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.
3,409
questions
0
votes
0
answers
136
views
The difference between classical and quantum entropies
The von Neumann entropy $-\mathrm{Tr}(\rho\ \log\rho)$ of a quantum thermal state with $\rho=\frac{1}{Z}e^{-\beta H}$ gives the thermal entropy, see e.g. this question.
The von Neumann entropy is a ...
- 111
2
votes
0
answers
50
views
"Entropy" of a set of correlators in a quantum system
Please forgive the ill-posedness of this question; I am hoping someone can help me formulate what I am asking more clearly.
Consider the ground state of a one-dimensional quantum spin chain on $N$ ...
- 472
0
votes
1
answer
122
views
Physical interpretation of unbounded trace class linear maps
Quite generally, quantum states are defined to be positive, trace-class linear maps with trace equal to one on a complex separable Hilbert space $\mathcal{H}$. If we require that these trace-class ...
- 644
3
votes
2
answers
215
views
If two quantum states have the same Schmidt bases at all times, are they equal?
In brief:
if two quantum states can be Schmidt decomposed using the same sets of joint basis at all times, no matter the evolution they go through, are the quantum states equal?
In detail:
Consider ...
- 121
3
votes
0
answers
180
views
Is there any notion of device independent test for correlation like quantum discord?
A Device independent test is a procedure used to characterise quantum resources with the minimal level of trust. If one wants to test correlations like entanglement in a device-independent way, we get ...
- 565
0
votes
1
answer
65
views
Can you project on an orthogonal basis for a multipartite quantum system using only local operations and classical communication?
Say Alice possesses one qubit, and Bob two, and that the joint state is $|\psi_{A, B_1, B_2}\rangle = \alpha|n_1\rangle + \beta |n_2\rangle$, where $|n_1\rangle$ and $|n_2\rangle$ are orthonormal ...
- 145
1
vote
1
answer
98
views
Stuck while deriving the Lindblad Master Equation
I was following Quantum Markov Processes from the book The Theory of Open Quantum Systems by Breuer and Petruccione. In the section The Markovian Quantum Master Equation they proceeds to 'construct ...
2
votes
2
answers
111
views
Why do we expect unitarity to be preserved in the black hole information paradox?
Consider the following way of describing the black hole information paradox:
Suppose we start with a pure quantum state and a black hole of mass $M$. Now we throw the pure state into the black hole ...
- 85
1
vote
0
answers
65
views
Representing quantum channels, and especially measurements, via C*-algebras
I have not been able to find in my searches a concise explanation of how to think of measurement channels in particular in the $C^*$-algebraic formulation of quantum mechanics. It is also difficult to ...
- 874
2
votes
2
answers
78
views
Can you apply non-unitary operators to a qubit?
I am wondering if it is possible to apply continuous, invertible transformations to a qubit which are not linear, i.e. not elements of $U(N)$ where $N=2^n$ where we have $n$ qubits.
Consider $n=1$. ...
- 565
2
votes
1
answer
164
views
Quantum Mechanics without Complex Numbers in a multipartite setting
I was fairly convinced that usual QM formalism didn't necessitate the use of complex numbers and that ultimately they're just a matter of convenience and utility rather than anything fundamental. This ...
- 195
7
votes
1
answer
227
views
A limit of a particular Quantum Fidelity
I have the following problem.
Let $\mathbf{\hat{\rho}}(t)$ and $\mathbf{\hat{\sigma}}(t)$ be two trace class positive operators acting on a Hilbert space of infinite dimension for all $t > 0$. More ...
- 90
0
votes
0
answers
77
views
Removing time dependence of the Hamiltonian by transforming to a rotating frame for a three-level maser
I was going through this paper, named Violating the Thermodynamic Uncertainty Relation in the Three-Level MASER. In the supplemental material, there is this calculation portion named Steady State of ...
3
votes
1
answer
137
views
Is there a relation between some kind of distance and the Schmidt basis?
Consider two bipartite quantum states $|\phi\rangle^{AB}$ and $|\psi\rangle^{AB}$ (in a finite dimensional Hilbert space $\mathcal H_A\otimes \mathcal H_B$), such that
$$\| |\phi\rangle\langle\phi|^{...
- 33
2
votes
1
answer
126
views
Is there a generic behavior of Spectral Form Factor for Integrable models?
The spectral form factor is defined as (usually taken at $\beta = 0$ by definition along with disorder average)
\begin{equation}\label{eq:SFF1}
g(\beta,t) = \left| \frac{Z(\beta,t)}{Z(\beta)}\...
- 11.8k
2
votes
2
answers
610
views
How do we prove that POVMs are the most general measurements?
It is often claimed that POVMs represent the most general measurement statistics possible. But what is the justification for this claim? Textbooks and university courses generally try to build up to ...
- 343
1
vote
1
answer
54
views
Under what conditions are rank-1 POVM unitarily implementable without an ancilla?
I am trying to understand the implementation of POVMs on a Hilbert space by using unitary operations and projective measurements in a larger Hilbert space. In A. Peres' Quantum Theory: Concepts and ...
- 343
0
votes
1
answer
33
views
Substituting qubit for classical memory
I recently came across a paper that argues that we can substitute a qubit for arbitrarily large number of bits in a physical system (https://arxiv.org/abs/quant-ph/0110166).
The notion of bit ...
- 101
1
vote
0
answers
130
views
Construct an operator using outer product of two MPS using TeNPy
I am fairly new to Matrix Product State (MPS) formalism, but I've used Density Matrix Renormalisation Group (DMRG) techniques before. I'm learning to use TeNPy, and a particular problem I am trying to ...
0
votes
0
answers
30
views
Why is it difficult to calculate the ground state of a many-body quantum system? [duplicate]
Assume N spin-1/2 particles, and only focus on the spin states. The dimension of the Hilbert space is then $2^N$. The ground state could be found by diagonalizng the Hamiltonian $H$. As is often ...
- 53
1
vote
1
answer
49
views
Link between the charge and the phase in a superconducting circuit
I have a question related to superconducting quantum circuits. Especially regarding the derivation of the transformation of $\cos(\phi)$ in the charge basis.
In this question, a user states that ...
- 11
1
vote
0
answers
35
views
How is a delocalised state realised and what is its wavefunction?
Gravitationally induced entanglement experiments aim at studying the quantum nature of gravity trough the interaction of a delocalised particle state with another system. The various papers on the ...
- 49
8
votes
1
answer
966
views
Can entropy of a closed system really change?
On the one side, in quantum computing, we have that quantum operations that are unitary and reversible. Information cannot be destroyed.
On the other side, in classical physics we read that entropy ...
- 207
1
vote
1
answer
192
views
Two-mode squeezing and EPR
Consider the two-mode squeezing operator $S(\xi)=\exp\left(\xi\hat{a}^{\dagger}\hat{b}^{\dagger}-\xi^*\hat{a}\hat{b} \right)$ with $\xi=r\exp(\text{i}\phi)$, and assume that the initial state of the ...
- 219
1
vote
0
answers
56
views
Is it possible that when measured more than one Cooper pair will have tunneled across the junction?
If I've understood the idea correctly a charge qubit is formed by a superconducting island coupled by a Joseph junction to a superconducting reservoir. The state of the qubit is determined by the ...
- 67
5
votes
1
answer
252
views
In what sense is Bell's inequality "probabilistic", while the GHZ experiment is "definite"?
I read the paper about the GHZ contradiction written by David Mermin and he said that Bell's inequality is probabilistic while GHZ experiment is definite.
Here is that paper:https://journals.aps.org/...
- 83
0
votes
1
answer
77
views
Where exactly lies the quantum supremacy?
What makes quantum computers faster in certain problems than normal computers? Does quantum computing means that many solutions are explored simultaneously instead of one at a time due to quantum ...
- 99
0
votes
2
answers
144
views
Kraus Operator for two-qubit basis
Let A and B each be a single qubit so that $\mathbb{H_{AB}}$ is a two-qubit system. In the basis {$|\uparrow\uparrow>,|\uparrow\downarrow>,|\downarrow\uparrow>,|\downarrow\downarrow>$, the ...
- 199
0
votes
0
answers
98
views
What is the benefit of using entangled photons for ghost imaging compared to just spatial correlated photons?
I am planning to work in quantum ghost imaging. I will be using a type 2 entangled spdc source which is already there in the lab. I need to know what will be the effect of using polarization entangled,...
0
votes
1
answer
80
views
Counterfactual communication - Photons absorbed by Bob make it non-counterfactual?
I have found this paper claiming that information can be transmitted between two parties without needing to send any physical particles (or energy). This is called quantum "counterfactual" ...
- 137
0
votes
2
answers
67
views
What are the implications of entanglement swapping for the Pusey-Barrett-Rudolph (PBR) theorem?
The derivation of the PBR theorem makes an assumption that "systems that are prepared independently have independent physical states". However, it is known that it is possible to entangle ...
- 732
0
votes
1
answer
126
views
Finding a complete eigenbasis for an "entangled" Hamiltonian?
Suppose we have a tensor product Hilbert space $\mathcal{H} = \mathcal{H}_1 \otimes \mathcal{H}_2$ and we have a Hamiltonian defined thereon which is given by
$H = H_{1e} \otimes I+ H_1 \otimes H_2$. ...
- 1,065
2
votes
0
answers
59
views
(Generalized) Jarzynski equality
Sagawa and Ueda ref, generalized the Jarzynski equality in the presence of a feedback control, leading to the following equation:
$$ \langle e^{-\beta(W-\Delta F)-I} \rangle = 1.$$
Can I interpret ...
- 357
0
votes
0
answers
102
views
Connection between momentum space derivative and Position operator
The crystal momentum $p_1 =\hbar\cdot k $ and this is defined in the reciprocal momentum, I am guessing this $p_1$ is not a real momentum since the reciprocal space is an imaginary space which we use ...
1
vote
1
answer
52
views
Unsure of $|A \times A|$ vector notation in quantum informatics [closed]
I am new to quantum informatics and am doing a course on it. The guy who runs the course keeps writing down this notation - $|0 \times 0|$ or $|1 \times 1|$ - although it is completely foreign to me....
- 21
2
votes
1
answer
79
views
Does including multiple particles "break symmetry" here, or is this a mistake?
It is fairly easy to show that the incoherent mixture of 50/50 spin-up vs. down in the z-direction is the same as 50/50 spin-up vs. down in the x-direction (for a spin-1/2 particle). This is encoded ...
- 1,065
0
votes
0
answers
49
views
Showing that time ordering does not matter for the measurement of commuting observables
Suppose I have two observables $R$ and $S$ who are represented by operator $R$ and $S$ which commute (I will hereafter ignore the distinction between observables and the operators representing them), ...
- 1,065
1
vote
3
answers
270
views
Do "cross terms" in a state operator necessarily correspond to a coherent superposition?
In his discussion (Chapter 9.2-9.3) of the measurement problem, Ballentine says "any terms [in the state operator $\rho$] that [are] nondiagonal [in terms of having "mixed projectors" $|...
- 1,065
0
votes
1
answer
106
views
A general theorem about state operators as a convex set?
I am trying to convince myself of a general theorem which fully "defines" the set of state operators. It is easy to prove that any convex combination of valid state operators is also a valid ...
- 1,065
3
votes
1
answer
100
views
On a constructive method of quantum state preparation
Ballentine, in his Chapter 8.1, appears to give the attached recipe for in principle preparing an (almost) arbitrary (pure) state (of a particle with no internal degrees of freedom) by the method of &...
- 1,065
2
votes
0
answers
75
views
Can a point in the quantum set of correlations violate more than one independent facet Bell inequality?
Usually, depictions of the quantum set of correlations and the local polytope look something like:
In this image it looks like non-local points belonging to the quantum set (in yellow) violate only ...
- 21
0
votes
1
answer
62
views
Are there non-trivial two-party stabilizers in bipartite entanglement for product states?
In this recent paper where the authors discuss finite classification of entanglement types, on pg. 29 in appendix A, it is claimed that in bipartite entanglement for product state $|00\rangle$ there ...
- 414
2
votes
1
answer
125
views
Why can't commuting operators allow for full state determination?
For the purposes of this question, suppose that the operator $R$ representing the observable $\mathsf{R}$ has nondegenerate eigenspaces.
In discussing state determination (for some given situation, ...
- 1,065
1
vote
1
answer
81
views
If a state operator factors, then it factors into partial state operators in particular -- why?
Suppose that we have a state operator for a bipartite quantum system $\rho = A \otimes B$. As far as I know, one must then have in particular $\rho^{(1)} = A$; that is, if a state operator factors ...
- 1,065
2
votes
0
answers
60
views
Discrimination of Quantum Ensembles
Consider the following quantum discrimination problem:
Suppose, there are two sets of states, $P = \{ \rho_i \}$ and $Q = \{\sigma_i\}$. Both Alice and Bob know which states are in each set. We can ...
- 21
11
votes
2
answers
929
views
Distributions "more singular than a Dirac delta" must have negativity
I am looking at properties of the Glauber P-functions, which are distributions (in the sense of a dirac delta) on the complex plane, normalized so that $\int_{\mathbb{C}} d^2 \alpha P(\alpha) = 1$. On ...
- 187
1
vote
0
answers
37
views
When I measure position again after a very short time, can't I calculate momentum? [closed]
In quantum optics, there are squeezed states that are very precise in one quadrature. You can analoguously have state squeezed in position instead of one quadrature. Can I perhaps make a slightly more ...
- 168
2
votes
0
answers
81
views
Hastings' "two" definitions of trivial mixed states
In https://arxiv.org/abs/1106.6026 (Definition 3), Hastings defines a density matrix $\rho$ in Hilbert space $\mathcal{H}$ to be trivial if one can tensor in additional degrees of freedom $\mathcal{K}$...
- 21
0
votes
0
answers
51
views
Confusion regarding the derivation of Lindblad master equation
I am reading theory of the master equation from Preskill's notes, section $3.5.2$. In the derivation, he writes
In the case of an open quantum system, Markovian evolution for the
infinitesimal time ...
- 423
-1
votes
1
answer
188
views
How much information is in a hydrogen atom?
How much information is contained in a hydrogen atom (a bound electron and proton) at room temperature?
There are bounds that set limits on the amount of mass/energy that can exist in a given region ...
- 565