Theoretical issues related to the quantum treatment of information

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How to do Tensor product of two qubits using gates [migrated]

I want to do tensor product of two qubits which are passed through two Hadamard gates. I understand feeding the control bit of CN gate the output of Hadamard gate and target bit |0> gives me the Bell ...
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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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192 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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241 views

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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209 views

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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75 views

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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140 views

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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134 views

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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817 views

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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329 views

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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170 views

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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247 views

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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558 views

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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664 views

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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144 views

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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299 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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123 views

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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157 views

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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294 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 ...
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Quantum capacity for ensemble of Pauli channels

In Preskill's quantum computing notes Chapter 7 approximate page 82, he shows that a Pauli channel has capacity $Q \geq 1-H(p_I,p_X,p_Y,p_Z)$ where $H$ is Shannon entropy and $p_I, p_X, p_Y, p_Z$ are ...
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Optimal measurement for MUBs

Let $\mathcal{B} = \{B_1, \dots, B_k\}$ be a set of Mutually Unbiased Bases (MUB) in $\mathbb{C}^n$, i.e. each $B_i$ is an orthonormal basis and for $v \in B_i, w \in B_j, i \neq j $ we have $|\langle ...
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Do the quantum communication complexity lower bounds hold when parties can send a “duplicated” qubits?

This question continues from the previous question where I mistakenly asked a question that is too general. In quantum communication complexity, we always assume that Alice and Bob have unlimited ...
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Are Alice and Bob allowed to copy qubits in quantum communication complexity model?

In quantum communication complexity, we always assume that Alice and Bob have unlimited computational power and are still prove lower bounds such as the $\Omega(n)$ lower bounds of parity. What ...
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Master Equations and Operator Sum Form

I'm more of a quantum optics guy than a quantum info guy, and deal mainly in master equations. I'm interested in operator-sum form, and I'd like to derive the errors in this form for a small quantum ...
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Non-tomographical certification of projectors, using product states?

I'm interested in operational ways of demonstrating (with high probability of confidence, in an error-free setting) that a POVM operator on n-qubit states is a projector. Specifically, I'm interested ...
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234 views

Proof that Entanglement Cannot Increase the Capacity of a Noiseless Classical Channel

I am aware that quantum entanglement cannot increase the asymptotic capacity of a noiseless classical channel. However, can anyone provide some type of reference in the literature that contains a ...
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Nonlocal Games and Quantum Communication

I'm currently on the look out for some good reference material relating non-local games with beneficial aspects in quantum communication. For instance, I am aware that non-local games are good at ...
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Quantum Bell-Type Inequalities

I'm curious if someone could recommend some supplementary material for gaining a deeper understanding of the paper : "Some Results and Problems on Quantum Bell-Type Inequalities - Tsirelson". ...
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Quantum Channel Decoding

Let a quantum channel $\Phi(\cdot)$ between two Hilbert spaces $\mathcal{H}_{in}$ and $\mathcal{H}_{out}$. What is the quantum channel $\Phi_{inv}(\cdot)$ that best reverses $\Phi(\cdot)$ ? $\forall ...
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Does cryptography have an inherent thermodynamic cost?

Reversible computing is a computational model that only allows thermodynamically reversible operations. According to Landauer's principle, which states that erasing a bit of information releases $kT ...
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Approximation of Quantum Channels

Background: In quantum information theory, a wide class of processes acting on stochastic quantum states can be described using the formalism of Quantum Channels: A quantum channel is a linear, ...
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Polynomial algorithms for UPB (Unextendable Product Bases)

Consider a Hilbert space $H = H_1 \otimes \dots \otimes H_n$. An Unextendable Product Basis (UPB) is a set of product vectors $\vert v_i \rangle = \vert v_i^1 \rangle \otimes \dots \otimes \vert v_i^n ...
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Is there any connection between the diamond norm and the distance of the associated states?

In quantum information theory, the distance between two quantum channels is often measured using the diamond norm. There are also a number of ways to measure distance between two quantum states, such ...
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Universities for Quantum Computing / Information?

Which universities have a strong quantum computing curriculum, and offer some type of quantum computing/information courses/research? The aim here is to collect a useful list for someone considering ...
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Does the trace norm of the difference of two density matrices being one imply these two density matrices can be simultaneously diagonalizable?

I believe the answer to this question is well-known; but, unfortunately, I don't know. In quantum computing, we know that mixed states are represented by density matrices. And the trace norm of the ...
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Quantum Computation - Postulates of QM

I have just started (independent) learning about quantum computation in general from Nielsen-Chuang book. I wanted to ask if anyone could try finding time to help me with whats going on with the ...