Questions tagged [quantum-information]

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 this system in a superposition?

Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition: \begin{...
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What sub-field is it? [closed]

If I were to choose a research field and add a sub-field, let's say that I want to work with quantum computing/quantum cryptography or developing quantum hardware. What field and sub-field should I ...
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Can measurements be used for quantum communication?

My understanding of quantum entanglement is that when you measure the state of an entangled particle, its counterpart will measure a correlated state, i.e. we know for sure that if for example ...
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Shor's algorithm entanglement verification

I would like to ask whether the entanglement verification is necessary in Shor's algorithm In the paper, Nature Photon 6, 773–776 (2012), they mentioned that they tried to factorize 21 to avoid the ...
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How to map the eigenvectors of a superoperator into the corresponding operators?

The set of linear operators acting on a $d$ dimensional Hilbert space, $H$ form a vector space, called operator space $\mathcal{L}(H)$. Elements of operator space are $d \times d$ matrices. Now the ...
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Indistinguishability of Quantum States and its Consequences

In the book Quantum Computation and Quantum Information, there is a discussion about how if states are not orthonormal then there is no quantum measurement capable of distinguishing the states. I am ...
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How do I prove the identity for ${\rm tr}_p [e^{-iS\Delta t}(\rho\otimes\sigma)e^{iS\Delta t}]$ in Seth Lloyd's 2014 Quantum PCA Paper?

Equation (1) in Seth Lloyd's paper on Quantum PCA says: $\text{tr}_{p}\text{e}^{-iS\Delta t} \rho \otimes \sigma \text{e}^{iS\Delta t} = \cos^2(\Delta t)\sigma + \sin^2(\Delta t) \rho - i \sin(\Delta ...
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What can the eigenvalues of unitary matrices tell us? [duplicate]

I'm searching for applications where the distribution of the eigenvalues of a unitary matrix are important. Example properties of the eigenvalues could be that the eigenvalues are clustered, that they ...
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What can the eigenvalues of unitary matrices tell us? [closed]

I'm searching for applications where the distribution of the eigenvalues of a unitary matrix are important. Example properties of the eigenvalues could be that the eigenvalues are clustered, that they ...
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Are all maximally entangled state the standard maximal entangled state in some basis?

$\newcommand{\ket}[1]{\left|#1\right>}$ Let $\cal{H}$ be a Hilbert space with dimension $d$. Define an MES (maximally entangled state) $\ket{\Phi} \in \cal{H} \otimes \cal{H}$ to be one with a ...
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Which is the correct equation to project density matrix and why? [closed]

Which is the correct equation to project density matrix and why? a) $\mathbb{I} \rho \mathbb{I} $ where $\mathbb{I}$ is the identity operator given as $$ \mathbb{I}= \sum_k \Pi_k$$ where $\Pi_k$ are ...
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Can this experimental setup generate a superposition of two distinguishable states?

Is it possible to generate a superposition state, $\hat{b}_1^{\dagger} = (\hat{a}_1^{\dagger}+\hat{a}_2^{\dagger})/\sqrt{2}$, in a way as demonstrated in this figure? Notice that this transformation ...
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How is information conserved when antimatter and matter annihilate each other?

According to quantum mechanics, information must be conserved. My question: How is information conserved when antimatter and matter annihilate each other? For example: Let's say there is an electron ...
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How to find the symmetry operator given a Hamiltonian? [closed]

Please,also explain it for both the transverse field Ising model (TFIM) and the spin-polarized superconductor(SPSC).
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Are polarization properties of light inherently quantum?

I'm reading Preskill's notes on quantum information theory, and in chapter 2 (full list here) he in particular explains how qubits are different from a probabilistic classical bit. Among examples ...
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How to diagonalise this free fermionic Hamiltonian?

I have the following $1$D fermionic Hamiltonian $H$, given by $$ H = H^A_0+H _0^B+H_I^{AB}=\sum_{jk\in A} H_{jk}^Ac^\dagger_j c_k + \sum_{jk\in B} H_{jk}^Bc^\dagger_j c_k + \lambda \sum_{j\in A, \ k \...
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What are the relations between mixed/pure/separable/entangled states?

I read this question which clarified the concepts of mixed/pure/separable/entangled states, but I can't see if one of "mixed/pure" implies one of "separable/entangled" and/or vice ...
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Can information travel faster than speed of light in this situation?

I know the answer is no but I have a thought experiment that seem to be violating that. Imagine two persons living on two different planets namely A and C which are 10 light years apart. There is a ...
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Clustering of correlations in extremal thermal states

Background Consider a quantum system described by an algebra $\mathcal{A}$ of local observables, which are supported on subsets of the lattice $\Lambda = \mathbb{Z}^{d}$. Given an observable $A$, let $...
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Derivative of a multimode squeezed vacuum state

Let us suppose we have a multimode squeezed vacuum state of the form \begin{equation} |\psi\rangle = \exp[A]|0\rangle= \exp \big[\sum_{ij}G_{ij}(t) (a_i a_j -a_i^\dagger a_j^\dagger)\big] |0\rangle\...
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Is there any general statement for quantum relative entropy involving CPTP maps on only one slot?

I was searching the internet extensively about some information on the behavior of quantum relative entropy under CPTP on only one slot. It is well known that $$S(E_1(\rho)\|E_2(\sigma)\leq S(\rho\|\...
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Entangled Photon Sources: how to choose the pump wavelength in SPDC?

I found several papers dealing with entangled pairs of photons generated by means of a setup consisting in a pump laser and a nonlinear crystal, such as BBO or KTP and here the incoming photons ...
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Proof: A channel is entanglement breaking if it separates maximally entangled states

I'm working my way through Mark M. Wilde's Quantum Information Theory (2nd edition) and am stuck on a proof regarding entanglement breaking channels (Exercise 4.6.2) Prove that a channel $\mathcal{N}...
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Where, exactly, does the boundary lie between 'entangled' particles and merely 'interacting' or 'coupled' ones?

Have scientists discovered, yet, the precise amount of interaction needed to actually 'entangle' a pair or more of particles, beyond mere interaction or even coupling? Is there a distinct difference, ...
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Does quantum entanglement, in and of itself, make the constituent particles more sensitive to external fields and forces?

I just watched PBS Space time episode called, 'Navigating with quantum entanglement'. At about 10:25, host Matthew O'Dowd says that Peter Hore of Oxford University reviewed the evidence for quantum ...
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In the context quantum computation, what is the evidence that querying classical oracles in superposition makes sense?

In quantum computation it is often assumed that if $f$ denotes some (classical) Boolean circuit $\{0,1\}^n \rightarrow \{0,1\}$, then a quantum circuit can have oracle access to $f$, that is the ...
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What is density matrix of a single qubit from quantum register?

Suppose we have quantum register of $n$ qubits in a pure state $\Psi=\sum_i\alpha_i\left|i\right>= \alpha_0\left|00...0\right> + \alpha_1\left|00...1\right> + ... + \alpha_{2^n-1}\left|11...1\...
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Is there a comparison table for quantum algorithms like VQE, QPE, QAOA, and so on?

I have one question: Recently, I studied about several algorithms like VQE, QPE, QAOA and so on. I would like to make some comparison tables about those algorithms, their strengths and weaknesses. If ...
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Can 2-qubit systems be represented in the Bloch sphere representation?

I am studying a system with 2 qubits, so I need, for a given state, a Bloch representation for each qubit. I am having difficulties because I get results that do not have sense at all. For example if ...
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Recommendations for topics at the intersection of QFT and applied QM

I'm looking for topics in elementary QFT (canonical quantization, path integrals, representations of the Poincaré group, and perturbative calculations) that intersect with applications of standard ...
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Are there any recommended texts for introduction to Lindblandian dynamics for third year undergraduate? [duplicate]

I am looking to learn Lindbladian dynamics and apply it to a system with multiple baths. Are there any texts available that only assume undergraduate Quantum Mechanics knowledge (My school offers ...
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Rigorous derivation of entanglement entropy bound of MPS

I am working on a summer project and am trying to prove the Von Neumann entropy of an MPS is bounded by a constant to gain some introduction. While this easily follows if we start with the MPS being ...
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Derivation of Jump Operators in Master Equation

I'm trying to understand the process of deriving the master equation in this article. The system in general is composed of two interacting qubits each of which is coupled to their local thermal bath ...
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Is it possible for two respectively closed systems to be entangled?

Is it possible for two respectively closed systems to be entangled? I was thinking something along the lines of, We have a 2-qubit system, prepared in e.g. a Bell state. Each qubit is carried off to ...
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The “Algorithm” for Derivation of the Master Equation

I'm trying to come up with a master equation for a spin system. So, I'm trying to understand in general how can we derive the master equation and the Lindblad operators if we know the system, bath and ...
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Why are electrons usually used to define qubit in silicon-based quantum dot, but not holes?

Usually, electrons spin are used to define qubit in sillicon. In contrast, holes are usually used in description of germanium qubit. Why is that?
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How to translate from a state/density matrix formalism to matrix product state representation?

From what I understand, MPS is just a simpler way to write out a state, compared to the density matrix. But how do I get those $A_i$ matrices? From all the examples I read, people just somehow "...
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In spin qubit of quantum dots, why $|S>$ and $|T0>$ state have energy difference?

As we know, the Zeeman splitting by magnetic field causes the energy difference between |↑> and |↓>, therefore states like |T+>=|↑↑> have a different energy from others. But why states ...
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Can you represent a diagonal density matrix with creation/annihilation operators?

Say I’m work with free fermions. In the computational basis one has two basis elements for each site $|0\rangle$ and $|1\rangle$ with creation $d^\dagger$ and annihilation $d$ operators (i.e. $d|1\...
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Is $\{Z, CZ\}$ an universal quantum gate set for diagonal gates with eigenvalues +1 and -1?

Consider diagonal quantum gates with eigenvalues $\pm 1$, i.e. all diagonal elements are either $+1$ or $-1$. Can these gates always be decomposed into a finite number of Z and controlled-Z gates? My ...
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Best initial state for maximum information

I was reading a paper (pdf) and eq.(4) states that the maximum Fisher information is obtained for the initial state $$\vert{\psi}\rangle=\frac{1}{\sqrt{2}}(\vert{\lambda_{\max}}\rangle+\vert{\lambda_{\...
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Where does the negative cosine relation for quantum mechanical CHSH correlations come from?

I have been lately looking into Bell's inequality. I have noticed a recurring graph that depicts the correlation of two spins when measured at different angles, for the quantum and the classical case: ...
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What does the master equation for this quantum autonomous absorption refrigerator imply?

I'm following this paper: https://arxiv.org/abs/0908.2076, about building minimal and autonomous quantum absorption refrigerators. The setup is 3 qubits, each coupled to their own baths, and with some ...
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Which paper introduced the concept of the “Bloch sphere”?

Everyone loves Bloch sphere, but which paper of Bloch was it introduced? The Wikipedia article on Bloch sphere (here), as of 17/May/2021 links to this paper of Bloch “Nuclear Induction” but it doesn’t ...
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Hilbert space of toric code on a lattice

Kitaev mentions that if one places a $k\times k$ square lattice on a torus, and place a qubit on each edge of the lattice then there are $n=2k^2$ total qubits. Why is this so? Shouldn't there only be $...
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Need help understanding the symmetrical quantum system

In some articles, I read this sentence: When the tripartite quantum system is symmetrical, i. e., the state of the whole system is invariant under the permutations of the three parties 10.1007/s11128-...
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Two distinct uses for the density matrix formalism

In areas of quantum mechanics related to information theory, open quantum systems, and foundations, I've seen the formalism of density matrices employed to model two distinct physical scenarios ...
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Can separable states display statistical correlations between global observables

In the following the notation $|a\rangle$ represents one single particle in the spin state $a$, so that $|0+1\rangle$ represents one single particle in a spin state superposition. On the other hand $|...
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Are uncorrelated states separable?

Consider spin population observables, a separable state can be correlated or uncorrelated. For example, if I consider the two particle state $$|+\rangle|-\rangle$$ it is separable and spin ...
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Transform two-mode squeezed state (TMSS) to its covariance matrix

The two-mode squeezed state can be written as: ${\left| \chi \right\rangle _{AB}} = \sqrt {1 - {\chi ^2}} \sum\nolimits_n^\infty {{\chi ^n}} {\left| n \right\rangle _A}{\left| n \right\rangle _B}$ ...

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