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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Law of Physics and a New Type of Camera [closed]
Do the laws of physics allow manufacturers to produce a vlogging camera capable of recording criminal incidents weeks later after they occurred in Washington, DC?
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Assigning Measurement Operators to POVM Operators
I'm trying to understand how different authors assign measurement operators to POVM operators so we can define the post-measurement state. In particular, it's not clear for me if both assignments are ...
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Should I partial trace the hamiltonian or partition function for a reduced system?
Suppose I have a quantum spin model, let's say e.g. the quantum transverse field model with hamiltonian $H$, on some lattice of particles, with partition function $\text{Tr}(e^{- \beta H})$ and I do ...
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Finding error in Choi matrix calculation which suggests a CP map is not CP
The question
Consider the following linear, trace preserving quantum map over $d \times d$ quantum states $\sigma$,
$$\Phi(\sigma) = \Pi_R \sigma \Pi_R + (1 - \text{Tr}(\Pi_R \sigma)) \frac{\Pi_R}{R}$$...
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Resources on representing quantum states as matrices/vectors?
I was wondering if anyone had any online resources for turning the bra-ket notation for a state or density matrix into a traditional matrix representation / a guide on how to do so easily?
As an ...
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Measurements on a GHZ quantum state for three entangled oscillators [closed]
Consider a system of three harmonic oscillators in the state described by the
vector $( |GHZ\rangle = \frac{1}{\sqrt{2}}(|000\rangle+|111\rangle) )$ where $( |nml\rangle )$ stands for $( |n\rangle |m\...
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Preserving the entanglement of a 2 qubit bellstate when including a third qubit: a general case?
So suppose we have two 2-qubit bell states $|\Psi_{AB}\rangle$ and $|\Psi_{BC}\rangle$ defined the usual way. I want to create a three qubit pure state from qubits A,B, and C such that the ...
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Is there a general construction for three-outcome qutrit POVMs?
For qubits, I can consider the General POVM elements: $M_{\pm} = \frac{1}{2}(I \pm \hat{n}\cdot\overline{\sigma})$ where $\sigma $ is a vector containing the Pauli matrices and $\hat{n}$ a vector with ...
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"Jump" operators from Lindblad equation where the external system is measurements
How do we derive the "jump operators" for the Lindblad equation if the external system is measurements? For example in this article for the Bose Hubbard system the Lindblad operators ...
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Is the optimal POVM of a mixed state the same as the optimal POVM of the pure states in its ensemble?
If I have a mixed state, where each pure state in the ensemble has the same optimal POVM (by optimal I mean POVM for which the classical Fisher information is the same as the quantum Fisher ...
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Is there such physical cryptography? [closed]
In chemistry and physics, is there some sort of science that studies cryptography physically?
Generally, cryptography exists in the world of computer science, logical cryptography or simply ...
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What is a general expression for a symmetric $N$-mode beam splitter?
BACKGROUND
A symmetric beam splitter can be represented as
\begin{equation}
\hat{B}^{(2)} = \frac{1}{\sqrt{2}}\begin{bmatrix}
1 & 1 \\
1 & -1
\end{bmatrix},
\end{equation}
and according ...
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What happens if we throw the observer in a black hole?
Sorry if this sounds like a silly question, but what would happen if a scientist observes Schrodinger's cat alive, but is then thrown into a black hole before he has leaked any information to the ...
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I'm stuck with the conversion of the 3 qubit $W$-state in terms of Pauli's spin matrices so that i can H-P transform them! [duplicate]
Given a state $|\psi\rangle=\frac{1}{\sqrt{3}}(|001\rangle+|010\rangle+|100\rangle)$. What is the density matrix in term of spin operators? Kindly give me detailed solution of this?
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How can partial transposition of the Wigner function be achieved in phase space for continuous variables in non-Gaussian states?
The wigner function in phase space is an equivalent description of the quantum-mechanical density matrix $\rho$. The formula for calculating negativity from the density matrix $\rho$ is $\mathscr{N}(\...
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Quantum phase transition in condensed matter
I want to know that, for any spin-chains in condensed matter Physics like X-Y spin model, Kitaev model 1-D only in which degenerate point is critical point. Is it necessary that the critical points ...
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Perfect correlations in bipartite (impure) density operators
Consider a bipartite system, defined on a Hilbert space $\mathcal{H}= \mathcal{H}_A \otimes \mathcal{H}_B$. Consider a basis $\{|A_i\rangle \otimes |B_j\rangle\}$. What is the general form of a ...
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How can we say that the states of spin (+1, -1) represent 2 dimensions when they lie on a 1D number line?
I am having issues understanding why +1, -1 are considered 2 separate dimensions of state in the context of spin. Since, the values lie on a 1 dimensional number line. For example, the number line of ...
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Sufficient Existence of a CPTP map based on piecewise state mappings
Suppose I want to determine whether there exists a CPTP map, $\mathcal{E}$, such that $\mathcal{E}(\rho_i) \rightarrow \rho_i^{'}$ for $i \in S$. I'm specifically interested in the case where $|S| = 2$...
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Quantum Behavior and Negativity of Wigner Functions
Let us consider a scenario where we have a dataset $\mathbf{X}$, which is a collection of vectors $\mathbf{x}_i \in \mathbb{R}^n$. We encode each component $x_j \in \mathbb{R}$ of $\mathbf{x}$ in a ...
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Reduced density matrix of 4 qubits
I am trying to find the reduced density matrix of a four qubit quantum system. The Hamiltonian is
$$H = -B(\sigma_z \otimes \mathbb{I}_8 + \mathbb{I}_2 \otimes \sigma_z \otimes \mathbb{I}_4 + \mathbb{...
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Arbitrary $2\times 2$ unitary matrix using waveplates
I'm studying about the quantum computation using quantum optics and I wonder about how to implement arbitrary $2\times 2$ unitary operation using waveplates such as half wave plates and quarter wave ...
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Why superconducting qubits need periodic calibration?
I want to understand in some detail why superconducting qubits need periodic calibration. The usual, hand wavy explanation is environmental effects that tend to vary from time to time. However, I ...
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What does a beam splitter look like in path-encoded notation for at most one photon?
Assume a Hilbert space that is (i) truncated to at most one photon, and (ii) is path-encoded such that $(1,0)^T$ and $(0,1)^T$ represent the photon in two separate optical modes, respectively. Here, ...
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The Lorentz-non-covariance of the Wigner Function
What does the fact that the Wigner function is not Lorentz-covariant imply?
My analysis so far led me to the (probably naive) understanding that there really is nothing special about it, just that it ...
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
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Can any Hamiltonian be expressed as a sum of free and pair-interaction terms?
Consider a number of systems $\{S_i\}$ with a Hilbert space $\mathcal{H}=\otimes_i\mathcal{H}_{S_i}$. Consider an arbitrary Hamiltonian $H$ defined on this Hilbert space. Can this arbitrary ...
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What is meant by entanglement in spatial degrees of freedom and how is it different from correlation in spatial degrees of freedom? [duplicate]
I am studying about SPDC (spontaneous parametric down conversion) and I come across phrases like "perfect correlation in spatial degrees of freedom" but never "entanglement in spatial ...
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What is the difference between quantum correlations and entanglement? [duplicate]
I have been reading about Spontaneous Parametric Down Conversion(SPDC). We usually use SPDC to generate polarization entangled photons. Now I am studying about correlations of the photons in the ...
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Bloch vector, maaster equation, and Bloch equation [closed]
I was confused about a derivation of Bloch equation in Breuer and Petruccione's The theory of Open Quantum Systems. Can someone gives some hints on derivation from Eq. 3.219 to Eq. 3.226? Specific ...
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Wigner function of $|n\rangle\langle m|$
For $n=m$, the Wigner function is given by,
$$
W_n(\alpha) = \frac{2}{\pi} (-1)^n \exp(-2 |\alpha|^2) L_n(4 |\alpha|^2),
$$
And for $n \neq m $, it is,
$$
f_{mn}=\sqrt{\frac{m!}{n!}} e^{i(m-n) \arctan\...
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Obtaining a Matrix Product State (MPS) using Schmidt Decomposition for a Tripartite State
I understand that one method to derive an MPS representation of a quantum state involves applying the Schmidt decomposition $ N−1$ times. While I'm familiar with the diagrammatic notation, I wanted to ...
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What guarantees a photonic quantum gate to be unitary?
So in my course of quantum computation i came across this question that "What guarantees a quantum gate to be unitary?" i was specially curious about photonic quantum gate.
At first i ...
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Question on Feynman's Improved Stern-Gerlach Experiment rotated about the $z$-axis
I'm having trouble understand Feynman's reasoning that particles in Fig. 6-5 (b) will end in an unknown state.
Feynman reasons quote:
Suppose that we put an apparatus in front of S which produces a ...
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Entanglement entropy (EE) of a non-contiguous subsystem
I know how to calculate EE for a contiguous sub-system using Schmidt decomposition aka SVD. Algorithm 9 on page 11 of this paper. Is there any similar SVD algorithm of restructuring the wave function ...
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MPS canonical form
If I express a MPS in its (left, right or anything else) canonical form, does this representation encode all Schmidt decompositions between a subsystem and its complement,rather than only the Schmidt ...
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Do completely positive maps have a leading eigenoperator with nonvanishing trace?
A completely positive map $\mathbb{W}$ is a map from $\mathbb{C}^{n\times n} \to \mathbb{C}^{n\times n}$ that can be written in terms of $n\times n$ matrices $K$ as
$$ \mathbb{W}(\rho) = \sum_{i=1}^N ...
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Why this scenario doesn’t count as conveying information through quantum entanglement [duplicate]
Supposed you have two electrons entangled on earth, and one is carried on a spaceship and one is left on earth. The spaceship has a program that if the observed x-spin through magnet is up spin it ...
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Query on Expectation value of Spin-X operator being Invariant with transformation of BASIS
Please correct my calculations below. Where did I go wrong? What did I assume wrong?
Thanks & Regards,
Sarath Chandra.
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References about advanced quantum mechanics
I have already studied quantum mechanics (Sakurai and Bransden Atomic/Molecular physics ) and all the relevant quantum field theory (Weinberg I + II, Schwartz and Birrell-Davies).
I'm searching for ...
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Is unpolarized light necessarily a semi-classical phenomenon?
I'm aware that unpolarized light can be represented by a mixed state $\frac{1}{2}(|x\rangle\langle x| + |y\rangle\langle y |)$. It bothers me that in this framework, unpolarized light is a symptom of ...
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How do we mathematically apply a Quantum Gate/Operation on a pair of Qbits in a Multi-Qbit system
I am trying to understand Quantum Gates and Quantum Operations (I am a layman and my background is CS). What I am conceptually aware of:
Any $N$ Qbit system can be written as a vector of $2^N$ complex ...
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Perfect determination and knowability in quantum mechanics?
In classical mechanics, it is postulated that in principle the position and velocity of particles are perfectly determined and can be perfectly known. And it is by using such determined properties ...
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General expression for $N$ qubit system
I know that if there are $N$ qubits then, there will be $2^N$ basis states. This is same as the dimension of the Hilbert space. Now I have seen here in discussion forms that there will be infinitely ...
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Notation of 2-qubit quantum gates as "Matrix exponentiated by Matrix"
I am currently studying this paper about Cartan's KAK Decomposition. In the end of the section "Canonical Class Vector" some there is a calculation on how to find the canonical class vector ...
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Dependency of Stark effect on Quantum numbers
I have read many sources which tell me that the Stark and Zeeman effects, which Bohr's theory had trouble explaining, were explained by the introduction of the magnetic quantum number. But doesn't ...
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"No local gauge invariant observables in gravity"... Is it a classical or quantum statement?
I have seen different explanations to understand why there are no local gauge invariant observables in gravity.
Some of them explain that diffeomorphisms are a gauge symmetry of the theory and thus ...
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How is the bomb represented mathematically in the Elitzur-Vaidman bomb tester?
... or more generally, how can one represent mathematically an obstacle in interaction-free measurements? Would it be reasonable to represent it as an "absorption" that transforms $\mid 1\...
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Writing a given unitary in the same basis as the Hamiltonian (Operator Representation and Confusion)
I have a simple question concerning how to write the representation of operators, such as unitaries, using a specific order for the basis elements. Let me give you an example.
Consider a tripartite ...
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Entanglement entropy and reduced density matrix
I'm learning about the definition of von Neumann entanglement entropy
$$S(\rho_1)=-\text{Tr}[\rho_1\ln\rho_1]$$
where $\rho_1$ is the reduced density matrix $\rho_1=\text{Tr}_2(\rho)$.
I was confused ...
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