) did know the state |w> , describing it precisely takes an ...
10
votes
0answers
179 views

In a universe with four spatial dimensions would there be elementary particles with intrinsic isoclinic spin?

Elementary particles have an intrinsic property called spin which is different from classical spin as it does not involve actual rotation and the magnitude of spin cannot be changed but particles with ...
3
votes
0answers
90 views

Improper integral of the product of exponential function and Laguerre polynomial

I saw this integral in the book [Gerry C.C.,Knight P.L.] Introductory quantum optics: $$\frac{1}{\pi^2}\int_{-\infty}^{\infty}L_n(\lvert\lambda\rvert^2)e^{\lambda^*\alpha-\lambda\alpha^*-\frac{1}{2}\...
4
votes
0answers
58 views

How long does it take to a local perturbation to propagate along a quantum system?

Imagine to have a one-dimensional system in its ground state, and to apply a local perturbation at one edge of the system. How does the system evolve after being perturbed? More specifically, how ...
3
votes
1answer
55 views

The entanglement of a two dimensional particle and the one of two one dimensional particles

Case 1: Usually, entanglement is a correlation between more than one particles. For example, the momentum $p_1$ of the particle $1$ and the one $p_2$ of the particle $2$ have the relation that $p_1 +...
3
votes
3answers
258 views

Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
2
votes
1answer
79 views

How do we take the limit of this quantum operation?

I am wondering how to take the following limit: \begin{align} L= \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} dy \, \left(1 - \frac{1}{\sqrt{ \pi} \sigma } \int_{-\tau/2}^{\tau/2}...
0
votes
1answer
82 views

How Quantum Fourier Transform equal to Hadamard Transform on 4-by-4 matrix?

I just don't understand why $QFT_4$ become the same as Hadamard Transform $H_4$ The Hadamard matrix is as follwoing, $$ H_2 = \frac12 \begin{pmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & ...
1
vote
2answers
90 views

Bloch sphere for more than 1 qubit [closed]

Of course in general the Bloch sphere is a representation for one qubit, but what if it's a higher-dimensional system which has only two eigenvectors with non-zero eigenvalues? You should be able to ...
8
votes
1answer
393 views

The minimum time for a quantum state to evolve to an orthogonal state

I'm reading this paper by Margolus and Levitin The maximum speed of dynamical evolution: http://arxiv.org/abs/quant-ph/9710043 about the so called Margolus-Levitin theorem. For the main result, ...
3
votes
0answers
119 views

What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
2
votes
0answers
107 views

How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
1
vote
1answer
161 views

Which is a good and short book for foundations of quantum mechanics? [duplicate]

I am looking for a book that has stuff on quantum states, entanglement, etc. I am aware of the book, Geometry of Quantum States. I have read Ballentine's book, Quantum Mechanics: A modern development
-1
votes
1answer
66 views

Is there a theory of reference and formal truth in quantum information theory? [closed]

Is there a theory of reference and formal truth in quantum information theory? I.e. a "quantization" of Frege Tarski or the Typographical Number Theory (TNT) system in "Gödel Escher Bach". Status ...
1
vote
1answer
82 views

Proof of inversion about the mean (Grover's) [closed]

I just have an probably trivial question, but i got stuck when deriving the inversion of the mean as used in Grover's search: I simply want to show that the application of $(2 \left| \psi \right>\...
1
vote
2answers
105 views

Theoretically, how does quantum decoherence induce noise?

The decoherence process has allowed us to explain various (classical and decoherence) sources of measurement noise in quantum systems. I intuitively understand this physical concept of decoherence-...
2
votes
2answers
340 views

What is meant by fermionic and bosonic “modes”?

The paper The Dirac quantum automaton: a short review (pdf) starts off by stating: The starting point for the construction of space–time and the physical laws therein is an unstructured, countably ...
0
votes
1answer
49 views

Bosonic qubits using BEC versus usual qubit implementations based on energy levels

All condensate atoms in a BEC (say like Rb, etc) effectively occupy the lowest energy-state. If it is that the case, then how are such bosons in a BEC encoded as a qubit? In particular, when Grover ...
0
votes
1answer
74 views

Why are simulated qubits less effective?

"We could map the whole Universe — all of the information that has existed since the Big Bang — onto 300 qubits" I've seen statements like this over the years coupled with the same explanation ...
1
vote
1answer
53 views

Reduced density operator of a maximally entangled state

Is the reduced density operator of a maximally entangled pure state always maximally mixed (trace being half)? I test it on 4 bell state and this claim is true. I wonder why and can the degree of ...
-1
votes
1answer
85 views

Trace representation of density matrix question [closed]

System $A$ and system $B$ form a composite system. https://en.wikipedia.org/wiki/Partial_trace I wonder why $\rho_{AB}$ cannot be represented as $(\text{tr}_{B}(\rho))\otimes (\text{tr}_{A}(\rho))$....
2
votes
2answers
190 views

The definition of Gaussian State

Could you clarify to me what is a Gaussian state? I know what is a Gaussian function and Gaussian distribution, but I don't know how to respond to other when they ask me to provide the definition of a ...
0
votes
1answer
66 views

State evolution for Dot product of quantum states (Llyod et al. 2013) [closed]

I was reading the paper by Lloyd et al. which is concerned with quantum machine learning algorithms. In the algorithm they use the evolution of the following kind (i use a reduced formula, which is ...
1
vote
1answer
251 views

Issues with the proof of the no-cloning theorem

The no-cloning theorem states according to Wikipedia that it is impossible to create an identical copy of an arbitrary unknown quantum state. As far as I am aware the theorem is usually proofen ...
0
votes
1answer
79 views

Quantum Mechanics and Causality

Causality coupled with special relativity states that no particle can travel faster than light. Interpreting in terms of quantum mechanics, it means that dirac delta wave-function at x=a, can't ...
0
votes
1answer
61 views

Generalized Born Rule for partial measurements

I'm looking for the mathematical formulation of this trait (from an introductory Quantum Computing course): How can I generalize this into higher dimensions? Or other observables? It does not seem ...
0
votes
2answers
53 views

Quantum Crypto infrastructure & hardware

To implement real quantum cryptography in the real world, does the physical link layer from Point A to Point B be an optical link for all parts? Is there any links or whitepaper containing prototypes ...
0
votes
0answers
16 views

Which are some good books to learn about quantum states? [duplicate]

I am aware of the book Geometry of Quantum states: An introduction to Quantum Entanglement by Bengtsson & Zyczkowski. I have read the book Quantum Mechanics: A Modern Development by Ballentine.
-1
votes
1answer
66 views

Checking correctness of partial trace

I am doing some simulations that requires me to take partial trace over a three qubit density matrix $\rho_{ABC}$. I find the mixed state density matrix of one qubit by tracing out the other two, $\...
-3
votes
1answer
110 views

If this were possible, would it count as a modification of quantum mechanics? [closed]

This question will be re elaborated to meet the standards of this site in shot
6
votes
1answer
128 views

Does Bekenstein bound imply that the number of possible states of a bounded system is finite?

Bekenstein bound limits the amount of information that can be stored in a system of bounded size and mass. Does that imply that the number of possible states is finite? Does that imply that the number ...
2
votes
1answer
59 views

Local operation on bipartite quantum system [closed]

Suppose we have a state: $$ |\Psi_{1234}\rangle = \frac{1}{2}\left(|\Psi_{14}^+\rangle \otimes |\Psi_{23}^+ \rangle + |\Psi_{14}^-\rangle \otimes |\Psi_{23}^- \rangle - |\Phi_{14}^+\rangle \otimes |\...