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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Energy dissipation in unitary dynamics

In the context of quantum mechanics it is often (e.g. in several Wikipedia pages, like on Quantum dissipation) stated, that: "If the time evolution of a system is unitary (e.g. always in the ...
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Clarification on DMRG computational complexity

I was reading a paper on the density matrix renormalization group (https://arxiv.org/abs/1008.3477). In DMRG, we gradually grow a chain by inserting a unit cell at the center of the chain (for ...
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Axiomatic Quantum Theory, and the complex numbers

In Lucien Hardy's influential paper "Quantum Theory from five reasonable axioms," Hardy states in the abstract: This work provides some insight into the reasons why quantum theory is the way it ...
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Stinespring dilation of a channel vs Naimark's theorem

I'm trying to understand the connection between the Stinespring dilation of a quantum channel and Naimark's theorem that shows that POVMs can be written as projective measurements in a larger Hilbert ...
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Does $U^T U$ have real eigenvectors if $U$ is unitary?

I was reading a paper by Kraus and Cirac on general two qubit gates. A crucial step is to decompose an arbitrary unitary operator acting on two qubit space into a special form: $$ U_{AB} = U_A\otimes ...
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Two-photon interference inside Mach-Zehnder interferometer

Imagine there's a strong laser beam, not just an attenuated stream of single photons, entering a balanced Mach-Zehnder interferometer. One-photon picture: Each photon interferes with itself on the ...
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Applying a General Lorentz Boost to Multi-Partite Quantum State in Dirac Notation

I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying ...
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3answers
124 views

Von Neumann entropy in terms of the mutual overlap?

I have $N$ pure, but nonorthogonal, states $|\psi_n\rangle$ with density matrix $\rho_n=|\psi_n\rangle\langle\psi_n|$. Say we call the the total density matrix $\rho=\frac{1}{N}\sum_n \rho_n$. Are ...
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Can quantum disentanglement be triggered by time dilation?

The question is really one question that leads to the final one: Is it possible to realize a qubit that naturally flips between two quantum states on a definite and fixed period without any ongoing ...
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52 views

Quantum secret sharing

I was reading the article "Multiparty quantum secret sharing". It had 3 parties Bob, Alice and Charlie. They agree on sharing a classical secret quantum mechanically. The steps they follow are for a ...
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Show $\langle \alpha| (\cos \mu)^{-a^{\dagger} a} | \alpha \rangle =e^{|\alpha|^2(\frac{1}{\cos \mu} -1)}$ for coherent states $|\alpha \rangle$ [closed]

I am reading "Quantum continuous variables, A primer of Theoretical Methods" by A.Serafini, page 120. Let $a$ be the annihilation operator for the Fock basis. I want to show $$\langle \alpha| (\...
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Topos quantum theory and distributive logic

I am reading an introductory review on topos quantum theory https://arxiv.org/abs/1106.5660 where in the motivation part it says (emphasis is mine): As we can see the non realism of standard ...
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47 views

Are states (always) a fundamental notion in QM?

When dealing with quantum mechanics one usually postulates states* as fundamental notions. They form basis of the Hilbert space(H) and are used to compute expected values of observables which we "...
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Can unitary probability theory (quantum mechanics) emerge from a lack of information about a deterministic process? [duplicate]

My initial question below appears to be unclear so I am rewording in more succinctly here. The pre-edit question remains below. There exists two types of probability theory: 1-norm (classic ...
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How to prove that a $d$-dimensional Hilbert space can only have $d^2$ equiangular vectors (i.e. that a SIC is a maximal collection of that kind)?

It is an open question if every $d$-dimensional Hilbert space contains a collection of $d^2$ states, such that every two have a scalar product of $\frac{1}{d+1}$, i.e. if a SIC-POVM exists for every ...
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59 views

Show for $r \in \mathbb R$, $e^{(a_1 ^\dagger a_2^\dagger - a_1a_2)r}|0,0 \rangle = \frac{1}{\cosh r} \sum_{j=0}^\infty (\tanh r)^j |j,j \rangle$

Let $ a_1, a_2 $ be annihilation operators for the first and second component in the product state $|m,n \rangle$ using Fock basis. Following "Quantum continuous variables, A primer of Theoretical ...
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Inequality for quantum probability

Let $H$ be a separable Hilbert space for a quantum mechanical system then $$w (x, y) = {{\langle y \mid x\rangle\langle x \mid y \rangle} \over \langle x \mid x \rangle\langle y \mid y \rangle}$$ is ...
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What is the difference between quantum sensing and quantum metrology?

The title is mostly self-explanatory. Both terms get thrown around a lot. I used to think quantum sensing uses harmonic oscillators / bosons and quantum metrology spins, but this doesn't seem to ...
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76 views

Does disentangling A and B always imply entangling A and B with an environment?

Does disentanglement of a bipartite entanglement between systems A and B entail actual breaking of this bipartite entanglement or is it rather the beginning of a tripartite entanglement between A, B, ...
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33 views

Does all measured quantities by Hamiltonian operator should be real valued? [duplicate]

am not familiar with QM , and i have checked web many times to know wether all measured Quantities of any arbitray system should be real since it is Hermitian ?
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40 views

Information containable in a volume depends on surface area, but a volume of space can contain a volume with a bigger surface area?

The holographic principle has me confused. I'm wondering, if a volume can contain more information if it has a larger surface area, how can it be that a volume with a bigger surface area can be ...
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91 views

Why do we need Jordan-Wigner transformation when simulating fermionic systems on quantum circuits?

Why do we need to do a Jordan-Wigner transformation when we want to simulate the fermionic systems with a quantum circuit model? I understand that the spin operator $\sigma_x, \sigma_y, \sigma_z$ on ...
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13 views

Sinkhorn Algorithm Normalization Issue

I was reading the Sinkhorn algorithm, from the following link: https://mindcodec.ai/2018/10/01/an-intuitive-guide-to-optimal-transport-part-iii-entropic-regularization-and-the-sinkhorn-iterations/ The ...
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1answer
79 views

Equivalence of POVM and projective measurement

Suppose I have a POVM whose elements are given by $\{M_i^\dagger M_i\}$ such that $\sum_i M_i^\dagger M_i = I_A$. Let it act on some state $\rho_A$. Everything here happens in the Hilbert space $A$. ...
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Why do excited states of charge qubits have higher charge sensitivity than the ground state?

Lets define charge qubits as two coupled superconductors connected by a Josephson tunnel junction governed by the Hamiltonian \begin{equation} H = 4 E_C \left(n - n_g\right)^2 - E_J \cos{\phi} \end{...
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Upper bound for norm of 1-body correlation tensor of qubit

Any $n$-qubit state can be expressed as $$\rho=\frac{1}{2^{n}} \sum_{\mu_{1}, \ldots, \mu_{n}=0,1,2,3} T_{\mu_{1}, \ldots, \mu_{n}} \sigma_{\mu_{1}} \otimes \ldots \otimes \sigma_{\mu_{n}}$$ where $...
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51 views

Question on an equality in deriving covariance matrix of a gaussian state

I am reading Quantum continuous variables by A.Serafini. (Equations are not rendered in this link. Please look at the second link) I have a question on the last equality of the equation (3.49) which ...
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61 views

Von neumann entropy for reduced density matrix

I have reduced density matrix of the form (corresponding to 2 coupled harmonic oscillators): $$\rho_r (x_1, x'_1)= \frac{\text{sech}(\eta ) \sqrt{\frac{m\omega \cosh (\eta )}{\hbar }} \exp \left(-...
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113 views

Can one derive Schrodinger's Equation from quantum information theory?

I know that some people think that quantum information theory/science is fundamental physics. I also know that there are many definitions, theorems and rules in the field of quantum information. They ...
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92 views

The Function of the Free Will Assumption in No-Go Theorems [closed]

I'm interested in the function played by the free will assumption made by any number of no-go theorems in quantum mechanics. While searching the archives for prior questions, I found this one from 5 ...
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130 views

Detuning in Rabi oscillations

Consider a two level atom interacting with the interaction Hamiltonian of the form $$\hat{H} = \hat{V}_{0}\cos(\omega t)$$ The probability of the state to be in the excited state is given by $$P_{e}=...
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Can quDit gates be non-unitary

I have derived a quantum quDit gate that is implemented by photon Fock state inteference. It turns out to be non-unitary. I thought I must have made a mistake, so I have checked several times. I know ...
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1answer
133 views

Is there a limit on the maximum rate of change of the position expectation value in quantum mechanics to be no greater than the speed of light?

Suppose a particle, constrained to the $x$ axis, is measured at $t_0$ to be at position eigenstate $x = 0$. Assume for all $t \gt t_0$, some external potential acts on the particle. Nevertheless, ...
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von Neumann entropy - calculation

How to calculate von Neumann entropy in continious case? Consider density matrix elements: $$ \rho(x,x') $$ Then: $$S = -Tr(\rho \log \rho) = -\int \rho(x,x')\log \rho(x',x)dx'dx $$ Is it true?
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how to construct a triple-controlled unitary gate?

I try to construct multiply-controlled qubit gates and I did. But I'm not sure how to construct a triple-controlled unitary gate for four qubits, starting from a version that controlled by only one ...
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Probing the relation between decoherence theory versus the arguments based on the smallness of $h$ in connection with the quantum classical transition

This question tries to relate the elementary account of quantum effects in the macroscopic domain in terms of the smallness of the quantum of action, which is usually presented in introductory quantum ...
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Is there a commonly accepted definition of a quantum phase definition for a finite lattice/set of particles?

As noted by Sachev, and in a previous question, https://www.physicsoverflow.org/41602/, there cannot be quantum phase transitions for finite systems (with bounded local Hilbert space dimension). The ...
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Does No-cloning theorem hold in time domain?

So for an unknown quantum state $|A\rangle$, it's impossible to make a copy of $|B\rangle$ such that $|A\rangle=|B\rangle$. However, I want to know that, suppose the unknown $|A\rangle$ is time ...
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Inverse covariance matrix for a Gaussian state

I was reading an article about Gaussian Boson Sampling (https://arxiv.org/pdf/1801.07488.pdf) and following some calculation appear an inverse covariance matrix when he defines the following matrix A. ...
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Is HaPPY code a certain type of MERA?

Pastawski, Yoshida, Harlow, and Preskill introduced the HaPPY code in their (now famous) paper, arXiv:1503.06237, as a way to model the AdS/CFT correspondence as a quantum error-correcting code. ...
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1answer
51 views

Trace distance expressed with maximization of probabilities

I'm studying chapter 9 of Nielsen and Chuang, where trace distance is defined by equation (9.1) $D(p_x,q_x)=\dfrac{1}{2}\sum_{x}|p_x-q_x|$ and later on the next page (also asked to be proven in ...
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45 views

Spin state of photons inside laser

Can the total spin state of photons inside a laser beam be written as a product of individual spin states ? Tentatively, the answer seems to be yes because single laser beam have a definite ...
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Strongly continuous dynamical maps

Let's say we have a bipartite system $\rho(0)=\rho_A \otimes \rho_B$ The evolution of system $A$ alone will be described by a dynamical map $\Phi_t$, such as: $\rho_A(t)=\Phi_t(\rho_A(0))$ If ...
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Using entangled qubits to communicate [duplicate]

After reading up on quantum mechanics considering entangled qubits I was asking myself this simple question: If one qubit (A) positioned on earth is entangled with another qubit (B) which is - say - ...
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Is the Second Law a consequence of the Many Worlds principle?

I've done a bit of browsing on this subject, and haven't found any papers that directly address this question. Here's the idea: In the Many Worlds View (MWV), there is no loss of information from ...
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88 views

Probability distribution of the overlap between two random quantum states in an $n$-dimensional Hilbert space? [closed]

Let two pure states $|\Psi\rangle$ and $|\Phi\rangle$ be drawn uniformly and independently from an n-dimensional Hilbert space $\mathbb{H}^n$. (see Note). What is the probability distribution of ...
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Confusion with identity operator

In the above example why the identity matrix ie ∑|x〉〈x|...is taken as ∫|x〉〈x| dx from negetive to positive infinity? or alternatively can someone explain the steps to expand the ket ψ into x basis
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Confusion with mixed state [duplicate]

I have read that mixed state is a collection of pure states ...while a pure sate is a collection ie suoerposition of eigen states is that right?..so it can be thought of as a superposition of ...
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42 views

Quantum Key Distribution via Modified Double Slit Experiment

Here's my reasoning: Setup 1: Take a traditional double slit experiment and turn on the photon source. Interference fringes should appear on a detector screen placed opposite the photon emitter, ...
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Finding the quadrature variance of a superposition of squeezed coherent states

How do you find the quadrature variance of a state $$\lvert x\rangle =\lvert a,b\rangle +\lvert a,-b\rangle$$ where $\lvert a,b\rangle = D(a) S(b) \lvert 0\rangle$? $\lvert x\rangle$ is a ...