Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
175
questions with no upvoted or accepted answers
7
votes
0
answers
89
views
Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?
In What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?, examples were given of separable states $\rho$ with separable decompositions requiring ...
glS♦
- 22.9k
7
votes
0
answers
122
views
How large can we make the fidelity between mixed states by allowing unitaries?
For pure states, it is known that one can always find a unitary that relates the two i.e. for any choice of states $\vert\psi\rangle$ and $\vert\phi\rangle$, there exists a unitary $U$ such that $U\...
- 457
6
votes
0
answers
112
views
Weak Schur sampling and state distinguishability
Consider the task of distinguishing between the following two $n$ qubit quantum states.
$$ \rho = \frac{\mathbb{I}}{2^{n}}.$$
$$ \sigma = \frac{1}{2^{n/2}}\sum_{x \in \{0, 1\}^{n/2}} |x\rangle\langle ...
- 1,181
6
votes
0
answers
87
views
Postselection and hardness of estimating amplitudes
Let $A$ be a class of quantum circuits such that
\begin{equation}
\text{Post}A = \text{Post}BQP,
\end{equation}
where $\text{Post}$ indicates post-selection. Is only this amount of information ...
- 1,181
6
votes
0
answers
152
views
Encoding bosonic degrees of freedom
A well-known way of encoding $N$ levels of a harmonic (bosonic) oscillator is as follows:
\begin{equation}
|n\rangle = |1\rangle^{\otimes n} \otimes |0\rangle^{\otimes N-n+1}
\quad,\qquad
...
- 1,810
6
votes
0
answers
141
views
How exactly is the stated composite state of the two registers being produced using the $R_{zz}$ controlled rotations?
This is a sequel to How are two different registers being used as "control"?
I found the following quantum circuit given in Fig 5 (page 6) of the same paper i.e. Quantum Circuit Design for ...
- 17.1k
5
votes
0
answers
119
views
Volume law spread after Hamiltonian evolution
Start with an $n \times n$ lattice, with each qubit initialized to the state $|0\rangle$. Then, apply the Hadamard gate on each qubit. Then, evolve the system under the Hamiltonian
\begin{equation}
...
- 315
5
votes
0
answers
63
views
Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states?
On p. 3 of "Separability Probability Formulas and Their Proofs for Generalized Two-Qubit X-Matrices Endowed with Hilbert-Schmidt and Induced Measures" (https://arxiv.org/abs/1501.02289), it is ...
- 879
4
votes
0
answers
58
views
How is this Variational Quantum Singular Value Decomposition paper efficient in any way?
Link to paper here.
This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...
- 89
4
votes
0
answers
163
views
How to implement a gate that generate a uniform superposition of all permutation of element
I'm looking for a quantum circuit that permits generating a uniform superposition of all possible permutations for example if we have as input $|0123\rangle$ the output will be the uniform ...
- 41
4
votes
0
answers
131
views
Can changing reference frames generate entanglement in identical particles?
Suppose we have a pair of qubits, physically realised as two spin-half particles in some separable pure state $|\psi\rangle$, separated by a distance '$l$', large enough to be regarded as ...
4
votes
0
answers
83
views
What does it mean that a qubit is a triple $(H,X,Z)$ with $H$ Hilbert space and $X,Z$ Pauli operators?
In this paper, http://users.cms.caltech.edu/~vidick/teaching/fsmp/fsmp.pdf, it gives the definition of a qubit as follows:
A qubit is a triple $(H, X, Z)$ consisting of a separable Hilbert space H and
...
4
votes
0
answers
209
views
What was the meaning of Lossless Quantum compression?
I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does ...
- 57
4
votes
0
answers
110
views
States used in lossless quantum compression?
I was reading about quantum compression in this article and have some doubts regarding an example mentioned. Specifically, I have two questions:
In example they represented $|a\rangle = \dfrac{1}{\...
- 161
4
votes
0
answers
52
views
If $\rho \approx_{\varepsilon}\sigma$, how to find $\Pi\rho\Pi$ to ensure that $\text{supp}(\Pi\rho\Pi)\subset\text{supp}(\sigma)$?
Let $\rho$ and $\sigma$ be positive semidefinite operators with trace less than or equal to 1. Let $\rho\approx_{\varepsilon}\sigma$ i.e. they are close in some distance, such as the trace distance.
...
- 41
4
votes
0
answers
145
views
Is the set of two-qubit absolutely separable states convex?
Companion question on MathOverflow
Let us order the four nonnegative eigenvalues, summing to 1, of a two-qubit density matrix ($\rho$) as
\begin{equation}
1 \geq x \geq y \geq z \geq (1-x-y-z) \geq 0.
...
- 879
4
votes
1
answer
256
views
Preparation of states that correspond to efficiently integrable probability distributions
I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph.
It is stated that there exists an ...
- 41
4
votes
0
answers
53
views
Finding separable decompositions of bipartite X-states using the methodology of Li and Qiao
Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of ...
- 879
3
votes
0
answers
83
views
Holevo bound and indistinguishability of non-orthogonal quantum states
I was trying to understand the fact that non-orthogonal quantum states cannot be reliably distinguished and I came across this link.
The explanation finishes with the result that the probability of ...
- 43
3
votes
0
answers
46
views
Is circuit cutting equivalent in anyway to quantum teleportation?
I've been introduced recently to circuit cutting, and after seeing the 4 orthogonal measurements with their 8 corresponding initializations but no initial transfer of classical info, the first thing ...
3
votes
0
answers
95
views
How to construct a quantum circuit that given $|\psi_0\rangle,|\psi_1\rangle$ outputs $\frac{1}{c}(|\psi_0\rangle+|\psi_1\rangle)$?
Suppose I have two arbitrary quantum states $\lvert \psi_1 \rangle $ and $\lvert \psi_2 \rangle$. Further suppose that we know $U_1$ such that $\lvert \psi_1 \rangle = U_1 \lvert 0 \rangle$, but we ...
- 455
3
votes
0
answers
159
views
How to find the Choi state of a bipartite quantum channel?
The Choi state of a quantum channel $\mathcal{N}_A$ acting on a system $\rho_A \in \mathcal{H}^A$ is given by:
$Choi(\mathcal{N}_A) =(
\mathcal{I}_{A'} \otimes \mathcal{N}_A)|\Phi^+\rangle \langle\...
3
votes
0
answers
239
views
Reduced density matrix of a Haar random state and its Schmidt decomposition
Consider a Haar random quantum state $|\psi\rangle$. Note that
$$\rho =\mathbb{E}[|\psi\rangle\langle \psi|] = \frac{\mathbb{I}_{n}}{2^{n}}.$$
$\mathbb{I}_n$ is the identity operator on $n$ qubits. ...
- 1,181
3
votes
0
answers
102
views
How to find minimum time needed for Hamiltonian evolution?
Database search can be looked upon as Hamiltonian evolution, with kinetic and
potential energy operators. Let the evolution follow the Schrodinger equation:
$$i\frac{d}{dt}|\psi⟩= H|ψ⟩$$
with $H = E|s⟩...
3
votes
0
answers
103
views
Schur transform and the outcome probabilities for a particular type of state
I was reading about the Schur transform and its applications in knowing about an unknown quantum state.
Consider $\rho^{\otimes k}$, which means $k$ copies of an unknown $n$ qubit quantum density ...
- 1,181
3
votes
0
answers
122
views
How to efficiently construct quantum circuits of oracles in multi-target quantum search?
In standard Grover's quantum search with only one target or its extension of multi-target quantum search, one of the two key parts is to quantize the boolean function
$$f(x):\{0,1,\cdots,N-1\}\...
- 193
3
votes
0
answers
59
views
Minmax theorem for optimization over isometries and states
I have the following minmax problem and I am wondering if the order of the minimum and maximum can be interchanged and if yes, why?
Let $\|\cdot\|_1$ be the trace norm defined as $\|\rho\|_1 = \text{...
- 2,439
3
votes
0
answers
51
views
Permutation invariant states have permutation invariant purifications - proof?
I don't remember where I came across the statement but I'm pretty sure it is true and am interested in understanding why it holds. For any $n-$ register state $\rho^n \in H^{\otimes n}$ that is ...
- 457
3
votes
0
answers
54
views
How does the quantum Fisher information provide bounds for the estimation of output states?
Assume you have some quantum process $Q$ (e.g. quantum state tomography) that intakes initialised states $\rho_{i}$, $i=1,\ldots,n$ and gives some output $\rho'_i$.
$$
\rho_1 \to Q \to \rho'_1 \\
\...
- 585
3
votes
0
answers
214
views
Calculating Dot Product of Two States
I've been reading Peter Wittek's Quantum Machine Learning. In chapter 10.2 of this book, the author explains how we can calculate the dot product of two states:
To evaluate the dot product of two ...
- 557
3
votes
0
answers
66
views
Can we characterise how correlated the expectation values associated with a pair of observables are?
Consider a state $\rho$ and two observables $P$ and $Q$.
Is there a good way to characterise how correlated the associated expectation values are? Be it in terms of mutual information or something ...
glS♦
- 22.9k
3
votes
0
answers
75
views
Quantum Boltzmann machine: How do you sample from the Boltzmann distribution on a quantum computer?
I am reading through the following article https://arxiv.org/abs/1601.02036.
Eq. (22) describes one of the terms of the gradient of the log-likelihood cost function, which can be estimated using ...
- 439
3
votes
0
answers
65
views
Preparing a state given access to projector
Let's say I am given access to a magical box that lets me apply a projector $|\psi\rangle \langle\psi|$, where $|\psi\rangle$ is a quantum state. I do not know anything about $|\psi\rangle$: just that ...
- 1,181
3
votes
0
answers
81
views
Quantum Ising model correlation function query
In this paper on quantum Ising model dynamics, they consider the Hamiltonian
$$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$
and the correlation function
$$\mathcal{G}...
- 747
3
votes
0
answers
76
views
Hyperspherical parametrization of a multi-qubit state
Can anyone please explain me in simple words how the hyperspherical coordinates can be used to parameterise multi-qubit states?
The state of an $n$-qubit system can be thought of as a point on the $\...
- 131
3
votes
0
answers
64
views
Deriving Bloch vector $dr$ from master equation
I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
- 31
3
votes
0
answers
46
views
Is there a measure similar to the Helstrom measurement which can distinguish between more than 2 pure quantum states?
My understanding is the Helstrom measurement distinguishes between 2 pure quantum states.
Is there a measure similar to the Helstrom measurement which can distinguishes between more than 2 pure ...
- 131
3
votes
0
answers
431
views
Show that quantum channels act as affine transformations in the Bloch sphere
I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture ...
- 455
3
votes
0
answers
52
views
Are there different orderings of the fifteen SU(4) generators in common use?
I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in
Separable Decompositions of Bipartite Mixed States , that is
\begin{equation} ...
- 879
3
votes
0
answers
52
views
Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability
In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...
- 879
3
votes
0
answers
70
views
Please clarify the following orthogonal property (quantum anonymous voting)
I am a beginner at QC, currently going through a paper on Quantum Anonymous Voting. Please clarify the orthogonal property described in the following scenario.
Consider $n$ voters $V_{0}, V_{1}, V_{2}...
- 87
3
votes
0
answers
81
views
Understanding shared Bell states from quantum entanglement
I'm trying to understand an entanglement swapping derivation provided in this PDF (pages 2 - 3)
I have several things about this process that I don't understand, and I was hoping someone could ...
- 299
3
votes
0
answers
128
views
How to define initial state $\rvert \Psi(0) \rangle \equiv \rvert 1, -1 \rangle \otimes \rvert 0 \rangle_{\text{cav}} $ of a system in QuTiP?
Say, we have a $\require{mhchem}\ce{^87Rb}$ atom having an electric dipole transition on the $D_{1}$ line and we have two hyperfine ground states, one on $F = 1$ and one on $F = 2$ level. So, we take ...
- 31
3
votes
0
answers
28
views
Synchronous Interactions Between Quantum and Macroscopic Systems
Synchronous Interactions Between Quantum and Macroscopic Systems
Lester Ingber
This project calculates synchronous quantum systems and macroscopic systems with well-defined interactions. I would ...
3
votes
0
answers
95
views
States of a qubit in a DC-SQUID
Does anybody of you know what are the two states $|0\rangle$ and $|1\rangle$ of a qubit in a DC-SQUID (2 Josephson junctions in a loop)?
- 377
3
votes
0
answers
70
views
Restoring an initial state after computation
Let me first tell my problem statement. Suppose I have a uniform superposition of states $$|A\rangle=\dfrac{1}{2^{9}}\sum_{i,j,k=0}^{2^6-1}|0\rangle^{\otimes 8}|i\rangle|j\rangle|k\rangle,$$ where $|0\...
- 1,400
3
votes
0
answers
68
views
Can "experimental data from a quantum computer" be used to test separability probability conjectures?
An article entitled "Experimental data from a quantum computer verifies the generalize Pauli exclusion principle" by Scott E. Smart, David I. Schuster, and David A. Mazziotti has just appeared
In the ...
- 879
3
votes
0
answers
66
views
Why does state preparation of 'off the shelf' qubits not follow from the Born rule (Mermin)?
In Mermin's Quantum Computer Science, section 1.10 (Measurement gates and state preparation), Mermin writes that:
This role of measurement gates in state preparation follows from the Born rule if ...
- 31
2
votes
0
answers
51
views
Complexity of the quantum circuits that are needed to implement communication protocol?
Consider the following simultaneous communication problem. Alice and Bob do not share any
entanglement or any common randomness, and cannot communicate directly with each other. As
inputs, x is given ...
- 21
2
votes
0
answers
43
views
General structure of the state with $I(A:B|C)_{\rho}{=}2 \log_2 \{\min (d_A, d_B)\}$
The conditional quantum mutual information (CQMI) of a state $\rho^{ABC}$ respects the dimension bound $I(A:B|C)_{\rho}{\leq}2 \log_2 \{\min (d_A, d_B)\}$ (Mark Wilde's book, exercise 11.7.9). One ...
- 133