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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96 views

Can quantum communication break the Shannon–Hartley theorem?

Just a random stupid thought. Quantum entanglement cannot be used to transfer information faster then speed of light. But can it "embed" information until a key is received? For exmample, assume ...
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62 views

Is there a way to measure the degree of superposition of a quantum state?

I am wondering if there is a way to calculate the amount of superposition that a quantum state is in. For example, if I have a $2$-qubit quantum system, with basis $\mathcal{B} = \{|00\rangle, |01\...
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Is it possible to know whether an arbitrary system is performing a quantum computation?

Without knowing in advance that a physical system has been configured to do so, is it possible to determine whether that system is preforming, or has just performed a quantum computation? That is, if ...
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Can all CFT state be prepared through scale invariant MERA

It is known that in numeric computation, scale invariant MERA is useful for representing a CFT vacuum state. Is the converse true? i.e. all CFT vacuum state (the quantum state with translation and ...
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43 views

What is the simplest circuit on a quantum computer that “proves” superposition/entanglement

I am a Physics Teacher at pre university level. Tunneling, wavefunctions and uncertainty are on the syllabus on a very vague way. Quantum superposition and entanglement are not but tie in well and I ...
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Do the pure states in the decomposition of a density operator need to be orthonormal to each other?

So, I was studying quantum computation using the book Nielsen and Chuang and it stated a theorem known as "Spectral Decomposition theorem" $$A=\sum _{i}\lambda _{i} | i \rangle \langle i|$$ I infer ...
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How to obtain a unitary time evolution that leads to the Lindblad equation on tracing out?

It is known that given the time evolution of an open quantum system by Kraus Operators, one can rewrite it as a unitary time evolution of a bigger system. That is, given Kraus operators on the Hilbert ...
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Is it possible that the speed of sound in some strange quantum material is faster than the speed of light in vacuum [closed]

If we believe the spacetime structure(including the limit of speed) could emerge from some vacuum structure(such as string-net condensation),then, is it possible that the speed of mode of excitation ...
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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5 qubit quantum error correction property [closed]

Having $$\eqalign{ |v_0⟩&=|00000⟩+|11000⟩+|01100⟩+|00110⟩+ {}\cr &\quad |00011⟩+|10001⟩−|10010⟩-|10100⟩− {}\cr &\quad |01001⟩−|01010⟩−|00101⟩−|11110⟩− {}\cr &\quad |...
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1answer
37 views

Transformation acting only on one of two qubits

Suppose you have a non-polarizing beamsplitter (NPBS) with 2 outputs: A and B. You place a polarizing beamsplitter (PBS) at the output A, and want to follow the evolution of the quantum state after ...
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171 views

Is a partial trace cyclic?

I want to know if a partial trace keeps the cyclic property of the trace. The partial trace is defined as $$ tr_B: \mathcal{B}_1(\mathcal{H}_A\otimes \mathcal{H}_B) \longrightarrow \mathcal{B}_1(\...
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39 views

Random quantum walk related to quantum computing

I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone ...
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Specialized Journals for Quantum Information

I recently wrote a short, fairly mathematical paper on the subject of quantum information and quantum mechanics. Although the results in the paper are not big results, I have not seen them before and ...
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Entangled states and separable states

B Two electrons in the same orbital is clearly an entangled quantum state since it is not a tensor product: $$|\psi\rangle=\frac{1}{\sqrt{2}}(|\uparrow\rangle \otimes|\downarrow\rangle-|\downarrow\...
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Expanding a density matrix in terms of operators

In Lukasz's paper: https://arxiv.org/pdf/0909.2654.pdf He writes "consider a density matrix ρ, written as a polynomial of the 2N Majoranas cj in such a way that each cj occurs to the power 0 or 1 in ...
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Direct Derivation of Kraus Operator from Interaction Hamiltonian

For the dynamics of open quantum systems, the Kraus operators $K_\kappa$ can be derived from the unitary orbit $U(t)\rho U(t)^\dagger$ for $\rho=\rho_S\otimes\rho_E$ of the composite system given by ...
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In quantum search algorithm, how to interpret the effect of $U(t)$ as a rotation on the Bloch sphere?

In Nielsen's QCQI, in page 259, it reads, $$U \left ( \Delta t \right ) = \left ( \cos^2 \left ( \frac {\Delta t} 2 \right ) - \sin ^2 \left ( \frac {\Delta t} 2 \right ) \vec \psi \cdot \hat z \...
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Necessary and sufficient conditions for a pure state

I've seen some claims that idempotency ($\rho^2=\rho$) is necessary and sufficient to guarantee the existence of some state $\psi$ such that $\rho=|\psi\rangle\langle\psi|$, as well as claims on the ...
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61 views

Topological phases and quantum information

I am concerned about the theorem saying that there is no topological order in 1d. According to the seminal paper https://arxiv.org/pdf/1008.3745.pdf, there are no non-trivial topological phases in 1d (...
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60 views

tensor products of exponential annihilation operators

I'm hoping to use this stackexchange to solve a gate decomposition problem, but I am stumped, so hoping for help. These definitions come from the Xanadu Strawberry Fields whitepaper on Table VI and ...
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Quantum Fisher information for Gaussian states without eigenproblem?

Given a Gaussian-preserving interaction (including a unitary operation and losses) for a Gaussian input, I want to know if there is an "easy" way to compute the Quantum Fisher information without ...
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65 views

What relation exists between Wolfram's model of the Cellular Automata universe and the Holographic Principle and the Bekenstein Bound?

Are computational models of the universe, like Stephen Wolfram's cellular automaton model of the universe (proposed in his book A New Kind of Science), somehow related to the Holographic Principle and ...
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Entanglement of Werner States

Let the Werner state $$\rho_W = W\mid\Psi^-\rangle\langle\Psi^-\mid + \frac{1-W}{4}\mathbb{I},\ W\in [0,1],$$ where $|\Psi^-\rangle=(|01\rangle-|10\rangle)/\sqrt{2}$. I have repeatedly heard that ...
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Does non-orthogonality of joint states follow from non-orthogonality of ALL marginals?

Suppose we have a composite system $AB$ and we are considering two joint (pure) states $$ \psi,\psi^\prime \in \mathcal{H}_{AB} . $$ Let's define the reduced or marginal states of $A$ and $B$ in the ...
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76 views

Can decoherence account for suppression of interference in all basis?

Let the system formed by particle(microscopic or macroscopic)- environment coupling be described by $|\phi><\phi| $ . In decoherence approach, to retrieve the classical properties, one focuses ...
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Can we define a parent Hamiltonian for a given Multiscale Entanglement Renormalization Ansatz (MERA) state?

Given a state represented by a MERA (Multiscale Entanglement Renormalization Ansatz), can we define a local Hamiltonian such that the MERA is the exact ground state of such a Hamiltonian? If this is ...
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61 views

Can we restore a state of a whole system from its subsystem?

I am thinking about the deletion error correcting codes for quantum information. In classical information theory, there exist some deletion error correcting codes. An easy example is the following ...
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29 views

Channel Capacity and the Rank of Channel

Let's say $\Phi$ defined a $d-$dimensional quantum system $I$ is a quantum channel with entanglement-assisted classical capacity no smaller than $\log d$. This means that there exists a bipartite ...
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48 views

How to differentiate between quantum states based on phase

Imagine you have a source of photons and a single-photon detector. The source emits photons that can be in any of the following four states: $ |1\rangle $, or $ -|1\rangle $, or $ i|1\rangle $, or $ -...
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Why doesn't Wigner's friend interact with the system?

So I was recently modelling something that turned out to be basically Wigner's friend. I saw there were some differences (in the Wiki page) in how it was modelled: Namely, that Wigner's friend ...
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1answer
110 views

Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality . It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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50 views

Topological superconductors

I have been reading a lot about quantum computation by using topological materials and I could see that the standard approach is to engineer a p-wave superconductor by using a 1-D semiconductor wire ...
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52 views

Single-particle QM

In learning device-independent QM from [https://arxiv.org/abs/1303.3081], Scarani tells us that all quantum statistics involving one particle can be reproduced with local (hidden) variables. He then ...
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Is this analysis contradictory with the $2$'nd measurment?

Summary and Motivation "The below idea is about making a mathematical statement on system $2$ which induces a measurement on system $1$ while $1+2$ obeys unitary evolution." Basically, I'm modelling ...
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2answers
57 views

Is there a maximum quantum advantage in sensing?

This is a rather conceptual question. Quantum sensing takes advantage of entanglement (and other quantum properties such as squeezing) to get variances that scale much better than the ones one can ...
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1answer
67 views

Expansion of Von Neumann entropy for small deviations

Suppose that your quantum system is described by $\sigma = \rho + \delta\rho$, where both $\sigma$ and $\rho$ are density matrices while $\delta\rho$ is "small". The Von Neumann entropy of the system ...
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Diagonalisation of quasi-thermal state

I have the following density operator $$\frac{1}{t \pi N} \int_{\mathbb{C}} \mathrm{d}^2\gamma \exp \left[ -\frac{|\gamma+r\alpha|^2}{t^2 N} \right] |{\gamma}\rangle\langle{\gamma}|,$$ where $0\leq t,...
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1answer
40 views

Swap operation with the Heisenberg Hamiltonian

According to REF 1 equation 3, a SWAP operation can be achieved via the Heisenberg Hamiltonian for spins $H=J(t)\mathbf{S}_1\mathbf{S_2}$ $U^{1/2}_{SWAP}=e^{-i\frac{\pi}{8}}\exp\left(i\frac{\pi}{2}\...
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2answers
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How can work be generated from quantum correlations?

There are several articles (like this or this one) concerning extracting work from (quantum and/or classical) correlations. Nevertheless, these articles appear to be quite dense and without showcasing ...
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3answers
149 views

Are superposition quantum systems really in two pure states at once?

I know that quantum systems can have properties of waves as well as those of particles. Also, I know that the mathematical description of quantum states is probabilistic, i.e. $$\Psi = \frac{1}{\sqrt{...
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22 views

Equality condition for relative entropy under partial trace

It is known that the relative entropy is non-increasing under arbitrary quantum operations. That is for some completely positive trace preserving map $N$, we have for all $\rho$ and $\sigma$ $$S(\rho ...
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1answer
121 views

Confusion about mixed states and pure states

Suppose I have a system composed of two subsystems (each is a 2-state system). I understand, that there exist two types of such systems: separable, and entangled. A separable system can be written as $...
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Difference between two definition expression of quantum Fisher information metric

The symmetric logarithmic derivative $L_i$ is defined as the operator solutions to equations $$\frac{1}{2}\left(L_i\rho_{\lambda}+\rho_{\lambda}L_i\right)=\partial_i\rho_{\lambda}$$ The quantum Fisher ...
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Energy cost of the measurement without perturbing the system?

Background Let's say I have a Hamiltonian $\hat H$ (assume the Schrodinger equation) and it be in an arbitrary eigen-energy state: $$ \hat H_{\text{system}} | m \rangle = E_m |m \rangle$$ And I ...
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1answer
53 views

Book Recommendations on Quantum Mechanics and Quantum Information processing (with specific topics mentioned in the description)

I an an undergraduate in 2nd year of study and doing an internship this summer on Quantum information Processing and related concepts. Since I had very less exposure to Quantum mechanics I was ...
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1answer
33 views

What happens to physical qubits when they decohere during quantum error correction?

Say you have a scaled up system with 98% fidelity so 2% decoheres. These are physical qubits doing error correction on information encoded on logical qubits. 98% of these entangled qubits will be ...
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29 views

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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1answer
48 views

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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0answers
103 views

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{...