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)

3
votes
3answers
169 views

The role of context in information theory

Consider Hofstaedter’s jukebox analogy: A jukebox that contains only one record, but many different record players, each of which interprets that one record in a different way to produce an entirely ...
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 ...
3
votes
2answers
1k views

How to apply a Hadamard gate?

How to apply a Hadamard gate to 3 qubits? by example how to apply $H$ to $(1/\sqrt{2})(\left|000\right> + \left|111\right>)$?
3
votes
2answers
350 views

Quantum Teleportation Fidelity

I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% ...
3
votes
2answers
759 views

The complementary variable to the qubit and spin-1/2

The qubit is a big topic of quantum information theory. A qubit is a single quantum bit. Physical examples of qubits include the spin-1/2 of an electron, for example, see page 39 of Preskill: ...
3
votes
3answers
116 views

Advantage of taking qutrits in place of qubits

In general, all the quantum algorithms which I have read so far use qubits (so the space is $\mathbb{C}^2$) and the tensor products of the qubit spaces (space is ${\mathbb{C}^2}^{\otimes n}$). So my ...
3
votes
4answers
451 views

Why is quantum entanglement so important?

Entanglement also allows multiple states to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum ...
3
votes
1answer
126 views

Quantum cryptography: encryptions

I am studying quantum cryptography and I have a very basic question. Suppose A and B share a secret key k, where k=0 or 1. A wants to send one qubit to B. What A does is, if k=1, she 'flips' the qubit ...
3
votes
2answers
176 views

Understanding a Physics Paper on Quantum Teleportation of Continuous variables

The paper I am trying to understand is here: http://pra.aps.org/abstract/PRA/v49/i2/p1473_1 The paper describes the quantum teleportation protocol in a general case with continuous dynamical ...
3
votes
2answers
345 views

Mathematically challenging areas in Quantum information theory and quantum cryptography

I am a physics undergrad and thinking of exploring quantum information theory. I had a look at some books in my college library. What area in QIT, is the most mathematically challenging and rigorous? ...
3
votes
2answers
1k views

What is postselection?

I was reading some questions here. I couldn't understand what it means by postselection. What is postselection? What is its use/significance? Where did it came from?
3
votes
3answers
360 views

What is the next step beyond quantum computation?

Assuming we develop quantum computers one day, what would be theoretically the next step? Would it be string-theory based computers? How would these computers differ performance-wise (ie what can they ...
3
votes
1answer
86 views

A tensor product of two spin-1 particles

I'm rather confused, and I was hoping if someone could help me figure out this (probably rather elementary) issue. I have two particles with spin 1, whose state I describe by $m_S$ and $m_I$ ...
3
votes
3answers
240 views

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 ...
3
votes
1answer
152 views

Intuition behind Hamiltonian

I am reading this paper by Das et al. which converts Deutsch's algorithm into an adiabatic quantum algorithm. I don't get the intuition behind the initial and final Hamiltonians. If defines the ...
3
votes
1answer
144 views

Canonical form of GHZ and W state

What is the Schmidt decomposition of the tripartite states$|GHZ\rangle=\frac{1}{\sqrt 2}[|000\rangle+|111\rangle]$ or $|W\rangle=\frac{1}{\sqrt 3}[|001\rangle+|010\rangle+|100\rangle]$? Are these same ...
3
votes
1answer
126 views

On Bell inequality and bound entangled states

I have recently seen some presentation slides of Michał Horodecki (slide number 77) in which he discussed the following conjecture. Bound entangled states satisfy all Bell inequalities The ...
3
votes
2answers
174 views

Composition of squeeze operators?

I'm wondering if it exists a composition law for the squeezing operation ? I guess so for geometric reason, since they are (generalized, and the phase is annoying of course) hyperbolic rotations of ...
3
votes
2answers
589 views

How do I calculate the position on the Bloch sphere of a quantum gate with a given diagonal matrix?

In quantum computation there are several principal quantum gates that have corresponding matrix representations. One of these is the Z gate, whose matrix is $\left[\begin{smallmatrix} 1 & 0 \\ 0 ...
3
votes
1answer
399 views

Can PEPS explain the holographic principle in quantum gravity?

Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the ...
3
votes
1answer
81 views

Couder-Fort Oil Bath Experiments and Quantum Entanglement Phenomena

The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit ...
3
votes
1answer
113 views

mixture of maximally mixed and maximally entangled state

Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the ...
3
votes
1answer
66 views

Reversible gates

Is it possible to make any gate reversible merely by retaining the input bits in the output and introducing ancilla bits as necessary? That is, given an irreversible gate with $k$ inputs and $l$ ...
3
votes
1answer
255 views

System with no entanglement but consuming quantum discord

I have come across an article which talks about quantum discord (Observing the operational significance of discord consumption. M. Gu et al. Nature Physics 8, 671–675 (2012) doi:10.1038/nphys2376), ...
3
votes
2answers
244 views

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 ...
3
votes
1answer
294 views

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 ...
3
votes
3answers
261 views

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 ...
3
votes
1answer
52 views

Mutually unbiased bases

This question can be formulated in two ways. Let there be two $d$-dimensional orthonormal bases $B_{1}$ and $B_{2}$. I refer to the elements of $B_{1}$ by $\lvert\nu_{i}\rangle$ and to the elements of ...
3
votes
1answer
88 views

Rotation about the $z$-axis on the Bloch sphere

I'm having some trouble with successfully working out a rotation about the $z$-axis on the Bloch sphere. Now, I know how this is performed, in principle. A rotation of the Bloch-sphere around an ...
3
votes
2answers
90 views

Smallest number of quantum gates to simulate other gates?

What is the smallest number of Fredkin gates needed to simulate a Toffoli gate? What is the smallest number of Toffoli gates needed to simulate a Fredkin gate? Where the Toffoli's gate is the CCNOT ...
3
votes
1answer
218 views

Bloch sphere representation

Suppose you know that a qubit is either is in state $|+\rangle$ with probability $p$ or in state $|-\rangle$ with probability $1-p$. If this is the best you know about the qubit's state, where in the ...
3
votes
1answer
266 views

Why are the equal probabilities for Bell state measurement outcomes essential for “quantum teleportation”?

I've recently been introduced to the basics of finite-dimensional quantum mechanics from a purely mathematical point of view (with a quantum-information theme to it). When discussing quantum ...
3
votes
1answer
80 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 ...
3
votes
1answer
191 views

Can spatial coherence be maintained in fiber optic cables over time?

I am doing research with a double slit experiment, using a beam splitter and 2 lengths of fiber optic cable, whose ends brought close together form the effective double slit. I notice that the ...
3
votes
0answers
48 views

What is the probability of quantum tunneling occurring in this CPU?

You may have noticed over the last few years that Moore's law is no longer applying to the real world. This observation states that over the history of computing hardware, the number of transistors on ...
3
votes
0answers
54 views

ER = EPR and Time Travel

In Maldacena-Susskind paper arXiv:1306.0533, they propose an idea of $$\text{ER = EPR}$$ the relation between the wormhole and the quantum entanglement. which ER means Einstein Rosen (ER) bridges, ...
3
votes
0answers
66 views

Finding the ground state of the toric code Hamiltonian

How do I write by proof, the ground state of the toric code (by Kitaev) Hamiltonian $ H=-\sum_{v}A(v)-\sum_{p}B(p) $ where $A(v)=\sigma_{v,1}^{x}\sigma_{v,2}^{x}\sigma_{v,3}^{x}\sigma_{v,4}^{x}$ and ...
3
votes
0answers
100 views

Does natural unit of information and entropy, nat, play special role in the freebit picture?

Please refer this question to understand why I consider the freebit picture important. In short, it is conjectured, that for certain real systems the most complete physical description possible ...
3
votes
0answers
53 views

Thermalising a sub-system of a larger, interacting system

I'm considering a joint system consisting of a spin-1/2 particle (qubit) and a spin-l particle (reference) coupled via a Hamiltonian $H_0$. At a certain point I want to couple the qubit to a bosonic ...
3
votes
0answers
62 views

on quantum steering

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, ...
3
votes
0answers
119 views

Optimality of product input state in quantum channel

Let $\mathcal N^{A_1\rightarrow B_1}_1,..,\mathcal N^{A_1\rightarrow B_1}_k$ be a set of valid quantum evolutions with equal input and output dimensions. And let the effect of a channel on a system ...
3
votes
2answers
155 views

Can the entangelement of basis vectors increase under local operations?

Say I have a bipartite state $\rho = \sum_ip_i|\psi_{i}\rangle \langle \psi_{i}|_{AB}$ Where $\{|\psi_{i}\rangle_{AB}\}$ forms an orthonormal basis. I now perform some local quantum operation on ...
3
votes
0answers
254 views

projective measurement & POVM

Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank ...
3
votes
0answers
121 views

POVM advantage in state discrimination

Suppose we are given the task of discriminating, with minimum error, between a set of states $\{|\psi_1\rangle,|\psi_2\rangle,\ldots,|\psi_N\rangle\}$. In other words, we are given an unknown state ...
3
votes
0answers
87 views

Concurrence in higher dimensions?

Does anybody know of any calculation of the concurrence for some mixed state other than the qubit-qubit case (which was solved by Wootters)?
3
votes
0answers
85 views

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 ...
3
votes
2answers
467 views

Size of a quantum computer to effectively calculate macroscopic reality from quantum mechanics

Assuming the correctness of QM: Would the size of such a computer be smaller than the observable universe? If it were to represent all available information in the universe it seems that it's minimal ...
3
votes
1answer
108 views

Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...
2
votes
2answers
230 views

Using delayed choice interference experiments as a computing device

I had an idea how to design a "quantum computer": How about designing interference-experiments where the design of the experiments itself represents algorithmical or mathematical problems that are ...
2
votes
2answers
181 views

How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?

I was going through arXiv:quant-ph/0001106v1, the first paper by Farhi on adiabatic quantum computation. Equation 2.24 says, $$\tilde{H}(s) = (1-s)H_B + sH_P$$ which means the adiabatic evolution ...