Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,823 questions
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Infinitesimal trace distance and metric
It is well known that the Bures distance between two infinitesimally close density matrices induces the Bures metric. Likewise the quantum Fisher information metric is related to the infinitesimal ...
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Could metronome synchronization entangle multiple qubits simultaneously?
Could some eventually consistent medium be used to entangle lots of qubits simultaneously?
I'm very much a novice, but I'm thinking something like metronome synchronization on a skateboard. Arrange a ...
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Low Fidelity For QFT on IBM
I implemented a 5-qubit QFT circuit using Qiskit and performed quantum state tomography using an IBM backend. However, the reported process fidelity is only ~20%, which seems very low. I am trying to ...
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connection between no-cloning theorem and accessible information
In the following paragraph Nielsen and Chuang give proof (with contradiction) that no-cloning theorem about non-orthogonal states lead to accessible information will be less than $H(p)$.
BUT no-...
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Advantages of using qubits for data storage
I have read much of the book Quantum Computation and Quantum Information by Nielsen and Chuang and I of course have been convinced that qubits have great advantages in many problems when we want to do ...
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Encoding circuit from Stabilizers and Logical operators stim
Given that I provide stim the stabilizer generators and the logical operator specifying the logical state that I want to encode (starting from the all 0 state), does something like
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applying Haar random unitary to projection and pure states and compute its trace
I have this question when I read the proof of Theorem 4 in This paper. Here are the settings:
\begin{align}
&|\phi\rangle^{BC}: \text{The reduction of a pure state $|\phi\rangle^{ABCD}$ where A,C ...
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Question about a Haar random state
Let's consider a Haar random state on $n$ qubits. We trace one qubit out. Can we prove that the reduced density matrix that remains is "close" to a convex combination of two Haar random ...
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Why would we need 512 classical bits to represent a two-qubit entangled state?
I am new to quantum computing. I see a claim in a video from IBM Research that $2$ qubits needs $512$ classical bits to represent an entangled state. I would like to understand where this comes from.
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Proof of Theorem 3 of Frenkel, and Weiner, Commun. Math. Phys. 340, 563 (2015)
Suppose Bob performs a $k$-outcome measurement, characterised by the POVM $E = \{E_j\}_{j=1}^k$, on $l$ qudits $\{\rho_i\}_{i=1}^l$ sent by Alice. This results in an $k \times l$ column-stochatstic ...
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Possible label mismatch in Box 8.5 of Nielsen & Chuang — are ρ₂′ and ρ₃′ swapped?
I’ve been working through Box 8.5 of Nielsen & Chuang’s textbook (Quantum Computation and Quantum Information) related to single-qubit quantum process tomography.
Specifically, in equations (8.175)...
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Mixed State vs Randomly Sampled Pure State
Suppose I have a set of orthogonal states
$$B := \{\psi_1, \ldots, \psi_m\}$$
Suppose I have $A$ that reads a quantum state and output 0/1. A want to verify the following are equivalent:
$$\Pr_{i}[A(|\...
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Is equality $Z |0\rangle = |+\rangle$ true?
I had thought $Z |0\rangle = |0\rangle$ but... it seems not according to this quiz?
$Z |0\rangle = |+\rangle \; (???)$ - can this ever be true?
Source: https://stem.mitre.org/quantum/quantum-concepts/...
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How to compute the full inner product (including global phase) between stabilizer states?
I am trying to compute the full complex inner product $\langle \phi_1 | \phi_2 \rangle$ between two stabilizer states, including the global phase.
I understand that stabilizer states represented, for ...
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After applying CNOT, is it equivalent to measure the control or the target?
This is a follow up to What happens after applying CNOTs and measuring either register?
I have been playing with some problem that involves intermediate measurements after applying a CNOT. Here are ...
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