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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Does a partially traced density operator also become a Boltzmann density operator under Wick rotation to Euclidean space?

I know that, under the Wick rotation $(i\Delta t/\hbar,p_0)\to(-\beta,-ip_{0,E})$, Feynman's path integral supposedly transforms into the traced-over Boltzmann partition function, $trace(e^{-\beta H})=...
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Is there a general relationship between the density operator and phase velocity?

I am trying to solve $\int v_pd\rho$ for a time-independent, 1-particle density operator $\rho$ (acquired, more or less, from a partial trace of complex scalar field operators projected upon the ...
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Numerical discretization and the Schrodinger equation, for a simulation

i'm solving numerically the Schrodinger time dependent equation, in this case simplified to one dimension, and i don't know at all how to discretize it, or if what i have done its okay. $$i\hbar\frac{\...
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124 views

Von Neumann entropy vs Shannon entropy for a quantum state vector

Is there some kind of information about a quantum system, which we might derive from von Neumann entropy, which is impossible to deduce from Shannon entropy? Let's say, that we have a bipartite system ...
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What is charge sensitivity?

I've been trying to wrap my head around what the concept of charge sensitivity even is. For example I've been reading this paper here, and the units of a stated value $6.3 \times10^{-6} e/\sqrt{Hz}$ ...
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How is the set of states $Q$ logically replaced by a Hilbert space?

Question is: How is the set of states $Q$ logically replaced by a Hilbert space if a classical Turing machine is described by a 7-tuple $M=\langle Q,\Gamma, b,\Sigma, \delta, q_ {0},F\rangle$? I read ...
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66 views

Why is measuring $M$ equivalent to measuring $UMU^{-1}$ after applying $U$?

I read a paper talking about Bell basis measurement circuit that simultaneously measures $XX, YY,$ and $ZZ$. It said: after applying a quantum gate $U$, a target measurement of $M$ on the original ...
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Does the act of storing information (not its erasure) locally increase entropy in Maxwell's demon's memory?

I have the following confusion with Maxwell's demon thought experiment and its resolution. According to this thought experiment, when the demon's memory space becomes completely full, it erases ...
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How to define the partial of the logarithm of a density operator?

I've been thinking about self-information ($I:=-\log (\rho)$) lately and I have a question on how to evaluate the derivative of such an operator... I realize that $i\hbar(\partial/\partial t)\rho=[H,\...
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The emergence of space-time from entangled states

I recently read an article by Yasunori Nomura (https://arxiv.org/abs/1711.05263), in which he says that space-time is an emerging phenomenon. At the same time, space-time disappears when the ...
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What meaning is Depth and T-Depth in Quantum Circuit?

I'm reading a paper about quantum cryptanalysis and circuits designs, but i really can't understanding what is Circuit Depth or T-Depth. Also T-gate and T-count. the paper is "Applying Grover’s ...
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Assuming complexity determines the curvature of spacetime, can you escape a blackhole?

I've been watching this lecture series https://www.youtube.com/watch?v=wjgkQG77pcc. (Complexity and Gravity by Leonard Susskind). It's got me thinking: can I make a quantum computer that functions as ...
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What is quantum local “unrealism”?

Bell's theorem is often interpreted to have destroyed local realism. This means something like the properties of the particle do not exist until they are being measured. I am not sure what does this ...
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138 views

When in $T \rightarrow \infty$ the eigenstates that contribute the most are the ones that lie in the middle of the spectrum?

Is the following intuition correct? Consider a 1D Ising model of length $N$ in a heat bath with inverse temperature $\beta$ (i.e. a canonical ensemble). The Boltzmann factor is given by $$ p(E_i) = \...
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Continuous variable Fourier gate and teleportation circuit

I am studying the teleporting circuit of continuous variable showed by Weedbrook, pag. 37. Fig. (164); in that, they propose an input state to the circuit as $$ \left|\psi\right>\left|0\right>_{...
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Are quantum fluctuations observable?

I know I am asking out of my limits, but i felt relaxed thinking about this. Now I read somewhere about quantum fluctuations (that energy can be generated in randomly at two positions where total sum ...
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Is information conserved in quantum mechanics (after wave function collapse)?

I have heard in popular science that there is a law of "conservation of information." Some times this is described as: for any event that happens, there is enough information to reconstruct ...
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Hamiltonian on qubit: necessarily induces rotation. What about the reflections? Are they impossible to implement?

Any Hamiltonian dynamic on a qubit is necessarily a rotation. I consider a two level system having a Hamiltonian $H$. Decomposing this Hamiltonian on the Pauli basis and using the fact it is Hermitian,...
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Question about Ekert protocol of quantum key distribution

recently I've self-studied the quantum computing from the book Quantum Computing for Everyone by Chris Bernhardt. Everything is so far so good until I came across with the Ekert protocol which ...
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What's the motivation behind the seemingly artificial setup of the no-deleting theorem?

If you asked me what physical result would be naturally referred to as "the no-deleting theorem", then I would probably guess something like this: Given a designated "blank" state ...
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How is deterministic state transfer related to entanglement generation between two qubits?

From a quantum information theoretical point of view, how is deterministic state transfer related to entanglement generation between two qubits? Or, more specifically, how can you exploit the former ...
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60 views

Calculating Entanglement Spectrum from reduced density matrix

Im reading about Entanglement Spectrum in very nice webiste here. It says: After a system is partitioned into subsystems {A} and {B}, a state of the entire system may now be expressed as a matrix with ...
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Is there a deep connection between the Heisenberg uncertainty principle and entropy?

(Just so you know my background) I have taken a graduate course in quantum mechanics. I have also learned about information entropy in various places (statistical mechanics, information theory, ...
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33 views

Measuring one particle on this entangled state

If we have a normalized entagled state: $$ |a\rangle=N (|1\rangle|2\rangle+|1\rangle|-2\rangle+|1\rangle|2\rangle-|-1\rangle|2\rangle) $$ Where $|2\rangle, |-2\rangle$ describes particles A and $|1\...
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Completely positive quantum channel

Let $\mathcal{E} \to CP(A \to B)$ (completely positive linear map) be a trace non-increasing $CP$ map. Show that any operator sum representation $\{M_x\}_{x=1}^{m}$ of $\mathcal{E}$ satisfes $\sum_{x=...
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33 views

Rotation of a Photon Polarisation with a Unitary

As an example of a qubit, one take the polarisation of a photon in which the two states can be taken to be vertical and horizontal polarisation, respectively. Rotation of a photon polarisation would ...
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116 views

Implications of the delayed choice quantum eraser experiment [duplicate]

The experiment says that if I split a photon into two coherent entangled photons, one towards a double-slit, one towards a which-way detector, I can control whether the interference pattern appears ...
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Does work need to be done to a quantum state to change it?

Today in Quantum we talked about a 3 component quantum channel; maximally mixed light flowing into a linear filter oriented to 0 degrees, to through a phase retarder, then through another linear ...
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46 views

Kraus decomposition [closed]

In the derivation of the Kraus decomposition, it is not clear to me how to get from the LHS to the expression on the RHS: $$ \text{Tr}_{env}[U(\rho_1\otimes \rho_{env})U^\dagger]=\sum_k\langle k|U|0\...
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112 views

How does relaxing counterfactual definiteness allows for CHSH inequality violation?

Scenario, I want to play a game with a group of students as a teacher, I ask two teachers to help. The students are from the central classroom, going to room A and room B where the teachers there asks ...
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How can information be preserved if quantum phenomena are uncertain?

Firstly, I am a layman with an interest in physics only so please forgive any ignorance I demonstrate here. This question puzzles me and I'm sure there's a good answer. I've heard it said repeatedly ...
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How to measure a multipartite density matrix?

I consider the tensor product $H_1 \otimes H_2$ for pairs of qubits. they are described by a 4*4 density matrix $\rho$. Bob and Alice share them and measure them randomly in many directions. At the ...
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88 views

Bloch sphere representations for multi-qubit quantum systems

Just a short mixed quantum state representation question. Given a single qubit density matrix $\rho$, since the Pauli matrices form a basis for 2x2 complex matrices, the Bloch sphere representation ...
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44 views

Can a trace function be represented as a Hilbert-Schmidt product with the density matrix?

Given a trace function, say the von Neumann entropy $S(\rho) = - \mathrm{tr}(\rho \log \rho)$, can it be express as a matrix $M$ where $S(\rho) = \mathrm{tr}(M^\dagger\rho)$ is given by the Hilbert-...
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77 views

Does an entangled pair remain entangled after the first measurement?

Consider an entangled pair described by the wavefunction $$\lvert1,0\rangle = \frac{1}{\sqrt{2}}(\lvert\uparrow_1\downarrow_2\rangle-\lvert\downarrow_1\uparrow_2\rangle)$$ in in the $S_z$-basis. If ...
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Entanglement networks and perspective

So, superposition is supposed to be fragile because, if any information leaks from the system, the wave function collapses. However, the very definition of 'information leaking' must set up an ...
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How does I show how the heat capacity and temperature relate for 2D graphene at low temperature?

I know that for 3D solids, heat capacity and temperature relate as C proportional to T^3. Graphene has 3 acoustic branches and one has a dispersion for which 𝜔 ∝ k^2. It's this branch at low ...
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38 views

What is the inverse of the cyclic shift operator?

I have given the cyclic shift operator $X(x) \in \mathbf{R}^{d \times d}$, the generalized pauli operator, for a qudit system. This operator is defined by the action it takes on an arbitary ket vector ...
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92 views

How to entangle two superconducting qubits?

I do understand qubits entanglement, and their spins but I do not understand that at circuit level how can we entangle 2 qubits? Is it related to 2 qubits gates?
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Pertubation Theory

For long-range barrier tunneling, consider three qubits governed by the Hamiltonian $H$. $$ H = -J(\sigma_1^+\sigma_2^-+\sigma_1^-\sigma_2^++\sigma_3^+\sigma_2^-+\sigma_3^-\sigma_2^+)+\frac{U}2\sigma^...
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Interpreting the amplitude damping channel

In page 380 of Nielsen and Chuang (Quantum information), there's a statement about the amplitude damping channel, which is defined by the operators $E_0 = \begin{bmatrix}1 & 0\\0 & \sqrt{1-\...
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How to understand the concept of a fluxon, the dual of the Cooper pair?

I've been reading the paper Bifluxon: Fluxon-Parity-Protected Superconducting Qubit by Kalashnikov et al. which deals with a novel type of superconducting qubit. Without going into too much of the ...
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A Venn diagram for: (non-)locality, (non-)realism, (non-)contextuality, (non-)signalling, (dis-)entanglement

I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a ...
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1answer
81 views

How to prove that a state is pure if and only if it cannot be expressed as a convex combination

Define a pure state to be one that can be expressed in the form $ \rho = | \psi \rangle \langle \psi |$. How can we show that this is equivalent to $ \rho \neq p \sigma_0 + (1-p) \sigma_1 $ for any ...
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Dual of IC POVM cannot be positive

I've read a claim about POVMs in my lecture notes, which I fail to prove. Hence, I would be grateful if some of you have some hints for me /can help me. Let $\{N_i\}_{i=1}^{d^2}$ be an informationally ...
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How to filter from $N$-fold coincidence to fourfold coincidence

Let's suppose that i have as a result, 8-fold coincidence, something like $[1,0,1,0,0,0,0,1]$ and we are just interested only in the first two and the last two of this output how can i filter it to be ...
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75 views

Lindblad from infinitesimal Kraus sum representation

I have a few basic queries regarding a proof in the set of notes MIT: Open Quantum Systems, the following is stated: We can derive the Lindblad equation from an infinitesimal evolution described by ...
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Is the $N$-fold coincidences relative to the number of quantum relays?

I'm working on a project where i have to use quantum relays to ensure the entanglement swapping, and i want to know if for one relay i'll get fourfold coincidences, am i supposed to get 8-fold ...
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Why “diagonal” polarization doesn't decohere?

It is often said, that qubit should be maintained under very low temperature and kept highly isolated not to decohere. But we can represent $|0\rangle$ with vertical polarization of light and $|1\...
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52 views

Is the Von Neumann entropy of two initially non-interacting systems always increasing?

Let $A$ and $B$ be two systems that does not interact initially ($t=0$), i.e., the density matrix of the initial total system is given by $\rho(0) = \rho_A (0) \otimes \rho_B (0)$. Suppose that ...

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