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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How does Hawking Radiation not violate energy conservation? [duplicate]

If Hawking Radiation is produced by particle-antiparticle pairs forming from the vacuum, with one particle being absorbed by the black hole and one escaping, how is the original energy required to ...
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Photon bunching and polarizers

I'm trying to understand how polarizers affect bunched photons. Or, more generally, how a projection operator affects a two-photon state corresponding to photon bunching. Toy example: Imagine you ...
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Open Quantum Systems: Born-Approximation and the preservation of Trace, Hermicity and Positivity

This is related to a previous question of mine. We consider a density matrix $\sigma(t)$ operating on a Hilbert space $\mathscr{H}_{s}\otimes \mathscr{H}_b$ with Hamiltonian $H = H_s \otimes \mathbb{...
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What is the area of physics/science called that deals with fundamental limits of computation?

I am interested in learning about the fundamental limits of computation and in particular would like to read textbooks on the subject if they exist. My background is in maths and computer science - I ...
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Is there a classical correspondence of the entanglement entropy in isolated quantum systems?

For an isolated quantum system, one can study the time evolution of entanglement entropy after a quantum quench (always a pure state), which has a rich behaviour in various different models. However, ...
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Quantum information = quantum gravity?

I have recently listened to a podcast by Sean Carroll and Leonard Susskind (strongly recommended https://www.preposterousuniverse.com/podcast/2019/05/06/episode-45-leonard-susskind-on-quantum-...
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174 views

Do observables only amount to computing functions of outcome probabilities?

It is well known that in quantum mechanics any Hermitian operator $A$ can be thought of as an observable. Given any (pure) state $\lvert\psi\rangle$, measuring such observable gives an average ...
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About Density Matrix of a Particle

The quantum state of a spin- 1/2 particle can be written, in the momentum representation, as a two-component spinor, $$\textit{Ψ}(\textbf{p})=\left(\begin{matrix}a_{1}(\textbf{p})\\a_{2}(\textbf{p})\...
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Averaging over outgoing radiation in the firewall argument

Following the AMPS paper, the Hawking radiation can be divided into an early and late part, decomposed as follows: $$ |\Psi\rangle=\sum_{i}|\psi_{i}\rangle_{E}\otimes |i\rangle_{L},$$ where $\lbrace|...
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76 views

Integrating of von Neumann equation for density matrix

Suppose we are given the Hamiltonian $$H=f \frac{\text{Tr}\sigma_x \rho}{\text{Tr}\rho}\sigma_x,$$ where $\rho$ is the density matrix, and $\sigma_x$ is the Pauli matrix $$ \sigma_x= \begin{...
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Is tracing out a subsystem always akin to discarding all information about it?

Suppose we have some quantum system with sub-systems A and B. It could be, for example, two qubits or groups of qubits. Is it fair to say that tracing out the sub-system A is always akin discarding ...
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What does $e^{i\alpha}$ stand for in the general expression for a qubit gate $e^{i\alpha}R_n(\theta)$?

All qubit gates can be written in the form of: $$U = \exp(i\alpha)R_n(\theta).$$ I know $R_n(\theta)$ is a rotation of $\theta$ about an arbitrary axis n in Bloch sphere, but what does $\exp(i\alpha)...
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Difference between an entangled pair of photon and two magnets in a box? [duplicate]

I try to understand quantum entanglement and especially what it’s called « Action at a distance » from my understanding, if you have a pair of entangled photon, after measuring the polarization of ...
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“Quantum information and quantum computation”: quantum period finding algorithm

The procedure for a quantum period-finding algorithm is described on page 236 of "Quantum Computation and Quantum Information" by Isaac Chuang and Michael Nielsen. In step 3 of the procedure, authors ...
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Is the Schmidt basis the one minimizing entanglement?

I know, that for a compound system $ |\psi \rangle_{AB} $ we can find the Schmidt basis, which is an unique one. Is it at the same time the basis, in which the two subsystems are minimally entangled? ...
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Operators acting on a single subsystem within a combined system's state

I was reading over combined systems and operators acting on a single system within the combined system, and am confused by the math. For example, we have individual qubit states for subsystems $A$ ...
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Entanglement Swapping of Werner states

I am provided with two Werner states \begin{equation*} \rho=F|\phi^+><\phi^+|+\frac{1-F}{3}(|\phi^-><\phi^-|+|\psi^+><\psi^+|+|\psi^+><\psi^+|) \end{equation*} or ...
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What quantum volume is needed to represent a single fault-tolerant logical qubit?

The quantum volume metric $V_Q$ is a proposed metric for quantifying and comparing the performance of quantum computers[1]. The quantum volume is defined as $$V_Q = \max_{n<N} \left(\min\left[n, d(...
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80 views

Can any 1D critical state be represented by a MERA tensor network?

My understanding of the Multiscale Entanglement Renormalisation Ansatz (MERA) is that it is designed to represent highly entangled, but low complexity states. Is MERA capable of representing high ...
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Why is EIT needed to story memory using rydberg atoms?

I was going through a paper explaining how the write-in and read-out efficiencies can be increased using cold atoms where they used Rydberg atoms, and mentioned that they were probed using EIT(...
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Doubt on application of uncertainty principle for an ion trap

Ion trap involves the application of an electromagnetic field to suspend and confine a charged particle. At the centre of this picture, you see a saddle shape. This means that the ions are pushed ...
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How would measuring the number of photons on a finite number of pulses break coherence of a weak coherent laser source in COW QKD protocol

I' m trying to understand attacks on Quantum key distribution protocols. In the COW QKD protocol, pulses from Alice are passed through an asymmetric coupler and a fraction 'T' of the photons are sent ...
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How many tensor product terms are necessary to express a separable state? [duplicate]

Wikipedia (https://en.wikipedia.org/wiki/Separable_state) defines a separable state, as a state $\rho$ which can be written as: $ \rho = \sum_{k=1}^l p_k \rho_1^k \otimes \rho_2^k $ where $\sum_{k=1}...
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Why can't measuring a system $B$ change a correlated system $A$?

I am reading Quantum computation & quantum information from Nielsen & Chuang. On page 187, he talks about the principle of implicit measurement. He says that if we have two system $A$ and $B$...
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What is the difference between fine-grained and coarse-grained entropy?

So I am not a native English speaker, but I understand the words "coarse" and "fine" grained. But I really don't know what to make of them in the context of entropy. I have encountered this many times ...
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Could the persistent effects of gravitational waves solve the black hole information paradox?

I am not bothered that much by the fact that two observers describe the same phenomenon differently. Something similar , in principle ,  happens with simultaneity in special relativity,  and special ...
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Can an arbitrary spin state be written uniquely in a Dicke state basis?

Consider a system of e.g. $N=3$ spin-1/2 particles. The state of the system $\vert\psi\rangle$ lives in a Hilbert space of dimension $2^N=8$. Now, consider the collective spin operator $$\mathbf{J} = ...
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An Experiment involving macrosopic quantum superposition

The field produced by a charged macroscopic body prepared in a superposition of different position eigenstates is also expected to be in a superposition, for if not, the field strength's give away the ...
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Isn't the Church-Turing-Deutsche (CTD) Principle an empirical question?

The Church-Turing-Deutsche (CTD) Principle is the idea that all physical processes are computable by a quantum computer (i.e. quantum Turing machine). Before I knew this idea had a name, I always ...
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Superoperator cannot increase relative entropy

So I have to show that a superoperator $\$$ cannot increase relative entropy using the monotonicity of relative entropy: $$S(\rho_A || \sigma_A) \leq S(\rho_{AB} || \sigma_{AB}).$$ What I have to ...
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How to identify whether a quantum state is entangled or separable if you can measure it only in one basis?

Suppose you have two qubits and don't know whether they're in an entangled state $ \frac{1}{\sqrt{2}}\left(|0,0\rangle + |1,1\rangle\right)$ or in an equal mixture of states $ |0,0\rangle $ and $ |1,1\...
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Can someone explain how does Gisin apply the No Signaling criterion here?

So given the density operator for the state. He uses the no signaling condition which says that "If we have an entangled state between Alice and Bob and Alice measures the state in any basis pair the ...
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Tensor networks and construction of PEPO

I have a basic understanding of how to construct the tensors of an MPO (matrix product operator), based on, in part, on PhysRevA.81.062337 (arXiv version), see their equations 5 and 6. I am looking ...
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How do I apply no signaling condition for the given Quantum Adder problem

The Unitary transformation for the Imperfect Quantum Adder problem is such: Both the states belong to two Hilbert Spaces and we are trying to add both states to one system using Ancillary qubit. I ...
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How does weak measurement affect quantum state?

I'm trying to understand how to describe the quantum state after weak measurement using these two toy examples. Hopefully, these simple examples and your answer will help others who want to learn ...
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Why can the partial trace be written as $\text{Tr}_B(\rho)= \sum_k (1 \otimes \langle k|) \rho (1 \otimes |k \rangle)$?

I don't really understand a notation that I stumbled upon regarding a partial trace. According to the definition I have, partial trace is $$\rho_A=\text{Tr}_B(\rho_{AB}):= \sum_k (1_A \otimes \...
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How to measure a Bell inequality violation in IBM Q? (Or analytically)

I made some circuit to prepare a 2 qubit state, but I am having trouble understanding how to measure Bell's inequality. I know the inequality is of the form $$|E(a,b)-E(a,b')+E(a',b)+E(a',b')| \leq 2$...
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Nature of the $W$-state in the thermodynamic limit

Consider a matrix product state on $\mathbb{C}^{d N}$: $$ \Psi = \sum_{\sigma_1,...\sigma_N} A_1(\sigma_1) ... A_N(\sigma_N) |\sigma_1 ... \sigma_N \rangle \quad \quad (\text{OBC MPS}) $$ with some ...
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Erasure channel Kraus operators

I'm following these notes https://www.tcm.phy.cam.ac.uk/~sea31/tiqit_complete_notes.pdf where in Section 4.6, the erasure channel is said to have the following Kraus operators. Similar descriptions ...
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Use of Uhlmann representation in proving the strong subadditivity of the von Neumann entropy

I am trying to prove strong subadditivity of the von Neumann-entropy, using joint convexity of the quantum relative entropy. The procedure is given in https://en.wikipedia.org/wiki/...
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Quantum Coherences of a Subsystem

I am reading some stuff on quantum mechanics and have seen references to a subsystem B (where A and B are both subsystems in the system) which has quantum coherences which can be selected. I was ...
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How is Mermin's magic square computed?

BACKGROUND The Peres-Mermin magic square consists of different combinations of tensor products of Pauli operators being applied on an arbitrary bipartite state. Suppose we're considering the entry in ...
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Constraints on higher-dimensional Bloch vectors

I'm interested in the constraints on the $(4^n-1)$-dimensional generalized Bloch vector (the Bloch vector for $n$ qubits). To the best of my knowledge, these are not analytically characterized for ...
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Simplest model of laser coupling

I am not familiar with classical/quantum optics. I have a possibly very basic question about physics of laser interaction. I think my question can be broken into two parts: (1) What is the simplest ...
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Showing that a set of errors is correctable (Knill-Laflamme conditions)?

I am confused about how to apply the Knill-Laflamme Quantum Error-correction conditions, which are the following: A code $C \leq H$ is correctable for $\mathcal{E} = \sum_{i=1}^{n}E_i \rho E_i^*$ ...
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Entanglement breaking quantum channels

An entanglement breaking quantum channel is defined as one where $\sigma_{AB}=(\Phi_A\otimes I_B)(\rho_{AB})$ is separable, even for entangled inputs $\rho_{AB}$. Of course, if the input $\rho_{AB}$ ...
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In standard quantum teleportation, when can quantum states be distinguished with certainty?

Through a few examples, I'd like to learn under what circumstances can different quantum states be distinguished from each other. So for example, the standard quantum teleportation scheme starts out ...
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77 views

Decomposition of the maximally entangled states

We know that the set of symmetric bipartite pure states is spanned by $S=\{|\phi\rangle^{\otimes 2},|\phi\rangle \in \mathbb{C}^d\}$. I want to know if the maximally entangled state $|\psi\rangle = \...
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Negativity of the real part of eigenvalues of Lindblad operators

I'm looking for a proof of the fact that the real part of eigenvalues of Lindblad operators is always negative. So far I have only found handwavy arguments such as "things should not blow up at ...
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Encoding infinite information in a qubit vs. classical system

In this Quantum Computing article by Michael Nielsen he argues about some of the limitations imposed by quantum measurement. In particular how the amplitude $\alpha$ of a single qubit $\alpha |0> +...