Is there a quantum state for a large system My understanding of quantum mechanics is that the state of a system is represented by a vector in multidimensional complex vector space. Is there, in principal, a state vector that represents a large, classical object such as, say, a cheeseburger, at an instant in time? If so, what is the physical meaning of that "state"?
 A: Quantum states of macroscopic systems are routinely considered in statistical mechanics. They used to derive both the thermodynamic properties of macroscopic materials and the way they deform and respond to external forces. 
However, these macroscopic quantum states are never described by state vectors (pure states) but always by density matrices (mixed states).
In practice, quantum derivations are restricted to simple and fairly homogeneous materials, because of the difficulty to work numerically with more complex states. But there is no limitation in theory of the size to which quantum mechanics applies; in particular, it would apply to a cheeseburger if one would model it as an $N$-particle system with $N$ of the order of $10^{25}$. For example, it is applied to derive the conditions of the hydrodynamic reactive flow in the interior of the sun. (Although the sun's apparent size is similar to that of a cheeseburger, its true size is much bigger.) 
The state of a quantum system (no matter whether consisting of a single qubit or of $10^{25}$ atoms) describes all properties of a system that can possibly be measured.
A: In principle yes, but the problem is that any system cannot be isolated from it's environment and interactions with the environment affect the wavefunction of your system. This is the principle behind decoherence. The larger the system the more quickly it interacts with the environment, and for something as large as a cheeseburger the interaction is so rapid we have no chance of observing any quantum behaviour.
A: You make two different answers: "Is there a quantum state for a large system?" and "Is there, in principal, a state vector that represents a large, classical object such as, say, a cheeseburger, at an instant in time?". The answers are "yes" and "no", respectively.
State vectors $|\Psi\rangle$ only represent pure states and therefore do not apply to non-isolated systems as cheeseburgers. The quantum state of such systems is given by a density matrix $\rho$.
The physical meaning of those states is the ordinary, they represent the properties of a given system in condensed form. Instead giving a list of properties you can compute any property of the cheeseburger using this state [*].
[*] In principle! Of course, the computation is very difficult and plagued with technical difficulties.
A: Sorry this was meant to be a comment. @Johnrennie you are wrong in that cmb photons cannot penetrate solid objects so an enclosed cheese burger will not be efected by them.  The thermal photons from the container may be refuced by cooling it.
