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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Is the reduction map completely positive? [duplicate]

I am struggling with proving the complete positivity of a general map ( granted it is CP ). The reduction map is defined as $$ \rho \rightarrow \mathrm{Tr}(\rho)I - \rho $$ It is a trivial job to ...
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134 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
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Different implementation of Feynman's clock

In equation 7 of the paper, Feynman's clock, a new variational principle, and parallel-in-time quantum dynamics, the clock register is different from Feynman's original proposal. According to this ...
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101 views

POVM positive density matrix decomposition

I have to prove that given a density matrix $\rho$ in a finite d-dimensional Hilbert space $\mathcal{H}_d$, it always exists at least one informationally complete POVM measure $\{E_i\}_{i=1}^{d^2}$ ...
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How do I write the Hamiltonian for a 3-level system?

I came across following types of three-level systems like V-system, Λ-system and 2-photon absorption It seems that their Hamiltonians can be written intuitively by checking out the coupled levels ...
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What is “k-Local Hamiltonian Problem” in quantum complexity theory?

An example of a QMA problem is the k-LOCAL HAMILTONIAN problem. What exactly is it?
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Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...
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Usage example of stabilizer codes QEC

This question directly follows the previous one about $X$ stabilizers and phase-flip errors: Practical example of stabilizer codes Let's now consider a second part of the quantum circuit that is ...
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Which model of computation can be viewed as being extended by the currently most relevant models of quantum computation?

Which model of quantum computation resembles most closely the attempts of implementation currently being made? And which non-quantum model of computation is the conceptually closest one to the above ...
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Adiabatic evolution for initial Hamiltonian on Hadamard basis and problem Hamiltonian as diagonal

This is spawned from a comment at the answer to one of my previous questions. Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out ...
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181 views

Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally recorded branches”?

I came across an unusual multi-partite generalization of the Schmidt decomposition in my work, which I describe below. Usually, when people say "a multi-partite Schmidt decomposition", they mean a ...
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336 views

What is the energy scale of a Hamiltonian?

On the second page of this paper a term 'fundamental energy scale' is used while talking about a Hamiltonian. The context is implementing Deutsch's algorithm using Adiabatic Quantum Computation. What ...
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Hamiltonian matrix propertu

A professor made an statement to prove the variational theorem: Because the Hamiltonian (H operator of quantum physics) is diagonal in its own eigenfunction, the terms in $\left \langle \Phi _{m} ...
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135 views

How large must the Quantum teleportation fidelity have to be in order for it to be useful?

This question relates and stems from my original question. Please read this one and the comments before answering this question. Quantum Teleportation Fidelity I know that for discrete variables ...
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Finding all marked element by Grover search(not in superposition)

Quantum search enables square-sped up search for marked element. When there are multiple maked element, grover search provides only superposition of them. If I want to find all the marked elements, ...
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90 views

Equivalence of simple formulations of qubit entanglement

I'm reading some very elementary treatments of quantum computation and am unsure about the correspondence among "definitions" of qubit entanglement. One definition states that (1) the bits of a ...
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255 views

Computing with qubits [closed]

We have a qubit in the state $|\psi \rangle= √3/2 |0\rangle + 1/2 |1\rangle$, which we want to measure in the $cos \theta\ |\theta\rangle + sin \theta |1\rangle, sin \theta |\theta\rangle - cos θ ...
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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 ...
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285 views

Could one 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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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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Number of States and Required Info for Bits vs Qubits

So with classical bits, if you have 2 bits, there are 4 possible outcomes that are possible. To determine these states, you only need 2 pieces of info, the state of each bit. With 3 bits, you can have ...
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Definition of Fermion [closed]

Recently, I encounter a problem about the definition of Fermion operator. In our standard textbooks, the Fermions are defined by their exchange/braiding property, that is, if a minus sign appears by ...
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53 views

What do operations on single Qubits of Unfactorable Superpositions Do?

So suppose I have the following Quantum Circuit: A ---- |Control| -----|Hadamard|---- B ---- |xxxxxxx|------------------------ Which is a 2 input Controlled Gate (applying some gate of two choices ...
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Quantum Teleportation between Entangled Qubits

My question refers to the experiment described in this article: http://www.sciencemag.org/content/345/6196/532.abstract Here's a popular science description: ...
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Entanglement of Tripartite States

Is there any simple algorithm to determine the entanglement of a tri-partite state? In particular, what is the proof for entanglement of $ |GHZ\rangle $ and $ |W\rangle $ states? $ |GHZ\rangle ...
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4answers
315 views

Can an arrangement of particles be duplicated precisly?

Is it possible to teleport or clone someone or something? After watching this TED talk by Max Tegmark - https://www.youtube.com/watch?v=GzCvlFRISIM I find myself wondering if it is then possible to ...
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120 views

How can all information be localized if local realism is dead?

I'm confused about whether quantum mechanics is local or not. The authors of a recent, much publicized experiment argue that their results "imply statistically significant rejection of the ...
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SPDC and single photon production

In Spatial Parametric Down Conversion, incoming photons are split into entangled photon pairs by passing through a non-linear optical medium. Since I get a photon pair as an output then how can I say ...
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Interpretation of position projection operator

Does the operator: $$\int_a^b \mathrm{d}x \, |x\rangle \langle x|$$ have physical meaning acting in a Hilbert space where it does not exactly correspond to the identity operator? Does it correspond ...
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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, ...
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64 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 ...
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The simulation hypothesis and the halting problem [closed]

I have a basic knowledge of classical and quantum information which isn't remotely enough to make me an expert on the subject. That being said, reading some questions about the simulation hypothesis ...
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3answers
100 views

The $n$-th root of the NOT gate

I simply can not find material containing facts about the $n$-th root of the NOT gate and it's realization in Q.M. and also in C.M.. Does anyone have material? A comparison of the $n$-th root NOT ...
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60 views

What is Absorption Grating

I came across the word "absorption grating" in a review article. I googled it tried to find out what it means but couldn't. Could you explain it to me?
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Increase path length for a photon with two mirrors vs optical fiber

Is it possible to build two mirrors in vacuum such that a light pulse (single photon) gets refleted many times in order to increase the distance it travels? For example like that? Say I want the ...
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29 views

quantum clone of orthogonal quantum states

I am a little bit confused about the no-cloning theorem for two orthogonal quantum states. In Nielson&Chuang page 24-25, it states that an unknown state $|\phi\rangle$ cannot be copied since ...
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Complexity of quantum simulation

Richard Feynman showed that Quantum simulation on a Turing machine will have an exponential slowdown. If that is so, does this put quantum simulation outside of P (complexity class)? I thought quantum ...
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how do you find a schmidt basis and how can the schmidt decomposition be used for operators?

There's a System in the state $|\Psi\rangle=\frac{1}{2}\left(|00\rangle+|01\rangle+|10\rangle+|11\rangle\right)$. I know that that's not an entangled state, since ...
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Would the quantum state of a photon be disturbed if it were traveling through fiber optic cabling?

See here... https://en.wikipedia.org/wiki/Linear_optical_quantum_computing https://en.wikipedia.org/wiki/Optical_fiber_cable I'm just worried that upon reflection within the cable the photon's ...
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84 views

Does quantum entangled particle release energy when its “twin” is measured? [closed]

So I was just thinking a bit, and I came up with a couple of questions. As we all know the scenario: We have two quantum entangled particles. Let's call them A and B. We like to measure the state of ...
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66 views

Why these quantum information processing protocols have a similar structure?

I noticed for some quantum information processing protocols such as teleportation, entanglement distillation, bound entanglement activation, entanglement catalysis, the protocols seem to have a ...
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100 views

What are typical error rates of quantum computers?

I read in an article that in order to perform error correction on a quantum computer there can only be one error per 10.000 calculations (=unitary transformations). This sounds pretty high but how ...
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166 views

What is the meaning of integrating over the state space?

If $\lvert\psi\rangle$ denotes the state space corresponding to a qubit, then what is the meaning of the $$\int d\psi$$ where the integral is over whole state space of a qubit? How do I evaluate it? ...
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Is a zero-energy universe necessarily also a zero-information universe?

The universe needs to be near zero energy to not crumple in on itself. Under the same logic, does it also need to have near zero information content to prevent the passage of time from burning it to ...
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61 views

Wigner-Yanase skew information [closed]

I am reading Eric Carlen's paper on Trace Inequalities and Quantum Entropy. I am currently reading about the Wigner-Yanase skew information which is defined as: $$I_{WY}(\rho)=-\frac{1}{2} ...
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Can a free falling observer localize the event horizon by calculations?

I'm think that in general relativity we can always pass the one curve in one coordinate system for another coordinate system. My intuition say that the free falling observer locate the event horizon ...
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What's the Cause of Quantum Entanglement? [duplicate]

What is the cause of quantum entanglement? When two particles become entangled what property of them basically changes as to establish a link between them and how the information is exchanged between ...
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1answer
82 views

About Shor's error correcting algorithm

In this paper, http://arxiv.org/abs/1301.4504 in equation 4.1 in what sense are the two states a "9-qubit state"? I did not understand this counting. Can someone explain what are the different $X_i$ ...
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181 views

Number of Parameters Required to Specify n-Qubit States and Quantum Operations

How many parameters are required to specify the density matrix of a $n$-qubit system, and how many parameters are required to specify a quantum operation (completely positive maps between states) on ...
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124 views

Landauer's principle vs Wien's displacement law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of kTln2? If it is so, can we also argue ...