Theoretical issues related to the quantum treatment of information

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Shor's quantum error correction code with unknown basis

$\newcommand{\ket}[1]{\lvert #1 \rangle}$I've met a problem in quantum secret sharing which involves the use of a quantum error-correction code. (let's make it simple to be the 9-qubit Shor code) In ...
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Travelling sales man with Quantum Computers [closed]

I know that it takes billions of years to solve the travelling sales man when n = 25 (Number of cities). I am wondering how fast can a quantum computer solve the travelling sales man problem (for ...
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339 views

The utility of Renyi entropies?

Most of us are familiar with — or at least have heard of — the Shannon entropy of a random variable, $H(X) = -\mathbb{E} \bigl[ \log p(X)\bigr]$, and all the related information-theoretic ...
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Proofs to verify quantum states without revealing their description

Consider the following function $$f_s: k \rightarrow \lvert \psi_k \rangle$$ where $s,k$ are bit strings, and $\lvert \psi_k \rangle$ is a $n$-qubit state. Assume the function is a one-to-one ...
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Hardness of finding similar (quantum) states

Consider a quantum state $\lvert \psi \rangle$, we know from the no cloning theorem, that it cannot be perfectly cloned. Also, loosely speaking, that it can be imperfectly cloned s.t. one can produce ...
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How well can an arbitrary (unknown) quantum state be imperfectly cloned?

How well can an arbitrary unknown (quantum) state $\rvert \psi \rangle = \alpha\rvert 0 \rangle + \beta \rvert 1 \rangle$, be imperfectly/approximately cloned? Given an unknown state ${\rvert \psi ...
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Why do we need a sphere to graphically represent a qubit? [closed]

Bloch sphere is a common visualisation of possible qubit values, but I fail to understand why do we need a sphere to represent them. Assuming we want to represent the single qubit a|0> + b|1> ...
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The Arrow of Time in a Non-Physical Realm [closed]

Could there be a logically consistent theory supporting the transmission of non-physical information to a point in time previous to the time it was sent using a computer network (quantum theory, etc)? ...
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Why are sub-normalized states studied in quantum computation?

By basic postulates of QM, any state of a system is described by a normalised density operator. Now i fail to see why people study sub-normalized states ( e.g.: In generalised fidelity etc). I'd be ...
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What is the Quantum Cheshire Cat experiments' import to Quantum Computing?

What is the significance of the Quantum Cheshire Cat to Quantum Computing? To recap, the Quantum Cheshire Cat experiment proved it was possible to separate a neutrons' spin from the neutron. Or, in ...
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Factoring as a decision problem

I've seen in multiple places stating that factoring is in BQP and referencing Shor's algorithm, but Shor's algorithm is not solving a decision problem. How can factoring be restated in a decision ...
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Prerequisites for theoretical computer science [closed]

I am a freshman and a Computer Science major,I have a very poor understanding in the area of electrical and electronics.I want to pursue a career in theoretical computer science esp. Quantum ...
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Applications of HHL's algorithm for solving linear equations

In HHL's algorithm for solving a system of linear equations (HHL = Harrow, Hassidim and Lloyd) the output is a quantum state rather than explicit information. Has anyone been able to apply knowledge ...
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Explicit error bounds on the abelian hidden subgroup problem

What are some explicit forms for the error probability in the typical quantum abelian hidden subgroup algorithm as a function of oracles queries? Ettinger, Hoyer, and Knill give a result that the ...
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394 views

Quantum algorithms based on transforms other than Fourier transforms

In Quantum Computation and Quantum Information by Nielsen and Chuang they say that many of the algorithms based on quantum Fourier transforms rely on the Coset Invariance property of Fourier ...
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Oracular separations between poly- and log-depth quantum circuits

The following problem appears in Aaronson's list Ten Semi-Grand Challenges for Quantum Computing Theory. Is $\mathsf{BQP}=\mathsf{BPP}^{\mathsf{BQNC}}$ In other words, can the "quantum" part of ...
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Quantum Fourier Transform question regarding measurement

When we use the quantum fourier transform, for a function, the output is entangled, so if a measurement is made on the output, the result may not be that of the function that one wanted in the first ...
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How the errors of the measured quantities of an adiabatic Hamiltonian are inversely proportional to the square root of the number of measurements?

I am going through the paper, Solving the graph-isomorphism problem with a quantum annealer, by Hen et. al. In the last line of the second paragraph of the second column of page 2, it says, Since ...
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Are two-qubit unitaries necessary for universal quantum computation?

I was going through Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians by Daniel Nagaj. In the first sentence of the fifth paragraph on the fourth page, he said, Two-qubit ...
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Any evidence that Linial, Shraibman lower bound on quantum communication complexity is not tight?

As far as I know, the factorization norm lower bound given by Linial and Shraibman is essentially the only lower bound known for quantum communication complexity (or at least it subsumes all others). ...
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240 views

Running Simon's algorithm on D-wave machine

I was wondering whether Simon's algorithm could be run on a D-wave machine. The Simon's algorithm is a promise problem. On the other hand the D-wave machine can run only quadratic unconstrained ...
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The quantum capacity of a trace-decreasing CP map

Assume a qubit quantum channel (trace-preserving CP (==completely positive) map) $\mathcal{N}:C^2\to C^2$ whose quantum capacity is known. Now I construct a new channel $\mathcal{M}:C^2\to C^{2+n}$ ...
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Is the sub-bit model of quantum computation equivalent to other models? [closed]

In a comment to this question Peter Shor asked me for a reference about the third described in the question point of view, namely, that quantum computers can be described as computers that can ...
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Games where $\omega(G) < \omega^*(G) < \omega^{ns}(G) < 1$?

A two player game $G = (I,O,V,p)$ is such that, if two non-communicating players Alice and Bob are given questions $(x,y)\in I^2$ drawn from the probability distribution $p$, they are supposed to ...
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Simulation of every physical quantum system on quantum computer

Let me quote from the section 9.3 of Classical and Quantum Computation by Kitaev, Shen and Vyalyi. With high confidence, we may claim that every physical quantum system can be efficiently ...
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From CHSH inequality to CHSH game

I have been going through Certifiable quantum dice: or, true random number generation secure against quantum adversaries by Umesh Vazirani and Thomas Vidick. They have used entangled particles as ...
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Confusion with the proof of constraints for a particular adiabatic quantum evolution

[This might be related to one of my previous unanswered questions.] This proof belongs to the paper, How to Make the Quantum Adiabatic Algorithm Fail by Edward Farhi, Jeffrey Goldstone, Sam Gutmann ...
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Questions about Farhi's pre-Adiabatic paper

I have been going through Eddie Farhi's 6-pages long pre-Adiabatic paper, An Analog Analogue of a Digital Quantum Computation. I guess I understand most of the math and physics but I am struggling ...
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Local Hamiltonian and combinatorial search problems

I was going through the PhD thesis of Daniel Nagaj. At the beginning of chapter two he indicated a relation between the local Hamiltonian perspective of adiabatic quantum computation and combination ...
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Implication of Bell test loopholes on Vazirani-Vidick random sequence generation scheme

I am trying to imagine what would be the implications of the loopholes on Bell test on the random sequence generation scheme proposed by Vazirani and Vidick (VV protocol) in the paper titled ...
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The computational complexity of spectral norm of a matrix

How hard is computing the spectral norm of a matrix? This paper says, ... it suffices to say that, except for few particular cases, the Matrix Norm problem is NP-hard. I expected that the ...
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Ising spin vs Pauli spin matrices [closed]

Are Ising spins scalar or operators? I am not a condensed matter physicist hence having some confusion. I have learnt about Ising models from adiabatic quantum algorithm papers. For example this ...
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Quantum annealing vs adiabatic quantum computation

I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions ...
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Is the D-Wave architecture a close implementation of quantum interactive proof?

A very high level architecture is, as mentioned here, shown in this picture. The component on the left is classical while the one on the right is the D-Wave box. I understand that in QIP, Arthur is ...
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Why spectral norms are used for computing the complexity of adiabatic Hamiltonian?

In the context of adiabatic quantum computation the spectral norm was first used in the first adiabatic paper by Farhi et. al. when he demonstrated the relation of it to the conventional quantum ...
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Is adiabatic quantum computing as powerful as the circuit model?

Much of the quantum computing literature focuses on the circuit model. Adiabatic quantum computing is not based on applying a sequence of unitary operators, but on changing a time-dependent ...
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1st & 2nd quantization from TCS

Last year I attended Scott Aaronson's talk Hawking Quantum Wares at the Classical Complexity Bazaar. Being intrigued by his argument that "[e]ven if quantum mechanics hadn't existed, theoretical ...
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Finding all solutions by Grover search(not superposition)

When there are multiple marked elements, grover search provides only superposition of them. If I want to find all the marked elements, not superposition, I could try this: 1) Do Grover search, get ...
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Polynomial speedups with algorithms based on semidefinite programming

This is a followup of a recent question asked by A. Pal: Solving semidefinite programs in polynomial time. I am still puzzling over the actual running time of algorithms that compute the solution of ...
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Is quantum annealing faster than simulated annealing/genetic/other state-of-the-art optimization algorithms?

There's the idea of quantum annealing being used to solve optimization problems in terms of a QUBO problem for D-Wave's quantum algorithm. I understand that the advantage of quantum annealing as ...
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Using MATLAB's CVX Package for Semidefinite Programming in Quantum Information

I'm attempting to formulate the semidefinite programs used in the paper "Hedging Bets with Correlated Quantum Strategies" (specifically those on page 7) into CVX so that I can play around with the ...
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Largest set allowing one-step unstructured quantum search

What is the largest set admitting a deterministic quantum search algorithm, for a single marked element, that operates with only a single call to the oracle? The question is interesting since ...
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Threshold for non-zero quantum capacity of depolarizing channels

In "Quantum-channel capacity of very noisy channels", DiVincenzo, Shor and Smolin showed that it is possible to perform quantum communication over depolarizing channels provided that the fidelity was ...
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Lower bounds on $Q_{\epsilon}(IP)$

I want to show that $Q_{\epsilon}(IP) \geq (1-O(\epsilon))n$, where $IP:\{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ is the usual mod 2 inner product. I have Nayak's lower bound, but I am not sure ...
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Communicating a string of zeros and ones quantumly

Alice wants to communicate an arbitrary $x \in \{0 ,1\}^n$ to Bob. Alice and Bob communicate in rounds, in each round Alice (or Bob) applies a unitary transformation on his/her part and transmits a ...
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343 views

Distinguishing between $N$ quantum states

Given a quantum state $\rho_A$ chosen uniformly at random from a set of $N$ mixed states $\rho_1 ... \rho_N$, what is the maximum average probability of correctly identifying $A$? This problem can be ...
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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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A promise problem to decide whether two given pure quantum states are close or far apart

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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Complexity of optimization over unitary group

What is the computational complexity of optimizing various functions over the unitary group $\mathcal{U}(n)$? A typical task, arising often in quantum information theory, would be maximizing a ...
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519 views

Best method of Error Correction in Quantum Key Distribution

As far as I can tell, almost all implementations of QKD use Brassard and Salvail's CASCADE algorithm for error correction. Is this really the best known method of correcting errors in a shared ...